Eco. 361——–24-3-2021 (Online Discussion Quiz 1 —Lewis-Fei-Ranis Model of Economic Growth and Haris-Todaro Model of Migration)

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The Harris – Todaro Theory
This is a theory of rural-urban migration that is usually studied in the context of employment and unemployment in developing countries. The purpose of this model or theory is to explain the reason why there is seriously urban unemployment problem in developing countries. The model also is applicable only to less successful developing countries or to countries at their earlier stages of development. The difference in this model is that the rate of migration flow is mainly determined by the difference between expected urban wage which is no actual and rural wages. One disadvantages to this model is that job or work creation in urban sector worsens the situation in rural migration as many people will start moving to urban areas in terms of finding greener pastures.The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
Assumptions of Harris – Todaro model
1. The model is a study of migration of workers in two sectors economic system which are rural and urban sectors. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods while that of urban sector is specialized in manufactural goods. Both of these sectors can be described using Cobb-Douglas production function: Ya=AaNa
2. Temporary Equilibrium
3. Long Run Equilibrium
My view
Having studied Harris -Todaro model and knowing it as the theory of rural-urban migration of employment and unemployment of developing countries, it is necessary that both sectors are developed at same time so as to prevent the creation of unemployment in other sector. Once both are simultaneously develop, it will reduces the rate of unemployment in both sectors and there will be a moderate or balance of economic growth of the nation
Conclusion
Therefore migration from rural areas to urban areas will increase if:

– Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
-Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision

Lewis-Fei-Ranis Model(surplus of labour)
The model is made up of three authors in whom Lewis is the chief proponent of the model. Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. FeiRanis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial. In the Lewis theory, an economy transits from the first, labour-surplus stage to the second, labour-scarce stage of development. Later, Ranis and Fei (1961) formalized the Lewis theory and defined three phases of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labor-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, illustrated in Diagram below, are distinguished by the marginal productivity of agricultural labor. The entry into each phase is marked three turning points: The breakout point leads to phase one growth with redundant agricultural labor. The shortage point leads to phase two growth with disguised agricultural unemployment. The commercialization point leads to phase three of self-sustaining economic growth with the commercialization of the agricultural sector.
At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the HarrodDomar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

Assumptions of the Lewis Model: Surplus Labour in the Subsistence Sectors

The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural laborers, petty traders domestic servants and women.
(1) The assumption that disguised unemployment exists in the agriculture sector has not been accepted by many economists. Schultz, Viner, Heberler and Hopper are a few of such economists. According to them, the production in the subsistence sector will be affected when labour is withdrawn from it.

(2) Lewis ignored the cost involved in training the unskilled worker transferred from the subsistence sector. Even if it is obtained at a constant wage rate, so for as its transfer from the subsistence sector is concerned, the supply curve may slope upwards so far as the capitalist, sector is concerned if the cost of training rises as more and more labour is transferred.

(3) When labour is transferred from the subsistence sector share of agricultural output falling to each one left in the agricultural sector will go a rising. This means the institutional wage will go on rising with every transfer and so will be the wages paid in the capitalist sector.

(4) The model assumes that, besides labour, there is unlimited supply of entrepreneurs in the capitalist sector. This is not true in the case of many of the underdeveloped countries.

(5) It is wrong to assume that a capitalist will always re-invest their profits. They are to indulge in un-productive pursuits. They can use their profits for speculative purposes.

(6) It is also wrong to assume that landlords always squander away their savings. The role of landlords of Japan in industrialization of the country is well known.
(7) The model assumes that there already exists a market for the industrial products in the country. This is wrong. People of an underdeveloped country may not be able to purchase the products perturbed by the expanding capitalist sector. Foreign markets, too, may not be available to the capitalist sector in the beginning.
(8) Inflation is not liquidating, as has been assumed by Lewis, Experience of various, countries shows that if once prices start rising, it, becomes difficult to control them.
(9) It is not easy to transfer labour from the subsistence Sector to the capitalist sector by offering them an incentive of a little higher wage.
Mobility of labour is very low. Many factors like family affection, difference in language, caste, religion etc. affect it adversely.
(10) Every underdeveloped country does not have surplus labour in the subsistence sector. As such, the model does not apply to countries which are sparsely populated.
The only positive point in the model is its general emphasis on the role of saving in economic development and on the potential that overpopulated countries have in developing themselves with the help of surplus labour.

Name: Chukwudi Christopher
Reg Number: 2017/249489
Dept: Economics

LEWIS-FEI-RANIS MODEL
Prof. Lewis developed a very systematic theory of economic development with unlimited
supplies of labour. The theory focuses on structural transformation of a subsistence economy into a modern industrial economy. The theory was later modified by John Fei and Gustar Ranis in the 1950s. Lewis believes that in many undeveloped countries an unlimited supply of labour is available at a subsistence age. The Lewis two-sector model became the general theory of development process in surplus labour. Economic development takes place when capital accumulates as a result of withdrawal of surplus labour from the subsistence sector to the modern sector (capitalist sector). In the Lewis theory the underdeveloped economy consist of two sectors. i. A traditional – over populated rural subsistence sector characterized by zero marginal labour productivity (surplus labour) which can be withdrawn from agriculture without any loss of output. ii. A high productivity modern urban industrial sector into which labour from the subsistence sector is gradually transferred. The primary focus of the model is on both the process of labour transfer and modern sector employment growth brought about by output expansion on that factor.
• The speed at which this expansion occurs is determined by the rate of industrial investment and capital accumulation in the modern sector
• Such investment is made possible by the excess of modern sector profits on the assumptions that capitalists invests all the profits.
• It is assumed that wages in the modern sector are higher than in the subsistence sector.

Depiction of Phase1, Phase2 and Phase3 of the dual economy model using average output.

One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.[4] They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development[5] In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages. Using the help of the figure on the left, we see that
Phase 1: AL = MP
According to Fei and Ranis, AD amount of labor (see figure) can be shifted from the agricultural sector without any fall in output. Hence, it represents surplus labour
PHASE 2: AP > MP

After AD, MP begins to rise, and industrial labor rises from zero to a value equal to AD. AP of agricultural labor is shown by BYZ and we see that this curve falls downward after AD. This fall in AP can be attributed to the fact that as agricultural laborers shift to the industrial sector, the real wage of industrial laborers decreases due to shortage of food supply, since less laborers are now working in the food sector. The decrease in the real wage level decreases the level of profits, and the size of surplus that could have been re-invested for more industrialization. However, as long as surplus exists, growth rate can still be increased without a fall in the rate of industrialization. This re-investment of surplus can be graphically visualized as the shifting of MP curve outwards. In Phase2 the level of disguised unemployment is given by AK. This allows the agricultural sector to give up a part of its labor-force until
MP = REAL WAGE = MP = CONSTANT
Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.
PHASE 3: MP = CIW
(I) The amount of labor that is shifted and the time that this shifting takes depends upon:The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
(III)The nature of the industry’s technical progress and its associated bias;
(III)Growth rate of population.
So, the three fundamental ideas used in this model are:
1) Agricultural growth and industrial growth are both equally important;
2) Agricultural growth and industrial growth are balanced;
3) Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.
This shifting of labor can take place by the landlords’ investment activities and by the government’s fiscal measures. However, the cost of shifting labor in terms of both private and social cost may be high, for example transportation cost or the cost of carrying out construction of buildings. In addition to that, per capita agricultural consumption can increase, or there can exist a wide gap between the wages of the urban and the rural people. These three occurrences- high cost, high consumption and high gap in wages, are called as leakages, and leakages prevent the creation of agricultural surplus. In fact, surplus generation might be prevented due to a backward-sloping supply curve of labor as well, which happens when high income-levels are not consumed. This would mean that the productivity of laborers with rise in income will not rise. However, the case of backward-sloping curves is mostly unpractical.
THE AGRICULTURAL SECTOR
Fei and Ranis emphasized strongly on the industry-agriculture interdependency and said that a robust connectivity between the two would encourage and speedup development. If agricultural laborers look for industrial employment, and industrialists employ more workers by use of larger capital good stock and labor-intensive technology, this connectivity can work between the industrial and agricultural sector. Also, if the surplus owner invests in that section of industrial sector that is close to soil and is in known surroundings, he will most probably choose that productivity out of which future savings can be channelized. They took the example of Japan’s dualistic economy in the 19th century and said that connectivity between the two sectors of Japan was heightened due to the presence of a decentralized rural industry which was often linked to urban production. According to them, economic progress is achieved in dualistic economies of underdeveloped countries through the work of a small number of entrepreneurs who have access to land and decision-making powers and use industrial capital and consumer goods for agricultural practices.
In (A), land is measured on the vertical axis, and labor on the horizontal axis. Ou and Ov represent two ridge lines, and the production contour lines are depicted by M, M1 and M2. The area enclosed by the ridge lines defines the region of factor substitutability, or the region where factors can easily be substituted. Let us understand the repercussions of this. If the amount of labor is the total labor in the agricultural sector, the intersection of the ridge line Ov with the production curve M1 at point s renders M1 perfectly horizontal below Ov. The horizontal behavior of the production line implies that outside the region of factor substitutability, output stops and labor becomes redundant once land is fixed and labor is increased

INDUSTRIAL SECTOR

Like in the agricultural sector, Fei and Ranis assume constant returns to scale in the industrial sector. However, the main factors of production are capital and labor. In the graph (A) right hand side, the production functions have been plotted taking labor on the horizontal axis and capital on the vertical axis. The expansion path of the industrial sector is given by the line OAoA1A2. As capital increases from Ko to K1 to K2 and labor increases from Lo to L1 and L2, the industrial output represented by the production contour Ao, A1 and A3 increases accordingly.

According to this model, the prime labor supply source of the industrial sector is the agricultural sector, due to redundancy in the agricultural labor force. (B) shows the labor supply curve for the industrial sector S. PP2 represents the straight line part of the curve and is a measure of the redundant agricultural labor force on a graph with industrial labor force on the horizontal axis and output/real wage on the vertical axis. Due to the redundant agricultural labor force, the real wages remain constant but once the curve starts sloping upwards from point P2, the upward sloping indicates that additional labor would be supplied only with a corresponding rise in the real wages level.
MPPL curves corresponding to their respective capital and labor levels have been drawn as Mo, M1, M2 and M3. When capital stock rises from Ko to K1, the marginal physical productivity of labor rises from Mo to M1. When capital stock is Ko, the MPPL curve cuts the labor supply curve at equilibrium point Po. At this point, the total real wage income is Wo and is represented by the shaded area POLoPo. λ is the equilibrium profit and is represented by the shaded area qPPo. Since the laborers have extremely low income-levels, they barely save from that income and hence industrial profits (πo) become the prime source of investment funds in the industrial sector.

Here, Kt gives the total supply of investment funds (given that rural savings are represented by So)
Total industrial activity rises due to increase in the total supply of investment funds, leading to increased industrial employment.
CRITICISM OF THE MODEL
The assumptions of this model do not fit the institutional and economic realities of most contemporary developing countries. 1. The model assumes that the rate of labour transfer and employment creation is proportional to the rate of modern sector capital accumulation. The faster the rate of capital accumulation, the higher the growth rate of the modern sector and the faster the rate of new job creation. At times capitalists do not reinvest their profits proportionately – capital flights.
2. The assumption of surplus labour in the rural areas might not hold seasonal
3. It is not always given that there is the tendency of increased urban wage rates. Institutional factors such as trade unions, bargaining power, service wage scales and multi-national corporate tend to negate competitive forces in LDCs modern sector, labour markets.
4. The concerns of diminishing returns in the modern industrial sector
5. Fei and Ranis assume a close model and hence there is no presence of foreign trade in the economy, which is very unrealistic as food or raw materials can not be imported.
This theory concludes that for a country to developed there must be balance between the agricultural and industrial sector, that labour can be utilized to get the efficient amount of output in both sectors, The theory has been used and tested by several countries namely England and japan

The Harris-Todaro Model
This model of economic development was developed by J. R. Harris and M. P. Todaro which is relevant for labour surplus countries like India. It is the best known model of internal migration in the context of present-day developing countries. The model has focused on migration of labour from rural to urban areas induced by certain incentives. They have referred to two types of migration—induced migration and internal migration. In the Harris-Todaro model, the probability of obtaining an urban job is defined as the number of urban jobs divided by the urban labor force. Implicitly, this specification assumes that persons living in rural areas have no chance whatever of finding urban job.
Harris-Todaro Model is bounded by the following assumptions:
• Two sectors: urban (manufacture) and rural (agriculture)
• Rural-urban migration condition: when urban real wage exceeds real agricultural product• No migration cost: there is little to no cost on migrating from one sector to another.• Perfect competition in the two sectors: Both the agricultural and manufacturing sectors are perfectly competitive in nature.
• Cobb-Douglas production function
• Static approach• Low risk aversion: the Migrants are not risk averse. That is, they are risk takers.
Under the Harris-Todaro Model, the decision to migrate is made upon differences in expected income between rural and urban areas. On a fundamental level, expected income accounts for the wage differential between urban and rural areas. The existence of a higher wage in urban areas compared to rural areas is a relatively constant observation. Rural to urban migration, however, does not clear the wage differential between the two labor markets as designated by demand and supply fundamentals. The reason for this is the lack of full employment in urban areas. The probability of finding a job in an urban area (i.e. the inverse of the unemployment rate) is never 100%. In other words, the urban labor market never fully clears due to institutionally determined urban wages; there will always be unemployment. This provides a technical rational to the reason why there is rural to urban migration amidst unemployment.

Lewis-Fei-Ranis model recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries
.

Okonkwo okechukwu Benjamin
Economics
2017/251833

Two Economists, John E. H Fei and Gustav Ranis, developed the model now known as the Fei-Ranis model of dual economy to explain how an increased productivity in agricultural sector would become helpful in promoting industrial sector, due to the fact that Lewis model did not pay enough attention to the importance of agricultural sector in promoting industrial growth.
The above model provides three stages whereby an Under Developed Country can move from stagnation to self-sustained economic growth. This model I treated as an improvement over Lewis model of Unlimited Supply of Labour.
The Assumptions of the Model
There is abundance of labour in such Under Developed Countries and shortage of Natural Resources.
The population growth rates are very high which results in Mass Unemployment in the Economy.
Agricultural sector generates surplus to finance the development of industrial sector.
The model is based on a closed economy unlike the Lewis model that is based on both Closed and open economy.
There is dynamic industrial sector in the Economy.
According to them, the Central problem of dual economy is transfer of labour from agricultural to non-agricultural sector.
The main social problem is over-population.
Industrial workers absorb the maximum number of agriculture workers.
The population rate is very high which results in Mass Unemployment in the Economy.
The major share of population is engaged in Agriculture. But agriculture sector is stagnant, hence, the marginal productivity of labour is zero and negative in agricultural sector.

The Model therefore suggests that Economic development would be taking place if agricultural labourers are transferred to industrial sector where their productivity will increase.
Honestly, the model is about a stagnant agricultural sector and dynamic industrial sector. The situation where Marginal Productivity of Labour is equal to zero i.e. (MPL)=0, labour can be transferred to industrial sector without any loss in agricultural output. Thus; the real wages in Industrial Sector remains fixed and it is equal to the initial level of real income in agricultural sector. Such wages are given the name of institutional wages.

Two Economists, John E. H Fei and Gustav Ranis, developed the model now known as the Fei-Ranis model of dual economy to explain how an increased productivity in agricultural sector would become helpful in promoting industrial sector, due to the fact that Lewis model did not pay enough attention to the importance of agricultural sector in promoting industrial growth.
The above model provides three stages whereby an Under Developed Country can move from stagnation to self-sustained economic growth. This model I treated as an improvement over Lewis model of Unlimited Supply of Labour.
The Assumptions of the Model
There is abundance of labour in such Under Developed Countries and shortage of Natural Resources.
The population growth rates are very high which results in Mass Unemployment in the Economy.
Agricultural sector generates surplus to finance the development of industrial sector.
The model is based on a closed economy unlike the Lewis model that is based on both Closed and open economy.
There is dynamic industrial sector in the Economy.
According to them, the Central problem of dual economy is transfer of labour from agricultural to non-agricultural sector.
The main social problem is over-population.
Industrial workers absorb the maximum number of agriculture workers.
The population rate is very high which results in Mass Unemployment in the Economy.
The major share of population is engaged in Agriculture. But agriculture sector is stagnant, hence, the marginal productivity of labour is zero and negative in agricultural sector.

The Model therefore suggests that Economic development would be taking place if agricultural labourers are transferred to industrial sector where their productivity will increase.
Honestly, the model is about a stagnant agricultural sector and dynamic industrial sector. The situation where Marginal Productivity of Labour is equal to zero i.e. (MPL)=0, labour can be transferred to industrial sector without any loss in agricultural output. Thus; the real wages in Industrial Sector remains fixed and it is equal to the initial level of real income in agricultural sector. Such wages are given the name of institutional wages.

Name: Ahamefula miracle Chisom
Reg no: 2017/249478
Dept Economics
Level:300 level
Email: ahamefulamiracle1@gmail

Lewis Fei Ranis model of economic development

After a long experience of military dictatorship, civilian rule in 1999 brought high expectations for peace and progress. However, democracy has failed so far to deliver good governance and in its place, insecurity, poverty, economic crisis and social problems have become the fate of Nigerians. The liberalization of the political atmosphere in 1999 brought by civil rule was used for the mobilization of primordial sentiments and identity politics (Alubo 2011). Therefore, insecurity and violence with its dire consequences in terms of loss of lives, properties has become the order of the day. According to Alubo (2011) in the first fifty-five months of civil rule December 2003, about 80 major violent eruptions were recorded. The economists reported that as at 2001, more than 6000 people have been killed. For instance, the cases of armed robbery on Nigeria’s high ways, banks, and households, the Niger Delta militants, the ethnic and religious crises as witnessed in Maiduguri (Bok o haram), Jos, Ibadan, and other parts of the country that claimed a lot of innocent souls and destroyed properties worth billions of naira are pointers to security lapses in the country. The cases of electoral violence in 2003, 2007 and 2011 elections and the recent by-election in Gombe, Bauchi, other parts of the state, the cases of kidnapping citizens and demand of ransom and worst of all the brutal killings of Nigerians by the police that are saddled with the primary responsibility of protecting the property and lives of citizens through torture in the name of investigation and direct shooting on the excuse of accidental discharge, as indicated by the Human Rights Report 2010, are all evidence their insecurity is in vogue in Nigeria. Security, including “human security”, is a critical foundation for sustainable development. This implies protection from systemic human rights abused, physical threats, violence, and extreme economic, social, and environmental risks, territorial and sovereignty threats. It is a primary prerequisite and goal for poor people to make a lasting improvement in their lives (UNIDIR, Report 2008). Cited by Ahmadu (2013)
Nigeria as a nation has had a long, history of religious upheavals. Religious uprising that gave birth to problem of insecurity especially the current Boko Haram insurgeney and others before it started in the northern city of Kano in 1980 and later spread to other cities, mostly in the north. The emergence and growth of the Boko haram sect has been attributed mainly to social malaise and absence of effective engagement of the nation’s youths. In an editorial (The Guardian 11/02/2011) newspaper noted that Boko Haram has a social root. It is largely populated by young and often educated but unemployed believers who are, in the circumstance, restless and disenchanted with a life of idleness and hopelessness. According to the National Bureau of Statistics (NBS) over the last decade, Nigeria’s infrastructure spending Ahamefumirac a 1.9% (approximately $4 billion) per annum to GDP.

The Harris–Todaro model of migration
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function: where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a 0 and g > 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya
The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:

NAME :Ozumba Rachel Chidinma
REG NO:2017/249573
EMAIL:chidinma.ozumba.249573@unn.edu.ng
BLOG:Chinmaoz.blogspot.com
DEPARTMENT:Economics

THE HARRIS –TODARO MODEL OF MIGRATION
INTRODUCTION
Migration from rural informal sector-urban formal sector is driven by wage differentials and the rational postulations by the rural worker .Given this wage differentials, people rationally migrate into the cities hoping to get an urban job. But the probability of getting an urban job is not completely dependent on that rational move ,rather it depends on the size of unemployment existing in the city in relation to the number of people employed in the urban manufacturing sector. Hence, under-developed countries are faced with the problem of urban unemployment which is caused majorly by rural-urban migration. The Todaro Paradox can equally occur when job creation in urban area further leads to unemployment. Generally,this essay attempted to expound the assumptions, characteristics and the core arguments of Harris –Todaro model of Migration, Initiate a comparison between the Harris-Todaro model with other models and more specifically, compare the model with the real world while drawing opinions ..
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ASSUMPTIONS OF THE HARRIS –TODARO MODEL OF MIGRATION ​
The following are the assumptions underlying the Harris -Todaro migration Model ;
(1) Urban wage is institutionally and legally fixed .
(2)Small open economy; the economy considered in Harris -Todaro model is a small open economy.
(3) Two sector economy; apart from the assumption of small open economy , the model further assumes two sectors economy. One an agricultural rural sector and the other , manufacturing urban sector economy.
(4) There three(3 )kinds of production factors , specific production factor in sector 1,K1 ,Specific production factor in sector 2, K2 and labour ,L, which is employed in both sectors and is mobile between sectors.
(5) The capital –labor ratio and the factor reward ratio are in one to one relation with the relative price of the product.
(6) There is equality between the probability of finding a job and the existing rate of employment.
(7) In the rural agricultural sector, it is assumed that wages are flexible and equal to the marginal product of labor according to profit maximization.

THE HARRIS-TODARO MODEL OF MIGRATION

The Harris-Todaro model of migration named after John R.Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and Welfare Economics to explain the issues concerning rural –urban Migration. The Harris-Todaro model is a pioneering general equilibrium model describing the labour migration mechanism from rural to Urban areas due to wage gap and the existence of urban unemployment and underemployment in developing countries.
Historically, the Harris- Todaro Model can be traced to the 1960s , when the government of newly independent Kenya faced a difficult situation: Unemployment in Nairobi and other major cities was high and obviously rising. In other to cope with this problem, a cross sectional agreements were reached between the private-sector and public-sector which the employers agreed to increase employment in exchange for unions agreeing to hold wages at their present levels. The newly created jobs was expected to reduce unemployment. Nevertheless, urban unemployment appeared to have increased rather than decreased.​
Consequent of this paradoxical event, John Harris and Michael Todaro theorized the Harris-Todaro model to explain the puzzle. At the core of the Harris-Todaro model were the following features. First, wages are higher in urban manufacturing-sector jobs than in rural agricultural-sector jobs. Second, to be hired for a manufacturing-sector job, one has to be physically present in the urban areas where the manufacturing-sector jobs are situated . Third, and as a result of the first two features, more workers search for manufacturing-sector jobs than are hired, employers hire some of the migrant but not all of them, and those not hired end up unemployed. Fourth, for equality to be maintained between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower-paying rural job, the equilibrium arising in such a setting is characterized by urban unemployment.
The Harris-Todaro model formulated two policy results. The first concerns the policy of manufacturing-sector job creation to employ the unemployed – (say migrants from the rural sector). This policy, they proposed, would increase the formal sector labor force by more than the number of new jobs created, thereby raising the number of urban unemployed. Hence, the solution to urban unemployment is not creation of urban employment.
The second policy option that Harris and Todaro considered was a policy of rural development. If such a program could increase the rural agricultural-sector wage, unemployment would then fall. Thus, in the Harris-Todaro model, the solution to urban unemployment is rural development. Soon after the publication of the model, the government of Kenya followed the Harris-Todaro prescriptions by putting into place a program of rural development. The result was a sharp decline in level unemployment in Kenya.
Harris and Todaro’s fundamental contribution was a building model that fits the intrigues of the labor market that was based on sound micro-economic foundations. The relevance of this model today as a part of the economist’s intellectual toolkit is a tribute to its basic insight and enduring analytic power.
Harris and Todaro formulated general processes for determining prices of the products produced by the two sectors and also for determining a rural-sector wage that varies inversely with the number of people in the rural sector. A simplified version of the Harris-Todaro model was developed in which product prices and rural-sector wages are taken as constant. Numerous additional analytic and policy results were derived in the simplified Harris-Todaro model. At the same time, some of the assumptions of the Harris-Todaro model were judged to be too restrictive, and so the model was generalized in the years that followed to annex their specific formulation within a broader framework. The initial Harris-Todaro model has been extended to allow for on-the-job search from a rural agriculture setting, the existence of an urban informal sector, preferential hiring of the better-educated, employment fixity, duality of production conditions and earnings levels within the rural sector, capital mobility, endogenous urban wage setting, risk aversion, and a system of demand for goods, among other factors.

As an early two-sector labor-market model, the Harris-Todaro model set forth a principal alternative framework for policy analysis. It showed how employment and wage levels in one labor market reflect supply, demand, and institutional conditions not only in that labor market but also in other labor markets.
In terms of pro-poor economic growth, the Harris-Todaro model and other two-sector-labor-market models can help policy makers avoid two mistakes. One is to assume that development efforts should be channeled to the sectors where the poor are. The other is to assume that efforts should always be focused on getting the poor out of the sectors in which they now are. Careful cost-benefit analysis based on well-specified labor-market models is required to decide among such alternatives.
The Harris –Todaro model is a specific form of the neoclassical two sector model , represented by the Heckscher-Ohlin and Samuelson Model and it can be understood as a specific factor model (S-F Model), proposed by Jones (1971). In the S-F model , each sector has its own specific production factor which cannot move between sectors , and the specific factor endowments are also fixed. The Harris-Todaro model is a shortrun model with specific capital endowment in each sector.
Given the wage rigidity in the urban area ,flexibility of wage in rural area and the mobility of labour assumptions, it is possible for workers to move freely due to wage gap between sectors. Put differently, workers move to the higher wage sector by comparing their expected wages in both sectors. The probability of finding a job equals the rate of employment. Since the rural area is agrarian , there is therefore no unemployment in the rural sector. Given this, the workers in the rural sector can always be employed, so that the probability of finding a job in the rural sector equals unity.
The Harris-Todaro migration Model assumes wage differential as the basis of migration ,hence in equilibrium migration between the rural and urban sectors will cease since the urban expected wage is equal to the rural-expected wage which is the same as the rural real wage.
Migration in any given time time depends on three factors;(a) The urban-migration wage gap (b) The urban employment rate and (c)The responsiveness of potential migrants to the resulting opportunities.
The Harris-Todaro Equilibrium as shown in figure 1. There are two sectors :agriculture and manufacturing. Each sector has a specific factor and labor which is mobile between these two sectors. There is the assumption of constant. The horizontal axis shows labor force. The marginal product curves are LL for agriculture and MM’ for manufacturing. OW* is the fixed minimum wage in the manufacturing sector, while corresponding employment is given at NO*According Harris-Todaro model the equilibrium the expected urban wage must be equal to the agricultural wage.

Since agricultural wage presented by ‘OV’ and then urban wage represented by ‘GR’ equal, we thus conclude that the Point ‘R’ in the graph fulfills the condition for equilibrium since the two rectangular are equal to each other.

LEWIS- FEI-RANIS MODEL OF ECONOMIC GROWTH

According to Todaro ,the Lewis-Fei model explains the historical scenario of migration obtainable in the western socio-economic milieu but is insufficient in explaining the trends of rural-urban migration in less developed countries.
The lewis’ surplus labour makes the assumption that faster capital accumulation will be invested in modern industry causing new jobs in abundance. It implies that there would be labour transfer at the rate proportional to capital accumulation.
Lewis’ assertion that rural sector has surplus labour and urban areas have full employment,does not hold true necessarily .In less developed countries particularly, there is less than full employment. According to reports M .S Smianthian Research Foundation and World Food Programme in 2002 unemployment was on the rise in urban india and the rate of urban unemployment was 9.5% for the lower expenditure classes.

The Fei–Ranis model of economic growth is a dualism model in developmental economicsor welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.
According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

The three fundamental ideas used in this model are:
1. Agricultural growth and industrial growth are both equally important;
2. Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.
Fei and Ranis emphasized strongly on the industry-agriculture interdependency and said that a robust connectivity between the two would encourage and speedup development. If agricultural laborers look for industrial employment, and industrialists employ more workers by use of larger capital good stock and labor-intensive technology, this connectivity can work between the industrial and agricultural sector. Also, if the surplus owner invests in that section of industrial sector that is close to soil and is in known surroundings, he will most probably choose that productivity out of which future savings can be channelized. They took the example of Japan’s dualistic economy in the 19th century and said that connectivity between the two sectors of Japan was heightened due to the presence of a decentralized rural industry which was often linked to urban production. According to them, economic progress is achieved in dualistic economies of underdeveloped countries through the work of a small number of entrepreneurs who have access to land and decision-making powers and use industrial capital and consumer goods for agricultural practices.
The Lewis model is criticised on the grounds that it neglects agriculture. Fei–Ranis model goes a step beyond and states that agriculture has a very major role to play in the expansion of the industrial sector. In fact, it says that the rate of growth of the industrial sector depends on the amount of total agricultural surplus and on the amount of profits that are earned in the industrial sector. So, larger the amount of surplus and the amount of surplus put into productive investment and larger the amount of industrial profits earned, the larger will be the rate of growth of the industrial economy. As the model focuses on the shifting of the focal point of progress from the agricultural to the industrial sector, Fei and Ranis believe that the ideal shifting takes place when the investment funds from surplus and industrial profits are sufficiently large so as to purchase industrial capital goods like plants and machinery.
It has been asserted that Fei and Ranis did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed. While mentioning the important role of high agricultural productivity and the creation of surplus for economic development, they have failed to mention the need for capital as well. Although it is important to create surplus, it is equally important to maintain it through technical progress, which is possible through capital accumulation, but the Fei-Ranis model considers only labor and output as factors of production, also the reluctant expansionary growth in the industrial sector of underdeveloped countries can be attributed to the lagging growth in the productivity of subsistence agriculture. This suggests that increase in surplus becomes more important a determinant as compared to re-investment of surplus, an idea that was utilized by Jorgenson in his 1961 model that centered around the necessity of surplus generation and surplus persistence, finally Stagnation has not been taken into consideration, and no distinction is made between labor through family and labor through wages. There is also no explanation of the process of self-sustained growth, or of the investment function. There is complete negligence of terms of trade between agriculture and industry, foreign exchange, money and price.

The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.
The formal statement of the equilibrium condition of the Harris–Todaro model is as follows:
• Let wr be the wage rate (marginal productivity of labor) in the rural agricultural sector.
• Let le be the total number of jobs available in the urban sector, which should be equal to the number of employed urban workers.
• Let lus be the total number of job seekers, employed and unemployed, in the urban sector.
• Let wu be the wage rate in the urban sector, which could possibly be set by government with a minimum wage law.
Rural to urban migration will take place if:
Wr Le/Lus(Wu)
At equilibrium
Wr = Le/Lus(Wu).
With the random matching of workers to available jobs, the ratio of available jobs to total job seekers gives the probability that any person moving from the agricultural sector to the urban sector will be able to find a job. As a result, in equilibrium, the agricultural wage rate is equal to the expected urban wage rate, which is the urban wage multiplied by the employment rate.
Therefore, migration from rural areas to urban areas will increase if:
• Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
• Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

Name: Asogwa Arinze Godwin
Reg no: 2016/235173
Department: Economics
The Harris Todaro model of migration
The key hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. The economic system simulated is characterized by the assumption originally made by Harris and Todaro.The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. What are the main features of the Harris-Todaro model of rural-urban migration? Rational economic decision of individual migrants. Their decision is based on expected rather than actual wage differentials. They are also well aware of employment situation in cities. In the Harris–Todaro model, the rising urban wage pushes up the expected wage in the urban sector and consequently encourages workers to migrate from the rural sector to the urban sector. This phenomenon is referred to as Todaro paradox.
The Lewis FEI RANIS model
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. Ranis and Fei, assumed that the labour in the industrial sector will be paid, in terms of the industrial products and they had to bring the hanging terms of trade into the picture.

So we find that whereas according to Ranis and Fei, Lewis’ turning point appears as soon as phase in their model ends, according to Lewis himself, the turning point will appear at the end of the phase II. If i.e. upto the point where labour in the agricultural sector is paid institutional wages. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

HARRIS TODAROS MODEL

The Harris Todaros model also known as the Harris Todaros Migration Model is a model of developed by John Rees Harris and Michael Todaro in the 1970s . It explains issues relating to rural Urban migration and main assumption that movements or migration of people from the rural to the urban centers is chiefly as a result of what is called the expected wage/income differences. This further turns to explain that as people will tend to migrate to urban centers from the rural areas due to the expected wage difference, it also justify unemployment increase or high presence in the urban areas as economically rational. The migration activities at equilibrium rate between the two sector is equal and thus zero, but not without a positive unemployment presence in the urban areas. In this view have China emerged to bridge the gap explained by this model seeing that in many cities urban unemployment is a major problem and through attempts in technology is creating a possible habitual rural sector such that will minimize choices and chances for migration of persons from the rural to the urban centers.

LEWIS FEI RANIS MODEL
The Lewis fei Rani’s Model unlike the Harris Todaros Migration Model is a two way model recognising two distinct economy which is comprised of the primitive and the morden sectors.
It is concerned with the issues of unemployment and underemployment of resources in both economic sectors. The model explains that the primitive sector has in it the usual agricultural sector and and that the urban sector or the morden sector is the fast growing little industrial sectors and that they both exist side by side in the economy. It is in this coexistence that the economic problem of development is situated. However on like in other models which sees the less developed or developing areas/countries as homogeneous entity, the Lewis fei Rani’s Model acknowledge the interdependence and coexistence of both sector in an economy. The way to development in this model is suggesting a total shift from agricultural economy, even though not to mean an aboundonment of the agricultural sector but a sustainable practices that would guarantee economic security to the industrial economy such that the output of the industrial sectors is greatly increased.

NAME: IJE VORDA GOODNESS
REG NO: 2017/249514
EMAIL : vordagoodness78@gmail.com
BRIEF DISCUSSION ON THE HARRIS-TODARO MODEL OF MIGRATION AND THE LEWIS-FEI-RANIS MODEL OF ECONOMIC GROWTH AND HOW IT APPLIES TI THE NIGERIA.

HARRIS-TODARO MODEL OF MIGRATION

The Harris-Todaro model is an economic model developed in 1970, named after John R.Harris and Micheal Todaro. It is used in development economics and welfare economics to explain rural-urban migration within a country. It arose in criticism of the Lewis model.

Harris and Todaro model holds that earnings differentials, economic incentives and the probability of getting a job at the destination have key influence on the migration decision of migrants. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage. More than one rural worker is likely to migrate to the urban sector for a single job created. So the agricultural output of 2 or more labourers is lost for each job created in the urban sector.

This migration can be internal migration or international migration. Internal migration is movement within a country.

The potential migrant first calculates the real income which he or she would get in the urban area for a job with his/her present effort. A subjective judgement of the probability of obtain­ing such a job. Comparison is made between the expected income with that which he/she hopes to obtain in the rural area. Migrants decision is based on the difference. For example, suppose the ex­pected rural income is #10,000 per month, and that real income of an urban job which is commensurate with her qualification is #20,000.

However, this information alone is not suffi­cient to make the migration decision. If the subjective probability of getting the urban job is 0.45, than the expected income would be #9000 (i.e 0.45 * #20,000) and no migration would take place on this case expected urban wage = actual urban wage x the probability of getting a job. If the migrant moves with his or her family members, it will be almost impossible for them (migrants family members) to get jobs since they don’t own lands in the urban area.

If the subjective probability of getting a job in the city is 0.9, then the expected wage rate is #18,000 ( 0.9 * 20,000 ) since it is high there’s incentive to move to the city and migration will likely take place till the point were urban and rural wages are equal.

It is important to note that the difference between the rural agricultural sector and the urban industrial sector are the type of goods produced, the technology used in production and the process of wage determination. The rural sector is specialized in the production of agricultural goods, production is labour intensive and wages are much lower relative to the urban sector. In contrast the urban sector specializes in the production of industrial goods, is capital intensive, wages are higher than the rural sector and is much smaller in developing countries.

Therefore, migration from the agricultural sector to urban areas will increase if:

▪️ Urban wages represented by (wu) increase in the urban sector represented by (le), increasing the expected urban income.
▪️ Agricultural productivity reduces, lowering marginal productivity and wages in the rural sector (wr), decreasing the expected rural income.
▪️ The responsiveness of potential migrants to the resulting opportunities in the urban areas is high.
As long as the rural wage rate (Wr) expected urban wages (Weu) there will be a reverse migration i.e a flow of disappointed urban jobseekers back to the rural areas.

As migration continues a point is reached where expected urban wages and rural income is equal. When that point is reached we have an equilibrium.
ASSUMPTIONS OF THE HARRIS-TODARO MODEL

▪️ This model assumes that there are only 2 sectors in the economy ( the rural agricultural sector and the urban indundustrial sector).
▪️ Migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This means that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income is greater than expected rural income.
▪️ This model assumes that no form of unemployment exist in the rural-agricultural sector.
▪️ Rural agricultural production and the subsequent labour market is perfectly competitive i.e agricultural rural wages equals agricultural marginal productivity.
▪️ The overall population of workers in the economy is kept constant during the whole period of study and is represented by N.
▪️ The relative price of the agricultural good in terms of the industrial good, p, varies according to the relative scarcity between industrial and agricultural goods.
▪️ In the Harris-Todaro model it is assumed that the urban wage is institutionally and legally fixed, so that as a result of the migration of workers, if the number of migrant workers exceed the number of new jobs created, some workers would necessarily be unemployed, underemployed or will be forced into the urban informal sector
RELEVANCE OF THE HARRIS-TODARO MODEL IN DEVELOPING COUNTRIES
Rural-urban migration has over the years been an important part of urbanization in developing nations. The Harris-Todaro model was used to explain migration patterns in China. Nigeria as a developing country over the years we have experienced rural urban migration since wages are relatively higher in the cities than the rural areas. This over the years has led to a loss in rural manpower and reduction in agricultural output but matching growth has not been seen in the industrial sector rather an exponential increase in unemployment and underemployment. The Harris-Todaro model explains this phenomenon. Nigeria is considered the Urban giant of Africa. Urban natural population increase has been the dominant characteristic of urban growth in the Nigeria post-colonial period and will likely continue in the immediate future period. As at 2010 Nigeria is said to have added about 62.5 million individuals to it’s urban population and is estimated to be 226 million in 2050. Historical account of urban rural migration state a positive relationship between urbanization and economic growth, however this has not been the case in Nigeria. It is important to note that this is not peculiar to Nigeria. During the period 1970 to 2010 agricultural employment fell by 19% with the service sector growing by 21% and a 5% decline in the manufacturing sector.

LIMITATIONS OF THE HARRIS-TODARO MODEL

▪️ Some of the assumptions of the Harris-Todaro’s model were seen to be too restrictive.
▪️ The assumption that there is a perfect competition in the rural sector is not realistic.
▪️ The Harris-Todaro model also assumes that potential migrants are risk neutral where the migrants will likely be risk averse i.e they are indifferent between a certain expected rural income and an uncertain expected urban income of the same magnitude.
▪️ It thought that the only factor influencing migration was economic no reference to better education or healthcare.
▪️ Rural migrants don’t necessarily migrate back to the rural areas if they don’t get job in the cities instead there’s an increase in the urban informal sector.

Furthermore, the migration dynamics generated by migrants that seek to adaptate to the economic environment that they co-create leads the economy toward a long run equilibrium characterized by urban concentration characterized by underemployment and unemployment. When this long run equilibrium is reached, the Harris-Todaro condition is therefore satisfied. There is a stabilization of the rural-urban expected wage differential.

CONCLUSIONS DRAWN FROM THE HARRIS-TODARO MODEL.

This model explains migration in developing nations and it makes us understand that:-
▪️ So long as expected urban wages exceeds rural agricultural wages migration to the cities will continue.
▪️ When rural wages (wr) exceed expected urban wages the there’ll be a reverse migration i.e people will move back to the villages.
▪️ At equilibrium the rural wages and expected urban wages are equal and so therefore there’s a no incentives to move to the cities or rural areas.

For government to reduce rural urban migration policies that encourage and increase agricultural production should be encouraged. This is fine through the introduction of technology to the brutal agricultural sector. This will create incentives for migrants to remain in the rural areas moreover rural wage rate will be giving a boost. So while agricultural is developed the industrial sector is developed simultaneously. If the number of labour in the rural sector continues to decrease then the price of Agricultural products will increase because it will become scare since production will drop.

THE LEWIS-FEI- RANIS MODEL.
The Lewis-Fei-Ranis model is a dualism model developed by John.C. Fei and Gustav Ranis. It is understood as an extension of the Lewis model. It is also known as the surplus labour model. This model recognizes the presence of the modern and the primitive sector. In this model there’s existence of unemployment and underemployment of resources. The primitive sector is already existing agricultural sector and the modern sector is the rapidly emerging but still small sector.
According to this model development is brought about by a transfer of labour from the primitive sector to the modern sector but warns that while there’s a shift in the focal point of progress in the economy from the agricultural to the modern sector, the agricultural sector growth should not be negligible and output should be adequate to support the whole economy with food and raw materials. Savings and development is also a driving force in economic development in developing countries.one of the drawback of Lewis was that although the model didn’t advocate for complete abandonment of the agricultural sector it undermined the role of agriculture in industrial growth.
This model recognizes 3 stages in development.
Phase 1: the agricultural labour force is infinite elastic and suffers from disguised unemployment and MP=0.
Phase 2: there is a fall in average product since agricultural labourers have more the industrial sector. The real wage of industrial labourers reduces due to shortage of food supply, since there are lesser agricultural labourers. The decrease in real wage reduces the level of profit and surplus size that could be re-invested to further boost industrialization. It is important to note that so long as surplus exists, growth rate can still be increased without a full in industrialization.
Phase 3: the amount of labour that moves from the agricultural to the modern sector depends on.
▪️The level of surplus growth generated within the primitive sector, the growth of industrial capital stock depends on industrial profit growth.
▪️ Population growth rate
▪️ The nature of industry’s progress and its associated bias.
From the Lewis-Fei-Ranis model we understand that agricultural growth is equally as important as industrial growth, agricultural growth and industrial growth are balanced, the economy will be able to overcome the Malthusian population tarp only if the rate of labour shift from the primitive to the modern sector is larger than population growth rate.
Landowners investment and government fiscal measures influence the shifting of labour. The private and social cost of shifting labour can be very high. Per capital agricultural consumption can increase and there is a wide gap between urban and rural wages. This changes leads to leakages that prevents the creation of agricultural surplus.
Fei and Ranis strongly emphasize the interdependency of the industrial-agricultural sector and holds that a strong connection between the 2 sectors will speed up development. According to them economic growth is brought about in developing countries through the work of few numbers of entrepreneurs who have access to land and decision making powers and use industrial capital and consumer goods for agricultural practices.
Fei and Ranis assume that there’s constant returns to scale in the industrial and agricultural sector and the main factors of production are capital and labour. In the Lewis-Fei-Ranis model the major source of labour supply to the industrial sector is the agricultural sector. Since Lewis placed little emphasis on agriculture sector Fei and Ranis placed greater value on agricultural and stated that the rate of industrial growth depends on the total amount of agricultural surplus and on the amount of Profit earned in the industrial sector.
As a developing country advances there’s reallocation of labour from the agricultural to the modern sector. The essence of labour reallocation has lies in Engel’s law that states that the proportion of income spent on food decreases with an increase in the individual’s income level. Assuming 80% of labour force is involved in agricultural, 20% is left to the industrial sector. As productivity of agriculture increases it becomes possible for just 36% labour population to meet food supply satisfactory and as a result 64% of labour is now in the industrial sector. This is very much desired for an economy since the growth of industrial goods depends on the rate of per capital income and the growth of agriculture goods subject to the population growth rate. Labour reallocation is also important because with time consumers begin to want more consumer goods. Labour reallocation is necessary for producing more capital investment good.
The Lewis-Fei-Ranis model also emphasise that government has a major role to play in the initial stages of growth. Government also need to work on the social and economic overheads by the construction of roads,bridges, railways and other capital projects.
In the model we understand that there’s a possibility of growth without development. As technology led to a shift in labour saving production technique, growth of the economy takes place with increase in profit but no really economy development.
CRITICISM OF LEWIS-FEI-RANIS MODEL
▪️It is emphasized that Fei and Ranis did not really understand the sluggish economic situation prevailing in developing countries. Feudalism inhibited development in developing countries.
▪️Fei-Ranis was criticised on the grounds that it assumed that the MPP of labour is zero during the early stage of Economic development, this is only true when agricultural labour is very large this therefore leads to a shift of labour to the cities. When labour in the cities is excess then they are absorbed in the informal sector.

RELEVANCE OF THE LEWIS-FEI-RANIS MODEL IN NIGERIA
This model is very important for developing nations as it explains the stages of economic development and why there’s a shift of labour concertration from the agricultural to the industrial sector. Although this is a slowing process. In Nigeria it’s no news that the majority of labour is employed in the agricultural sector. If this model is applied in understanding the Nigerian situation then we understand that when Economic development is happening in Nigeria they’ll be a shift of labour from the agric sector to the industrial sector. From this model we understand that government also has a major role to play in the Economic development of Nigeria by providing capital goods.
Capital accumulation will also give the Nigerian economy a boost.

ASSUMPTIONS OF HARRY’S AND TODARO MODEL OF MIGRATION (DEVELOPMENT ECONOMICS)

AYOGU UCHECHI EUPHEMIA
2017/244738

ASSUMPTIONS OF THE LEWIS FEI-RANIS MODEL

Lewis in 1954 proposed a seminal theory of dualistic economic development for over-populated and under-developed economies with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus “stage” to the second, labour-scarce “stage” of development. Later, Ranis and Fei in 1961 formalised the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, are distinguished by the marginal productivity of agricultural labour.
The entry into each phase is marked three turning points:
• The breakout point leads to phase one growth with redundant agricultural labour.
• The shortage point leads to phase two growth with disguised agricultural unemployment and
• The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.

The Lewis-Ranis-Fei theory of dualistic economic development therefore provides a suitable theoretical framework for studying the growth path of labour-surplus developing economies such as China.

ASSUMPTIONS OF THE MODELS

The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage.

Lewis model makes the following assumptions:

(i) There is a duel economy i.e., the economy is characterized by a traditional, over-populated rural subsistence sector furnished with zero MPL, and the high productivity modern urban industrial sector.

(ii) The subsistence sector does not make the use of ‘Reproducible Capital’, while the modern sector uses the produced means of capital.

(iii) The production in the advanced sector is higher than the production in traditional and backward sector.

(iv) According to Lewis, the supply of labor is perfectly elastic. In other words, the supply of labor is greater than demand for labor.

The followings are the sources of unlimited supply of labor in China.

(i) Because of severe increase in population, more than required number of labors are working with lands, the so called disguised unemployed.

(ii) In China, so many people are having temporary and part time jobs, as the shoe-shines, loaders, porters and waiters etc. There will be no fall in the production even their number are one halved.

(iii) The landlords and feudals are having an army of tenants for the sake of their influence, power and prestige. They do not make any contribution towards production, and they are prepared to work even at less than subsistence wages.

(iv) The women in China do not work, but they just perform house-hold duties. Thus they also represent unemployment.

(v) The high birth rate in UDCs leads to grow unemployment.

Basic Thesis of the Lewis Model

Lewis model is a classical type model which states that the unlimited supplies of labor can be had at the prevailing subsistence wages. The industrial and advanced modern sector can be developed on the basis of agri. to traditional sector. This can be done by transferring the labor from traditional sector and modern sector.

Lewis says that the wages in industrial sector remain constant. Consequently, the capitalists will earn ‘surplus’. Such surplus will be re-invested in the modern sector leading to absorb the labor which are migrated from subsistence sector. In this way, the surplus labor or the labor which were prey to disguised unemployment will get the employment. Thus both the labor transfer and modern sector employment growth are brought about by output expansion in that sector. The speed with which this expansion occurs is determined by the rate of industrial investment and capital accumulation in the modern sector. Though the wages have been assumed constant, yet Lewis says that the urban wages are at least 30% higher than average rural income to induce the workers to migrate from their home areas.

In the fig., the production function regarding traditional sector has been demonstrated. Here in the upper part of the fig., by employing LF of labor, the OT of food production has been produced, while the amount of capital is fixed here. In the lower part of figure we have APL and MPL in the subsistence farming sector which have been derived from the TPF curve in the upper part of the fig. This is the behavior of a UDC where 80% to 90% of population lives and works in rural areas.

Lewis makes two assumptions regarding traditional sector:

(i) There is surplus labor because MPL = 0 (as MPLF curve cuts x-axis).

(ii) All rural workers share equally in the output so that rural real wage is determined by the APL, and not by MPL. Thus it is OA, which has been attained by dividing OT by OLF labor in subsistence sector.

the upper segment we have the production functions regarding modern industrial sector. In case OL, labor are employed, having the production function TPM(K1), TP1 is being produced. In the lower segment of fig., the demand for labor is D1(K1) at the constant wages (OW) which are 30% higher than the average rural wages.

In the Lewis model, the modern sector capital stock is allowed to increase from K1 to K2 and K3 as a result of reinvestment of profits by capitalist industrialists. This causes the TP curve in the upper part of fig., to shift upward from TPM(K1) to TPM(K2) and to TPM(K3).

The process that will generate these capitalistic profits for reinvestment and growth is illustrated in the lower part of fig. (b).
The modern sector MPL curves have been derived from the TPM curves of the upper part of the fig. (b).
These curves are demand for labor curve because of assumption of perfect competition.

The OA in both lower parts of fig (a) and (b) represents the average level of real subsistence income in the traditional rural sector. But in the modern sector the real wages have been represented by OW (the 30% higher than rural wages).

At such wages the supply of rural labor is assumed to be unlimited or perfectly elastic as shown by WSL curve in fig (b). This means that modern sector employer can hire as much labor as he likes without any fear of rise in wages. It is also told that in traditional sector the supply of labor is in the millions, while the employment in modern sector is in thousands. In the modern sector the employment is made by the employer to the point where MPL = W. (the point F in the lower part of fig. (b). Thus the basic employment is OL1, with this employment of labor CD1FL, output in manufacturing sector is being produced. While the share of such employed labor will be OWFL1.

The balance of output shown by the shaded area WD1F would be the total profits (surplus) that accrue to the capitalists. As Lewis assumes that all of these profits are reinvested, the total stock of capital in the modern sector will rise from K1 to K2. As a result, TPM will shift from TPM(K1) to TPM(K2) which in a turn leads to increase MPL. In other words, the demand for labor will increase as shown by the curve D2(K2) in the lower part of fig (b).

Now the new equilibrium in the modern sector takes place at point G where OL2 labor are being employed. The total output rises to OTP2 or OD2GL2 while total wages and profits increase to OWGL2 and WD2G, respectively. Once again, these larger (WD2G) profits are reinvested, the total stock of capital will increase to K3. Again the TP curve will shift upward, as the TPM(K3), and demand for labor curve will shift to D3(K3).

CONCLUSION
From the assumptions of the model, the process of modern self sustaining growth and employment expansion will continue till all the surplus rural labor is absorbed in the new industrial sector. Thereafter, additional workers can be withdrawn from agri. sector only at a higher cost of lost food production because this will decrease the labor to land ratios. In this way, the MPL will be no more zero. Here, labor supply curve will become positively sloped along with the growth of modern sector. The structural transformation of the economy will take place through shifting traditional rural agriculture to modern urban industry.

LEWIS FEI RANIS MODEL
A prominent Economist Lewis was well known with his model “Economic Development with unlimited supplies of Labour”. This model pictured the capital accumulation in the modern industrial sector with the aim of getting labour from the subsistence agricultural sector. The model was further modified by Fei and Ranis, but the essence of the two models is the same. The Lewis model and that of Fei-Ranis assume the existence of surplus labour in the economy, the main component of which is the enormous disguised unemployment in agriculture. Further they visualize ‘dual economic structure’ with manufacturing, mines and plantations representing the modern sector, the salient features of which are the use of reproducible capital, production for market and for the profit, employing labour on wage payment basis and modern methods of industrial organization. Furthermore, agriculture represents the subsistence sector using non-reproductive land on self-employment basis and producing mainly for self-consumption with inferior techniques of production and containing surplus labour in the form of disguised unemployment. Hence, the productivity or output per head in the modern sector is much longer than that in agriculture. Though the marginal productivity in agriculture over a wide range is taken to be zero, the average productivity is assumed to be positive and equal to the bare subsistence level.

ANALYSIS OF THE LEWIS MODEL
The authenticity of the Labour-surplus model of Lewis for developing countries like Nigeria; depend of course on the extent to which their underlying assumptions, explicitly or implicitly, made in this model. In our views the basic premise of this model is wrong and that it unrealistic and irrelevant for framing a suitably development strategy to solve the problem of surplus labour and unemployment. The basic premise of the model is that industrial growth can generate adequate employment opportunities so as to draw away all the surplus labour from agriculture in an overpopulated developing country like Nigeria where population is currently increasing at the annual rate of around 1.6%. This premise has been proved to be a myth in the light of generation of little employment opportunities in the organized industrial sector during over sixty years of economic development in India, Latin American and African countries.
Putting India into consideration, for instance, in the 30 years (1951-81) of industrial development in India during which fairly good rates of industrial production had been achieved, the organized industrial employment increased by any 3 million which was too meager to make any significant impact on the urban unemployment situation far from providing a southern to rate labour-surplus problem in agriculture. Thus the generation of adequate employment opportunities and as a result the absorption of surplus labour from agriculture in the expanding industrial sector has not proceeded as predicted by the Lewis model.
One can notice that the migration of workers for example in Nigeria has occurred as a result of urbanization in the various censuses but these immigrants to the urban area has not been absorbed into modern high productivity employment, as pictured by Lewis Fei Rranis. These immigrants to urban areas have been mainly employed in petty trade and domestic services in the country.

THE MODEL WITH SURPLUS LABOUR
In the model, the wage rate is put into consideration; such wage in the modern industrial sector is determined by the average productivity in the agriculture. To this average productivity is added a margin, According to Lewis this margin is fixed at 30% which is required for furnishing an incentive for labourers to transfer themselves from the countryside to the urban industries as well as for melting the higher cost of urban living. In this setting, the model shows how the expansion in the industrial investment and production or, in other words, capital accumulation outside agriculture will generate sufficient employment opportunities so as to absorb all the surplus labour from agriculture and elsewhere.
Furthermore, profit in the Lewis ‘unlimited supply of labour constitutes the main source of capital formation. The greater the share of profits in national income,the greater the rate of savings and capital accumulation. Thus with the expansion of the modern or capitalist sector, the rate of saving and investments as percentage of national income will continuously rise. As a result rate of capital accumulation will also increase relative to national income. It is of course assumed that all proofs or a greater part of the profits is saved and automatically invested. It will be important to note that as the capitalist expands, the share of profits in national product will rise. The rise in the share of profits in national product is due to the assumption of the model that wage rate remains constant and prices of the products produced by the capitalist sector do not fall with the expansion in output. To quote Lewis himself, “If unlimited supplies of labour are available at constant real wage rate, and if any part of the profits is reinvested in productive capacity, profits will grow continuous relative to the national income.”

ASSUMPTIONS AND CRITICISM OF THE MODEL
Labour-absorptive capacity of the modern industrial sector: Lewis Fei and Ranis assumed that the growth of industrial employment will be greater than the growth in labour force. This is one of their shortcomings, they believed only then the organized industrial sector can absorb surplus labour from agriculture. The employment far from withdrawing labour currently employed in the organized industries and services, in the basis to absorb the new entrants to the labour force.
One of the important setbacks of the Lewis model is that it has neglected the important of agricultural growth in sustaining capital formation in the modern industrial sector. When as a result of the expansion of capitalist modern sector, transfer of labour form agriculture to industry takes place, the demand for food grains will rise. If the output of food grains does not increase through agricultural development to meet the additional demand for food grains wages of industrial labour will slow down or even choke off the process of capital accumulation and economic development. Thus, if no allowance is made for agricultural growth, the expansion of modern sector and capital accumulation is bound to be halted.
Lewis model neglects the importance of Labour Absorption in Agriculture: We can find weaknesses in the models of Lewis and Fei-Ranis in the scenario that they have ignored the generation of productive employment in agriculture. No doubt, Lewis is this later writings and Fei-ranis in their modified and extended version of Lewis model have pictured and important role for agricultural development so as to sustain industrial growth and capital accumulation. But they visualize such an agricultural development strategy that will release labour force form agriculture rather than absorbing them in agriculture. Thus, to quote Fei and Ranis: “In such a dualistic setting the heart of the development problem lies in the gradual shifting of the economy’s centre of gravity from the agricultural to the industrial sector through labour reallocation.” In this process each sector is call upon to perform a special role: productivity in the agricultural sector must rise sufficiently so that “smaller fraction of the total population can support the entire economy” with food and raw materials, thus enabling agricultural workers to released; simultaneously, the industrial sector must expand sufficiently to provide employed opportunities for the released workers….labour reallocation must be rapid enough to swamp massive population increase if the economy’s centre of gravity is to be shifted over time.”
The above shows that employment potential of organized industrial sector is so little that labour reallocation between agriculture and industry and “smaller fraction of the total population being employed in agriculture” is just not possible in labour-surplus developing countries like India. Indeed, a good amount of employment opportunities can be generated in agriculture itself by capital accumulation in agriculture, adoptive proper agricultural technologies and making appropriate institutional reforms in the pattern of land ownership. Even about the African countries most of which do not suffer from the Malthusian problem of overpopulation but are currently faced with acute urban unemployment (especially of what is known as “UNEMPLOYMENT OF SCHOOL LEAVERS” majority of which have migrated from the villages to the urban areas) the expert opinion was veered round to the view of seeking solution of labour-surplus problem within agriculture.

CONCLUSIONS

In the above explanations, we could figure out difference lapses of the model, other than that, the model still maintains high degree of analytical value. It clearly points out the role of capital accumulative in raising the level of output and employment in labour-surplus developing countries. The model stipulates the systematic analysis of the growth problem of dual economies and brings out some of crucial importance of such factors as profits and wages rate of capital accumulation and economic growth. It also stipulates relationship in growth process most

TODARO MODEL OF MIGRATION .
Prominent men behind this model are John R. Harris and Michael Todaro, this model was developed in 1970 and used in development economics and welfare economics to undertand issues con.cerning rural-urban migration. Major assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. In the model, an equilibrium is attained when the expected wage in urban areas is equal to the marginal product of an agricultural worker. Partially like the classical, the model assumes that unemployment does not exist in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labour market is perfectly competitive, because of this the wage equals the marginal productivity.In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban inomes.

ASSUMPTIONS OF THE MODEL, TOGETHER WITH IT’S APPLICATION TO REAL LIFE SITUATIONS
Here, we discuss the assumptions together with the equations that describes them. The structure of the model is based on the assumption that a fixed wage leads to an outbreak of distortion and urban unemployment. In the model, we have two sectors , Sector one Agricultural rural sector, sector two manufacturing urban sector.There are three kinds of production factors, specific production factor in sector 1, K1, specific production factor in sector 2, K2, and labor, L, which is employed in both sectors and mobile between sectors.The specific production factor in the urban sector, K2, includes not only equipment and facilities for production but also social infrastructure, such as airports, roads, and industrial parks, which are related to production. Therefore, an improvement of the social infrastructure means an increase in K2.
Quoting Harris Todaro,”In the Harris–Todaro model, the necessary and sufficient condition for the increase in the specific production factor in the urban sector to decrease urban unemployment is that the slope of the marginal product curve of labor in the rural sector exceeds the per-capita wage difference between the institutional minimum wage and the expected wage in the urban sector”.
Putting agricultural productivity into consideration, if the productivity of Agricultural products rises together with the income of the individual,invariably, there would be no need for the rural workers to migrate to the urban area. Mostly in some of the Asian countries developing infrastructurrs such as industrial parks, roads e.t.c gives rise to the model. In the case of metro cebu, in Philippines, the Todaro paradox occurred in 1990s. As the Metro Cebu economy developed with ODA projects supported by the Japanese Government, workers from surrounding areas migrated to the region and increased urban unemployment.

CONCLUSIONS
Talking about the economy of the less developed country, the capital accumulation is very important, The accumulated capital forms many production bases and creates job opportunities in the urban sector.At the same time, the increase in employment raises the wage level in the urban sector. In the Harris–Todaro model, the rising urban wage pushes up the expected wage in the urban sector and consequently encourages workers to migrate from the rural sector to the urban sector.

OBI PROSPER UCHE
REG NO: 2017/241318

THE HARRIS-TODARO MODEL

Harris-Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain the issues concerning rural-urban migration. An assumption of the model suggest that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This somply implies that rural-urban migration in the context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income. A typical dualistic model in development economics contains exactly two sectors, an agricultural or traditional sector in the rural area and a modern or manufacturing sector in the urban area. The most familiar single-sector model is the growth theory of Harrod-Domar (1946), also the most representative and influential dualistic framework is that of Lewis (1954) which has the idea of surplus labor, subsistence wages, and turning points in the development of a dualistic economy. The work of Lewis (1954) wasa later rigorously and diagrammatically reformed by Ranis and Fei (1961). Their work (Ranis and Fei) showed how agricultural surplus could lead to the growth of industries. According to Jorgenson (1961), the production relations of a dual economy is characterized by an asymmetry.

If the formal sector and the rural sector are assumed to be fully flexible, then wages must be equalized at equilibrium in order to make all workers indifferent to migration.

Basic Assumptions

➢ Migration is a primarily economic decision.
➢ There is no unemployment in the rural sector and it is perfectly competitive such that wage is equal to marginal product
➢ Members of the labor force rationally compare the expected value of potential wages to current wages to make the decision to migrate or not.
Let’s represent the two sector capital version of the Harris–Todaro (1970) model which is also known as the Corden and Findlay (1975) model. A small open economy with two sectors, rural (sector X) and urban(sector Y), is considered. Sector X produces an agricultural commodity using labour and capital while sector Y produces a manufacturing good using the same two inputs. Capital is perfectly mobile between the two sectors and its economy-wide return is r. On the contrary, labour is imperfectly mobile between the sectors. Workers in the urban sector are unionised and receive a higher wage, WY, than their counterparts in the rural sector who receive a low competitive wage, WX. So WY > WX and this intersectoral wage differential leads to rural–urban migration of labour. Markets are perfectly competitive except in the urban labour market. It is assumed that neoclassical production functions exhibit constant returns to scale with positive but diminishing marginal productivity to each factor.

Application of Harris-Todaro model to the Nigerian Economy

Throughout the developing world, countries are experiencing rapid rates of urbanization. In Africa using Nigeria as a case study, urban growth rates are among the highest in the world averaging about 7 percent annually, with several cities having growth rate in excess of 10 percent. Association with this urbanization has been a large increase in the open urban unemployment which generally exceeds 10 percent of the urban labor force and consists largely of young school leavers.

Although rapid urbanization and it’s associated unemployment is due partly to high population growth rates, rural-urban migration accounts for over half the growth of most African cities. At the same time, out-migration of labor from agriculture has been one factor leading to national food do and rising food prices in many African countries.

For these reasons, there is a widespread concern that the rate of rural-urban migration should be slowed. From Nigeria’s economic view point, the mass of unemployed coupled with at least seasonal labor deficits in rural areas represents under- utilization of resources and contributes to inequitable distribution of income.

Therefore, migration from rural areas to urban areas will increase if:

Urban wages increase in the urban sector, increasing the expected urban income.

Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector, decreasing the expected rural income.

However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

LEWIS-FEI-RANIS MODEL

Current literature on growth and development continues to be influenced by the one sector Solow-type models or the two-sector Uzawa-type models, both of which have now been complemented by endogenous growth. While these endogenous growth models have recently begun to confront such issues as poverty traps at a theoretical level, they generally share the neoclassical feature of full employment and market clearing. In contrast, the surplus labor models advanced by Lewis (1954), and expanded upon by Ranis and Fei (1961, 1964, 1997), described a two-sector economy depicting an initially large traditional sector and a relatively small commercialized sector, with the key feature that the traditional sector does not adhere to the neoclassical full employment labor market clearing assumption. While various micro foundations can be constructed to detail why this might be so, at the macro level, which was the focus of these early dual economy models, it was sufficient to posit that labor was in excess supply relative to cooperating factors at the prevailing wage and technology, and thus that the commercialized sector faced an essentially infinitely elastic labor supply at any moment in time.With unskilled rural labor the abundant resource in many developing countries, especially at an early stage of their development, what determines the price of labor has continued to be a controversial issue, although it is clear that, in recent years, the neoclassical model and market clearing approaches have enjoyed increasing popularity in not only the theoretical but also the applied literature. The notion of an institutional or bargaining wage not based on marginal productivity fundamentals has been especially repugnant to orthodox economists. The rejection of the labor surplus model has, in part, been due to some confusion as to which of its assumptions are necessary as opposed to which are sufficient.

Assumptions of the lewis-fei-ranis model

1. There is a presence of dual economy. Traditional or agriculture sector is passive and stagnant in nature while the capitalist sector is active and progressive in nature.2. Supply of land is fixed, and both A sector and K sector makes use of the land. 3. Population is an exogenous factor i.e. it is determined by factors other than those present in the model. 4. Real wage rate in the industrial sector is fixed. This wage rate is equal to initial level productivity and is also called constant institutional wage rate.

5. There are constant returns to scale with respect to labour where labour acts as a variable factor in both A Sr and K Sr. 6. There is no accumulation of K in the A Sr. except in one form, i.e., land reclamation. It means that if there is no technological breakthrough in agriculture, the sector will become non-remunerative and it will be characterized by fatigue. Therefore, land’s fertility has to be maintained. 7. Output of the A Sr. depends upon land and labour, while that of the K Sr. depends upon labour and capital.8. Marginal product of labour is zero at some points and such labour force can be transferred from A Sr to K Sr, where the productive capacity is more without any loss to A Sr.

Application of the lewis-fei-ranis model to the Nigerian economy

The per capita income (in local currency unit – naira) rose at decreasing rate from 1981 to 1998, rising at increasing rate from 1999 till 2014. However, the agricultural contribution to productivity was rising and falling but fell in most of the years from 1981 to 2014. This suggests that agricultural productivity might not be responsible for the increase in income per head in Nigeria during the period

Uwaezuoke Stephen Chinonso
2017/242432
Economic Department
The Fei–Ranis model of economic growth is a dualism model in developmental economicsor welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.
According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

The three fundamental ideas used in this model are:
1. Agricultural growth and industrial growth are both equally important;
2. Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.
Fei and Ranis emphasized strongly on the industry-agriculture interdependency and said that a robust connectivity between the two would encourage and speedup development. If agricultural laborers look for industrial employment, and industrialists employ more workers by use of larger capital good stock and labor-intensive technology, this connectivity can work between the industrial and agricultural sector. Also, if the surplus owner invests in that section of industrial sector that is close to soil and is in known surroundings, he will most probably choose that productivity out of which future savings can be channelized. They took the example of Japan’s dualistic economy in the 19th century and said that connectivity between the two sectors of Japan was heightened due to the presence of a decentralized rural industry which was often linked to urban production. According to them, economic progress is achieved in dualistic economies of underdeveloped countries through the work of a small number of entrepreneurs who have access to land and decision-making powers and use industrial capital and consumer goods for agricultural practices.
The Lewis model is criticised on the grounds that it neglects agriculture. Fei–Ranis model goes a step beyond and states that agriculture has a very major role to play in the expansion of the industrial sector. In fact, it says that the rate of growth of the industrial sector depends on the amount of total agricultural surplus and on the amount of profits that are earned in the industrial sector. So, larger the amount of surplus and the amount of surplus put into productive investment and larger the amount of industrial profits earned, the larger will be the rate of growth of the industrial economy. As the model focuses on the shifting of the focal point of progress from the agricultural to the industrial sector, Fei and Ranis believe that the ideal shifting takes place when the investment funds from surplus and industrial profits are sufficiently large so as to purchase industrial capital goods like plants and machinery.
It has been asserted that Fei and Ranis did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed. While mentioning the important role of high agricultural productivity and the creation of surplus for economic development, they have failed to mention the need for capital as well. Although it is important to create surplus, it is equally important to maintain it through technical progress, which is possible through capital accumulation, but the Fei-Ranis model considers only labor and output as factors of production, also the reluctant expansionary growth in the industrial sector of underdeveloped countries can be attributed to the lagging growth in the productivity of subsistence agriculture. This suggests that increase in surplus becomes more important a determinant as compared to re-investment of surplus, an idea that was utilized by Jorgenson in his 1961 model that centered around the necessity of surplus generation and surplus persistence, finally Stagnation has not been taken into consideration, and no distinction is made between labor through family and labor through wages. There is also no explanation of the process of self-sustained growth, or of the investment function. There is complete negligence of terms of trade between agriculture and industry, foreign exchange, money and price.

The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.
The formal statement of the equilibrium condition of the Harris–Todaro model is as follows:
• Let wr be the wage rate (marginal productivity of labor) in the rural agricultural sector.
• Let le be the total number of jobs available in the urban sector, which should be equal to the number of employed urban workers.
• Let lus be the total number of job seekers, employed and unemployed, in the urban sector.
• Let wu be the wage rate in the urban sector, which could possibly be set by government with a minimum wage law.
Rural to urban migration will take place if:
Wr Le/Lus(Wu)
At equilibrium
Wr = Le/Lus(Wu).
With the random matching of workers to available jobs, the ratio of available jobs to total job seekers gives the probability that any person moving from the agricultural sector to the urban sector will be able to find a job. As a result, in equilibrium, the agricultural wage rate is equal to the expected urban wage rate, which is the urban wage multiplied by the employment rate.
Therefore, migration from rural areas to urban areas will increase if:
• Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
• Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

Name: Ike Godswill Chinedu
Reg no: 2017/249515
Dept: Economics
Answer;
The Lewis Fei-Ranis Model of (Surplus
Labour Theory).
The Fei-Ranis model of economic growth was developed by John C. H. Fei and Gustar Ranis, and can also be regarded as the surplus labour model. It has also been understood to be a dualism model in development economics. It is an extension of the Lewis model. The model takes into consideration the presence of a dual economy, which comprises of the modern and primitive sectors and takes into account an economic situation of unemployment and underemployment. According to this theory, the primitive sector comprises of existing agricultural sector and considers the modern sector as rapidly growing but small industrial sector. The both sector exist together in the economy, such that there is augmentation of the industrial output. This was done through the transfer of labour supplied. And at the same stance, growth in agricultural sector must not be ignored or neglected and its output must be sufficient enough to support the whole economy with food and raw materials.
The assumptions of the model was rooted on the falls of the Lewis model in which; one, he underestimated the role of agriculture in boosting the growth of the industrial sector. It also did not acknowledge the fact that an increase in productivity of labour should take place as regards to the shift in labour between the two sectors. These two ideas were taken into considerations in the Fei-Ranis dual economy model of three growth stages. They further propose that the model lacks in their application of concentrated analysis to the changes that takes place with agricultural development. In phase one of the Fei-Ranis model, the elasticity of the agricultural labour force is infinite and thus suffers from a disguised unemployment. The marginal product of labour (MPL) is zero. This phase is therefore similar to the Lewis model. In the phase two of the model, there is a rise in agricultural productivity which leads to industrial growth such that it prepares the base for the next stage. In this stage there may be agricultural surplus, as average product (AP) increases, higher than marginal product and not also equal to the subsistence level of wages. Note that in phase one; MPL = 0 and thus, an actual amount of labour can be shifted from the agricultural sector without any fall in output. This therefore shows the surplus labour. While in the phase two, AP>MP and industrial labour rises to a value greater than zero and APL begins to fall. This fall in the APL is due to the agricultural labourers shift to the industrial sector, the real wage of the industrial labourers’ decreases due to shortage of food supply, since less labourers are now working in the food sector. The real wage decreases the level of profit and the size of surplus that could have been reinvested for more industrialization. Phase three, is the point of commercialization. This is where the economy becomes completely commercialized in the absence of disguised unemployment. Here the supply curve becomes steeper and both sectors starts equally for labour. In this phase, the amount of labour shifted and the time it takes, depends on; the growth surplus generated within the agricultural sector, and the growth of the industrial capital stock dependent on the growth of industrial profit and; the nature of the industry’s technical progress and its associated bias and; finally the growth rate of population.
The assumptions or fundamental ideas behind the model thus becomes;
Agricultural growth and industrial growth are both important
Agricultural growth and industrial growth are necessarily balanced
Only if the rate at which labour is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself from the Malthusian population trap. This shifting can take place through the landlord’s investment activities and through the government fiscal measures. Moreover, the cost of shifting of labour in terms of both private and social cost may be higher. Also the per capita agricultural consumption can increase, rather there could exist a wide gap between the wages of urban and rural workers. These three scenarios could be referred to as leakages, which prevent the creation of agricultural surplus.
Fei and Ranis laid a strong emphasis on the industry-agriculture relationship and suggested that a healthy relationship between the two would enhance development. They made reference to the japan dualistic economy in the 19th century and argued that connectivity between the two sectors of Japan was promoted by the decentralized rural industry which was linked to urban production. They further posit that economic progress is achieved in dualistic economies of underdeveloped countries through the work of a small number of entrepreneurs who have access to land and decision making powers and use industrial capital and consumer goods for agricultural practises. They developed a concept they labour utilization ratio R, which they defined as the unit of labour that can be productively employed (without redundancy) per unit of land.
Thus labour utilization is calculated as; R=ts/ot.
They also developed the concept of endowment ratio S, which is a measure of the relative availability of the two factors of production. It is given by; S=te/ot.
Where te is agricultural labour and; ot represents agricultural land. They finally developed the concept of non-redundancy coefficient T, being measured as; T= ts/te
These concepts together forms a relationship between T, R and S. therefore T can then be said to be calculated as; T=ts or ot/te or ot= R/S thus, T = R/S.
The mathematical relation shows that non-redundancy coefficient T, is directly related to labour utilization and inversely related to the endowment ratio. The Fei and Ranis model assumes constant returns to scale in the industrial sector like in the agricultural sector. They assumed the main factors of production to be capital and labour, the expansion path of the industrial sector thus given by a line OA0 A1, A2. As capital increases from K0 to K1 to K2 and labour increases from L0 to L1 to L2, the industrial output thus increases accordingly. According to the model, the main source of labour supply of the industrial sector is the agricultural sector, due to the redundancy in the agricultural labour force. Total industrial activity rises due to increase in the total supply of investment funds, leading increased industrial employment.
Agricultural surplus is seen as the produce from agriculture which surpasses the needs of the society for which it was produced, and may either be exported for income or stored for future use. Fei and Ranis in their model hypothesized that if this agricultural surplus is equivalent to the real wage, it is therefore known as the constant institutional wage hypothesis. It is also equal in value to the ratio of total agricultural output to the total agricultural population. If a section of the redundant agricultural labour force is removed from the total agricultural labour force and absorbed into the industrial sector, now the difference in the output produced by the remaining labour force and the real income of the labour force produces the total agricultural surplus of the economy. This surplus is produced by the reallocation of labour such that it is absorbed by the industrial sector. Thus, it could be seen as the use of hidden rural savings for the expansion of the industrial sector. We can therefore say that, the agricultural sector plays a crucial role of a wage fund. The unproductive labour force from the agricultural sector turns productive once it absorbed by the industrial sector simultaneously and produces an output, earning a total wage income. The agricultural surplus created is needed for consumption by the same workers who left for the industrial sector. The agricultural sector thus provides successfully not only the manpower for the production activities but also the wage funds required to run the process.
Importance of Agriculture in the Fei-Ranis
modell of Surplus Labour.
The model goes beyond, stating that agriculture plays a vital role in the development of the industrial sector unlike the Lewis model. They argued that the rate of growth of the industrial sector depends on the amount of total agricultural surplus and on the amount of profit that are earned in the industrial sector. The model focuses on the shifting of the focal point of the progress from the agricultural to the industrial sector. Fei and Ranis believed that this shifting takes place when investment fund from surplus and industrial profit are sufficiently large so as to purchase industrial capital goods like plants and machinery. Thus, the condition for a successful transformation by Fei and Ranis is that; the rate of increase of capital stock and rate of employment opportunities > Rate of population growth.
The Necessity of Labour Reallocation.
The essence of labour reallocation lies in the Engel’s law which posits that the part of income being spent on food decreases with an increase in the income level of an individual, even if there’s a rise in the actual expenditure on food. As underdeveloped country passes through development processes, labour is reallocated from the agricultural to the industrial sector. This labour reallocation becomes a necessity over time as consumers begin to want more of industrial good than agricultural good on relative terms. Although the Fei-Ranis model noted the importance of labour reallocation being linked to the need to need to produce more capital goods as opposed to the thought of industrial consumer goods following the theory of the Engel’s law. This is due to the fact that the assumption that the demand for industrial good is high seems to be unrealistic, as the real wage in the agricultural sector is very low and this prevents the demand for industrial goods. As the growth process observes a slow-increase in the consumer purchasing power, the dualistic economies follow the path of natural austerity, being characterised by more demand and thus, importance of capital goods industries when juxtaposed to the industrial goods industries.
In the Fei-Ranis model, it’s quite possible that technological progress takes place and there’s a shift to labour-saving production techniques, growth of the economy takes place with increases in profit but no economic development takes place. Since growth takes place with increases in profits but development is at a standstill and since employment and wages of labourers remain the same.
Weaknesses of the Fei and Ranis model.
The Fei and Ranis model failed to take into account the sluggish economic situation prevailing in the developing countries. If not, they would have noticed the backwardness existing in the agricultural sector was due to the institutional structure, primarily the system of feudalism that prevailed.
They assumed that MPPL is zero (I.e. MPPL = 0) during, the early phases of economic development, this has been criticized by Harry T. Oshima and some other economists that MPPL of labour is zero only if the agricultural population is very large and if it is very large, some of that labour will be shift to cities in search of jobs.
In the Fei-Ranis the question of whether MPL = 0 is that of an empirical one. The underdeveloped countries mostly exhibit seasonality in food production, which suggests that especially during favourable climatic conditions, for instance, that of harvesting or sowing, MPL would definitely be greater than zero (i.e. MPL > 0).
Application of the model in the real world.
The Lewis Fei-Ranis model of dualistic economic development was employed in china as a framework to investigate the rapid growth in china in 1965-2002. It discovered that the economic growth of china can be mainly attributed to the development of the non-agricultural sector which was the industrial and service sector, being driven rapid labour migration and capital accumulation.
Conclusion.
We can therefore conclude that since the Lewis Fei-Ranis model was not successful when applied to the study of the success of the rapid growth in China, thus is not applicable in the real world

Harris-Todaro Model of Migration.
The Harris-Todaro model, was named after John R. Harris and Michael Todaro. The model was developed in 1970. It was used in development and welfare economics to explain issues relating to rural-urrban migration. The primary assumption of this model is that, the decision to migrate is based the expected income differentials between rural and urban areas other than just wage differentials alone. This in essence means that rural-urban migration in acontext of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
In the model, equilibrium could be reached if the expected wage or actual wage adjusted for unemployment rate in urban areas is equal to the marginal product of an agricultural worker. It assumes that there’s no unemployment in the rural agricultural sector.it further assumes that rural agricultural production and subsequent labour market is perfectly competitive. Therefore, the agricultural rural wage is equal to agricultural marginal productivity. To be in equilibrium, the rural-urban migration rate will have to be equal to zero, since the expected rural income equals the expected urban income. Thus, in this equilibrium there will be a positive unemployment in the urban sector.
The equilibrium conditions is thus stated as follows;
Let Wr be the wage rate (i.e. marginal productivity of labour) in the rural agricultural sector.
Let Le be the total number of jobs available in the urban sector, which should be equal to the number of employed workers.
Let Lus be the total number of job seekers, both employed and unemployed, in the urban sector.
Let Wn be the wage rate in the urban sector which could possibly be set by government with a minimum wage law.
Therefore, rural to urban migration will take place if:
Wr Le/Lus Wu
And at equilibrium if:
Wr = Le/Lus Wu
Matching workers randomly to the available jobs, the ratio of the available jobs to the overall job seekers thus gives the probability that any person moving from the agricultural sector to the urban sector will be able to find a job therefore in equilibrium, the agricultural wage is equal to the expected urban wage rate, which can be calculated as the urban wage multiplied by the employment rate.
In conclusions, migration from rural to urban areas will only increase if:
Urban wages increase the urban sectors, leading to an increase in the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector, leading to a decrease in the expected rural income.
Therefore, though this migration might create unemployment, causing growth in the informal sector, this behaviour is economically rational and maximizes utility in the Harris-Todaro model. Therefore, for the fact that the economic agents migrating are well informed or have complete information about rural and urban wage rates and probabilities of being employed, they will make an expected income maximizing decision
Application to the Real World via Nigeria.
The model was successful in explaining the internal migration within China as the regional income gap has been proved to be a primary drive to rural-urban drift. While urban unemployment is local government main concern in many cities. Therefore it is not applicable to Nigeria
.

HARRIS-TODARO MODEL OF MIGRATION AND UNEMPLOYMENT
In recent years, the urban areas in less developed countries have grown very rapidly. Between 1950 and 1960, urban areas in Africa grew by 69%, in Latin America by 67%, and in Asia by 51%, while rural areas grew by only 20% over the same period. Since biological growth rates rarely exceed 3% per annum, much of the urban growth is due to rural-urban migration. There is a growing consensus on a number of aspects of the migration question. Both economist and non-economist agree that rural-urban migration can be explained primarily by economic factors: the “push” from agriculture and the “pull” of relatively high urban wages. There is such migration is quite rational despite the existence of urban unemployment. The essence of this relationship is summarized clearly in perhaps the best-known article on the subject, that of Harris and Todaro: “…migration proceeds in response to urban-rural differences in exoected earnings (defined below) with the urban employment rate acting as an equilibrating force on such migration”
The Harris-Todaro model, named after John R. Harris and Michael Todaro is an Economic model developed in 1970 used to explain some issues concerning rural-urban migration in development economics. Todaro migration model seeks to explain rural-urban migration as an economically rational process despite high urban unemployment. Migrants calculate (present value of) urban expected income (or its equivalent) and move if this exceeds average rural income. The Todaro migration model has four(4) basic characteristics:
1. Migration is stimulated primarily by rational economic considerations of relative benefits and costs, mostly financial but also psychological.
2. The decision to migrate depends on expected rather than actual urban-rural real-wage differentials where the expected differential is determined by the interaction of two variables, the actual urban-rural wage differential and the probability of successfully obtaining employment in the urban sector.
3. The probability of obtaining an urban job is directly related to the urban employment rate and thus inversely related to the urban unemployment rate.
4. Migration rates in excess of urban job opportunity growth rates are not only possible but also rational and even likely in the face of wide urban-rural expected income differentials .High rates of urban unemployment are therefore inevitable outcomes of the serious imbalance of economic opportunities between urban and rural areas in most underdeveloped countries.
On the other hand, Harris-Todaro model shows equilibrium version of the Todaro migration model which predicts that expected incomes will be across rural and urban sectors when taking into account informal sector activities and outright unemployment. Its main assumption is that migration decision are based on expected income differentials between rural and urban areas rather than wage differentials.
The Harris-Todaro model produced two powerful policy results. The first concerns the policy of formal-sector job creation to employ the unemployed. Secondly, there (Harris and Todaro) considered a policy of rural development. If such a program could increase the rural traditional-sector wage, unemployment would then fall. Thus, in the Harris-Todaro model, the solution to urban unemployment is rural development.
The Harris-Todaro model is also based on the following assumptions:

1. There are two sectors in the economy; the rural or agricultural sector (A) and the urban or manufacturing sector (M).
2. The rural sector produces XA units of agricultural goods and the urban sector produces XM units of manufactured goods. Each sector produces only one unit.
3.The model operates in the short run and capital is available in fixed quantities (K ) in the two sectors
4. The number of urban jobs available (NM ) is exogenously fixed. In the rural sector some work is always available. Therefore, the total urban labor force comprises N–NA along with an available supply of rural migrants. In other words, the total urban labor force equals N–NA with (N–NA ) – NM unemployed.
5. The urban wage is fixed at WM and the rural wage at WA , WM > WA .
6. The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.
7. Rural-urban migration continues so long as the expected urban real income is more than the real agricultural income.
8. The expected urban real income is equal to the proportion of urban labour force actually employed multiplied by the fixed minimum urban wage.

THE HARRIS-TODARO MIGRATION MODEL

Assume only two sectors, rural agriculture and urban manufacturing. The demand for labor (the marginal product of labor curve) in agriculture is given by the negatively sloped line AA’. Labor demand in manufacturing is given by MM’. The total labor force is given by line OA OM . In a neoclassical, flexible-wage, full-employment market economy, the equilibrium wage would be established at W*A = W*M, with OA LA workers in agriculture and OM LM workers employed in urban manufacturing. All available workers are therefore employed. But what if urban wages are institutionally determined (inflexible downward) as assumed by Todaro at a level WM , which is at a considerable distance above W*A. If for the moment we continue to assume that there is no unemployment, OMLM workers would get urban jobs, and the rest OALM , would have to settle for rural employment at OAWA** wages (below the free-market level of ). So now we have an urban-rural real wage gap of WM – WA**, with WM institutionally fixed. If rural workers were free to migrate (as they are almost everywhere except China), then despite the availability of only OMLM jobs, they are willing to take their chances in the urban job lottery. If their chance (probability) of securing one of these favored jobs is expressed by the ratio of employment in manufacturing, LM, to the total urban labor pool, LUS, then the expression
WA = LM/LUS (WM)
shows the probability of urban job success necessary to equate agricultural income WA with urban expected income (), thus causing a potential migrant to be indifferent between job locations. The locus of such points of indifference is given by the qq’ curve.
POLICY IMPLICATIONS

MR is the production possibility curve of the manufacturing (urban) and rural sectors. Given the initial minimum wage in the urban sector. The initial equilibrium at point B where OXM output is produced in the rural sector. The rural-urban migration is not possible at point B due to the expected wage differentials. Point E on the production possibility curve is the wage differential point at which OXM output is produced in the urban sector and OXA output in the rural sector.
1. Imbalances in urban-rural employment opportunities caused by the urban bias, particularly first-city bias, of development strategies must be reduced. Because migrants are assumed to respond to differentials in expected incomes, it is vitally important that imbalances between economic opportunities in rural and urban sectors should be minimized. When urban wage rates rise faster than average rural incomes, they stimulate further rural-urban migration in spite of rising levels of urban unemployment.
2. Urban job creation is an insufficient solution for the urban unemployment problem; This follows that for any given positive urban-rural wage differential, higher urban employment rates will widen the expected differential and induce even higher rates of rural-urban migration. For every new job created, two or three migrants who were productively occupied in rural areas may come to the city. Thus if 100 new jobs are created, there may be as many as 300 new migrants and therefore 200 more urban unemployed. Hence a policy designed to reduce urban unemployment may lead not only to higher levels of urban unemployment but also to lower levels of agricultural output due to induced migration.
3. Indiscriminate educational expansion will lead to further migration and unemployment; The heavy influx of rural migrants into urban areas at rates much in excess of new employment opportunities necessitates rationing in the selection of new employees. Although within each educational group such selection may be largely random, many observers have noted that employers tend to use educational attainment or number of years of completed schooling as the typical rationing device. For the same wage, they will hire people with more education in preference to those with less, even though extra education may not contribute to better job performance. Jobs that could formerly be filled by those with a primary education (sweepers, messengers, clerks, etc.) now require secondary training; those formerly requiring a secondary certificate (clerks, typists, bookkeepers, etc.) must now have a university degree. It follows that for any given urban wage, if the probability of success in securing a modern-sector job is higher for people with more education, their expected income differential will also be higher, and they will be more likely to migrate to the urban (cities).
4. Wage subsidies and traditional scarcity factor pricing can be counterproductive; A standard economic policy prescription for generating urban employment opportunities is to eliminate factor price distortions by using “correct” prices, perhaps implemented by wage subsidies (fixed government subsidies to employers for each worker employed) or directs government hiring.
CRITICISM;
The Harris-Todaro model suggest non-distortionary lump sum tax to finance subsidy.
Harris-Todaro model does not take into considerations the generation of saving as a source of financing subsidy. Savings are low in LDCs.
This model does not incorporate the cost of rural-urban migration or the relatively higher cost of urban living which the migrants have to incur in the urban sector.
The model does not specify alternate policy prescriptions such as giving a wage subsidy to the urban sector and the same time restricting the migration of those rural workers.

SUMMARY AND CONCLUSIONS;
With a summary of what appears to be the consensus of most economists on the shape of migration and employment strategy. This would appear to have the following key elements:
1. Creating an appropriate rural-urban economic balance; A more appropriate balance between rural and urban economic opportunities appears to be indispensable to ameliorating both urban and rural unemployment problems and to slowing the pace of rural-urban migration. The main thrust of this activity should be in the integrated development of the rural sector, the spread of rural nonfarm employment opportunities, improved credit access, better agricultural training, the re-orientation of social investments toward rural areas, improving rural infrastructure, and addressing shortcomings of rural institutions (including corruption, discrimination, and stratification), the presence of which has the effect of raising the cost of delaying out-migration.
2. Expansion of small-scale, labor-intensive industries. The composition or “product mix” of output has obvious effects on the magnitude (and in many cases the location) of employment opportunities because some products (often basic consumer goods) require more labor per unit of output and per unit of capital than others. Expansion of these mostly small-scale and labor-intensive industries in both urban and rural areas can be accomplished in two ways: directly, through government investment and incentives and improved access to credit, particularly for activities in the urban informal sector, and indirectly, through income redistribution (either directly or from future growth) to the rural poor, whose structure of consumer demand is both less import-intensive and more labor-intensive than that of the rich.
3. Eliminating factor price distortions; There is ample evidence to demonstrate that correcting factor price distortions primarily by eliminating various capital subsidies and curtailing the growth of urban wages through market-based pricing would increase employment opportunities and make better use of scarce capital resources.
4. Choosing appropriate labor-intensive technologies of production; One of the principal factors inhibiting the success of any long-run program of employment creation in both urban industry and rural agriculture is the almost complete technological dependence on (typically laborsaving) machinery and equipment from the developed countries. Domestic and international efforts can help reduce this dependence by developing technological research and adaptation capacities in developing countries.
5. Modifying the linkage between education and employment; The emergence of the phenomenon of the educated unemployed is calling into question the appropriateness of the massive quantitative expansion of educational systems, especially at the higher levels. Formal education has become the rationing tunnel through which all prospective jobholders must pass.

NAME: UDUMA IKECHUKWU OBASI
REG: 2017/241441
EMAIL: ikechukwuuduma9@gmail.com

Lewis-Ranis-Fei model (surplus labour model):

The Lewis (1954) theory of dualistic economic development provides the seminal
contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to
comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow
the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, ). The non-agricultural sector accumulates capital by drawing surplus labour out of the agricultural sector. The expansion of the non-agricultural sector takes advantage of the infinitely elastic supply of labour from the agricultural sector due to its labour surplus.
When the surplus labour is exhausted, the labour supply curve in the non-agricultural
sector becomes upward-sloping. Ranis and Fei (1961) formalised Lewis’s theory by combining it with Rostow’s (1956) three “linear-stages-of-growth” theory. They disassembled Lewis’s two-stage economic development into three phases, defined by the marginal productivity of agricultural labour. They assume the economy to be stagnant in its pre-conditioning stage. The breakout point marks the creation of an infant non-agricultural sector and the entry into phase one. Agricultural labour starts to be reallocated to the non-agricultural sector. Due to the abundance of surplus agricultural labour, its marginal productivity is extremely low and average labour productivity defines the agricultural institutional wage. When the redundant agricultural labour force has been reallocated, the agricultural marginal productivity of labour starts to rise but is still lower than the institutional wage. This marks the shortage point at which the economy enters phase two of development. During phase two the remaining agricultural unemployment is gradually absorbed. At the end of this process the economy reaches the commercialisation point and enters phase three where the agricultural labour market is fully commercialised

Conclusion and policy recommendations:

Having tested the Lewis-Ranis-Fei theory for the Chinese economy over 1965-2002 we will in the case of this study substitute the economy of Nigeria to that of China and implement the policy recommendations therein.The test shows that China’s economic growth is mainly attributable to the development of the non-agricultural sector(which is similar to that of Nigeria). This is driven by rapid capital accumulation as well as
employment growth. The reallocation of labour away from agriculture has made a
positive net contribution to China’s rapid economic growth by around 1.23 percent. The
rise in the marginal productivity of agricultural labour indicates the absorption of
redundant agricultural labour since the 1978 Economic Reform. However, the marginal
productivity of agricultural labour is still lower than the initial low average productivity
of agricultural labour. This implies the continued existence of disguised agricultural
unemployment. This suggests that the Chinese economy has entered the
Lewis-Ranis-Fei phase two of development but has not yet achieved phase three. The
continuing widening productivity gap between the two sectors calls for the removal of
market restrictions and government interventions so as to allow the continued
absorption of surplus labour.
Several policy recommendations are tentatively suggested. First and foremost, more
effort should be made in promoting employment to effectively absorb the remaining
labour surplus and promote China’s economic development. This can be achieved by
further relaxing the Hukou restrictions on migration, increasing labour market flexibility
and improving the allocative efficiency of labour. It can also be achieved by
encouraging the development of private enterprise to create more employment
opportunities. Second, China’s government should continue implementing the Sunshine
Policy, initiated in 2003, designed to provide rudimentary job training, recruitment
information and information about conditions in the destination cities to rural migrants.
This will not only help facilitate employment of rural migrants but also satisfy the
increasing demand for skilled labour in the growing non-agricultural sector. Third,
agriculture could be promoted by tax breaks, direct subsidies and most importantly, by
removing price controls on agricultural products. Agriculture could thus be
commercialised and the economy would enter phase three of economic development.

Harris Todaro migration model:

In the 1960s the government of newly independent Kenya faced a difficult situation: Unemployment in Nairobi and other major cities was high and apparently rising. To cope with this problem, Tripartite Agreements were reached in which private-sector and public-sector employers agreed to increase employment in exchange for unions agreeing to hold wages at their current levels. The larger number of jobs was expected to reduce unemployment. However, in the event, urban unemployment appeared to have increased following the Tripartite Agreements rather than decreased, as far as anyone could tell.
In light of these events, John Harris and Michael Todaro formulated the Harris-Todaro model to explain the puzzle. At the core of the Harris-Todaro model were the following features. First, real wages (adjusted for cost-of-living differences) are higher in urban formal-sector jobs than in rural traditional-sector jobs. Second, to be hired for a formal-sector job, one has to be physically present in the urban areas where the formal-sector jobs are located. Third, and as a consequence of the first two features, more workers search for formal-sector jobs than are hired, employers hire some of the job seekers but not all of them, and those not hired end up unemployed. Fourth, for equality to be maintained between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower-paying rural job, the equilibrium arising in such a setting is characterized by urban unemployment. And fifth, any temporary difference in the expected wages between one sector and another is eroded as workers migrate from the low-expected-wage labor market to the high-expected-wage labor market.
The Harris-Todaro model produced two powerful policy results. The first concerns the policy of formal-sector job creation to employ the unemployed (who, in the Harris-Todaro model, are all in urban areas, because that is where the formal-sector jobs are assumed to be located). Such a policy, they concluded, would increase the formalsector labor force by more than the number of new jobs created, thereby raising the number of urban unemployed. Thus, the solution to urban unemployment is not to create urban employment.
The second policy option that Harris and Todaro considered was a policy of rural development. If such a program could increase the rural traditional-sector wage, unemployment would then fall. Thus, in the Harris-Todaro model, the solution to urban unemployment is rural development.
Soon after the model was published, the government of Kenya followed the Harris-Todaro precepts by putting into place an integrated program of rural development. The result was that unemployment in Kenya fell.
Harris and Todaros fundamental contribution was building a model that fit the stylized facts of the labor market they were analyzing and that was based on sound micro foundations. The fact that the model remains part of the economists intellectual toolkit today is a tribute to its basic insight and enduring analytic power.

The original model has been both simplified for some purposes and expanded for others by later contributors, including Stiglitz, Bell, Khan, Anand and Joshi, Bourguignon, Corden and Findlay, and others (Fields 2005). Harris and Todaro formulated general processes for determining prices of the products produced by the two sectors and also for determining a rural-sector wage that varies inversely with the number of people in the rural sector. A simplified version of the Harris-Todaro model was developed in which product prices and rural-sector wages are taken as constant. Numerous additional analytic and policy results were derived in the simplified Harris-Todaro model. At the same time, some of the assumptions of the Harris-Todaro model were judged to be too restrictive, and so the model was generalized in the years that followed to nest their specific formulation within a broader framework. The initial Harris-Todaro model has been extended to allow for on-the-job search from a rural agriculture setting, the existence of an urban informal sector, preferential hiring of the better-educated, employment fixity, duality of production conditions and earnings levels within the rural sector, capital mobility, endogenous urban wage setting, risk aversion, and a system of demand for goods, among other factors.
As an early multisector labor-market model, the Harris-Todaro model set forth a principal alternative framework for policy analysis. It showed how employment and wage levels in one labor market reflect supply, demand, and institutional conditions not only in that labor market but also in other labor markets.
In terms of pro-poor economic growth, the Harris-Todaro model and other multisector-labor-market models can help policy makers avoid two mistakes. One is to assume that development efforts should be channeled to the sectors where the poor are. The other is to assume that efforts should always be focused on getting the poor out of the sectors in which they now are. Careful cost-benefit analysis based on well-specified
labor-market models is required to decide among such alternatives.

Findings and recommendations:

The fundamental contribution of Harris and Todaros rural-urban two sector migration model was to build a model that fit the stylized facts of the labour market. On the lines of the theory, developing countries (e.g Nigeria) adopted program on integrated rural development which could encouraged an increase in the rural traditional sector wage. The theory proves that the higher the unemployment rate, the lower is the probability of new migrants from the countryside actively seeking formal sector employment who are unable to find it. The significant findings of the theory are:
first, if the expected urban wage equals rural income, there is no incentive to migrate.
Second, if the expected urban wage is greater than rural income, there is a great incentive to move from rural to urban area.
Third, if the expected urban wage is less than rural incomes, there would be an incentive to move in other direction.
Fourth, the expected urban wage depends on what type of job migrant is engaged in. Therefore, the Haris Todaros model helps policy-makers to avoid two mistakes. One is to assume that development efforts should necessarily be channeled to the sectors where the poor are. The other is to assume that efforts should necessarily be focused on getting the poor out of the sectors in which they presently are.
Thus, recommended policies should be the ones poised to eradicate both poverty level and unemployment rate among the dwellers of rural areas. Reduction/ eradication of poverty in the form of poor wage gain will on the other hand reduce the incentive of moving to the urban areas for greener pasture search such that the problems of high immigration rate will be avoided.

Lewis-Fei-Ranis Model of Economic Growth

One of the best known early theoretical models of development that focused on the structural transformation of a primarily subsistence economy was that formulated by Nobel Laureate W. Arthur Lewis in the mid-1950s, and later modified, formalized, and extended by John Fei and Gustav Ranis. The Lewis two-sector model became the general theory of the 1960s and early 1970s, and it is sometimes still applied, particularly to study the recent growth experience in China and labor markets in other developing countries.
The Fei-Ranis model is an improvement over the lewis model. John Fei and Gustav Ranis analyze the transition process through which an underdeveloped economy hopes to move from a condition of stagnation to one of self-sustained growth.
The theory relates to underdeveloped labor surplus and resources; poor economy in which the vast majority of the population is engaged in agriculture amidst widespread unemployment and high rates of population growth.

ASSUMPTIONS OF THE MODEL

1. There is a dual economy divided into a traditional and stagnant agricultural sector and an active industrial sector.
2. The output of the agricultural sector is a function of land and labor alone.
3. There is no accumulation of capital in agriculture except in the form of land reclamation.
4. Land is fixed in supply.
5. Population growth is taken as an exogenous phenomenon.
The real wage in the industrial sector remains fixed and is equal to the initial level of real income in the agricultural sector. It is called an institutional wage.
6. Workers in either sector consume only agricultural products.
Given these assumptions, Fei and Ranis analyze the development of a labor surplus economy into three phases;
In the first phase, the disguised unemployed workers who are not adding to agricultural output are transferred to the industrial sector at a constant institutional wage.
In the second phase, agricultural workers add to agricultural output but produce less than the institutional wage they get. Such workers are shifted to the industrial sector. If the migration of the workers to the industrial sector continues, a point is eventually reached when farmworkers produce output equal to the institutional wage.
In the third phase, which makes the end of the take-of and the beginning of the self-sustained growth when farmworkers produce more than the institutional wage they get. In this phase, the surplus labor is exhausted and the agricultural sector becomes commercialized.

CRITICISMS OF FEI-RANIS MODEL
1. Commercialization of agriculture leads to inflation. According to the model, when the agricultural sector enters the third phase, it becomes commercialized, but the economy is not likely to move smoothly into a self-sustained growth because inflationary pressure will start.
2. Supply of land is not fixed. Fei-Ranis begins with the assumption that the supply of land is fixed during the development process. In the long run, the amount of land is not fixed, as the statistics of crop average in many Asian countries reveal.
3. Institutional wage not constant in the agricultural sector. The model assumes that the institutional wage remains constant in the first two phases even when agricultural productivity increases. This is unrealistic because with a general rise in agricultural productivity farm wages also tend to rise.
CONCLUSION
However, these limitations do not undermine the importance of the Fei-Ranis model for the economic development of labor surplus countries. It systematically analyses the development process from the take-off to self-sustained growth through the interaction of the agricultural and industrial sectors of an underdeveloped economy.

THE HARRIS-TODARO MODEL OF MIGRATION
The Harris-Todaro model is based on the experiences of tropical African facing the problems of rural-urban migration and urban unemployment. The labor migration is due to rural-urban differences in average expected wages. The minimal urban wage is substantially higher than the rural wages. If more employment opportunities are created in the urban sector at the minimum wage, the expected wage shall tend to rise and rural-urban migration shall be induced leading to growing levels of urban unemployment. To remove urban unemployment, Harris and Todaro suggests a subsized minimal wage through a lump sum tax.

ASSUMPTIONS OF THE HARRIS-TODAROS MODEL
1. There are two sectors in the economy: the rural or agricultural sector (A) and the urban or manufacturing sector (M).
2. The model operates in the short run.
3. Capital is available in fixed quantities in the two sectors.
4. The number of urban/manufacturing jobs available is exogenously fixed.
5. Rural-urban migration continues so long as the expected urban real income is more than the real agricultural income.
6. The rural wage equals the rural marginal product of labor and the urban wage is exogenously determined.
7. There is perfect competition among producers in both sectors.

MATHEMATICAL EXPRESSION OF THE HARRIS-TODARO MODEL
Output in the rural sector is suppose to be a function of labour so that the production function for agricultural good is;
Xa = f (Na, L-bar, K-bar) f’>0; f”0; f ” 0.
P is the price of agricultural good in terms of the price of manufactured good which is a function (p) of the relative output of agricultural and manufactured goods.
The agricultural wage equals the value of marginal product (MP) of labor expressed in terms of the manufactured good,
Wa = f’a (Na) = p(f’m).
In the urban sector the producers are wage- takers and they aim at profit maximization which means that the urban market wage is;
Wa = f’m (Nm).
The urban expected wage which leads to the migration of workers from the rural to the urban sector is given as;
Wu = W-bar m x Nm/Nu, Nm/Nu ≤ 1.
Where the expected real wage (Wu) in the urban sector is equal to the urban real minimum wage (Wm) adjusted for the proportion of the total urban labor force (Nu) actually employed.

POLICY IMPLICATIONS OF THE H-T MODEL
Harris-Todaro have drawn a few important policy implications of their model. According to them, the payment of minimum wage to the additional industrial worker will induce more rural-urban migration. To solve this problem of an institutional determined wage that is higher than the equilibrium level, labor should be employed according to a shadow wage and /or at a payroll subsidy wage. Since the opportunity cost (I.e shadow wage) of an agricultural worker is lower than the marginal product of an industrial worker, the implementation of shadow wage criterion will have important effects on the level of agricultural output and on urban unemployment.

CRITICISM OF THE HARRIS-TODARO MODEL
1. The Harris-Todaro model does not specify alternate policy prescriptions such as giving a wage subsidy to the urban sector and at the same time restricting the migration of those rural workers who are not able to find jobs in the urban sector.
2. Harris-Todaro suggest non-distortionary lump sum tax to finance subsidy, but a lump sum tax is seldom non-distortionary.
3. This model does not consider or incorporate the cost of rural-urban migration or the relatively higher costs of urban living which the migrants have to incur in the urban sector.
4. The model does not take into consideration the generation of savings as a source of financing subsidy. Though savings are low in LDCs, yet they are an important source of non-distortionary finance to subsidise wages.
CONCLUSION
Despite these criticisms, the Harris-Todaro model is more realistic than the other dual economy models because it tries to tackle the problem of rural-urban migration that actually exists in LDCs. For instance the Lewis model assumes that there is no unemployment in the urban sector and when rural-urban migration takes place, the number of new jobs created in the urban sector exactly equals the number of migrants. This is unrealistic.

The Lewis Fei-Ranis model is for overpopulated and under developed economy. It is based on dualistic economic development because The theory explains a way the industrial sector and agricultural sector can grow simultaneously without a lapse in the other or in the improvements rather than at its expense. There is always a unique, sole characteristic of surplus agricultural labor found in this kind of economy. The model is an attempt to balance agricultural and industrial growth in these economies. Lewis previously held that Economic growth in such economy can be achieved by investments in the non-agricultural sector by extracting surplus labor in the agricultural sector. But John Fei and Gustav explained how increase in productivity in agricultural sector would be helpful in promoting industrial sector too. The model explains that the complete shift the focus of progress from the agricultural to industrial economy does not mean that agricultural sector should be negligible rather its output should still be sufficient to support the whole economy with food and raw materials. With the assumption that large proportion Of the high population in these countries is engaged in agriculture and still agriculture is stagnant therefore marginal productivity of labor is zero and negative in agricultural sector while there are certain non agrarian sectorsIn the economy where there is reduced use of capital. This model suggests that if this surplus labor in the agricultural sector is transferred to industrial sector where their productivity will increase, economic development will be taking place.
They argue that an economy goes through three phases of development. In phase 1, marginal product of labor is equal to zero. The first phase is where surplus labor Can be withdrawn from agricultural sector without changing agricultural output. In the second phase of the development, additional output due to an increase in labor begins to rise as transfer takes place from agricultural sector to industrial sector, average Product falls showing an increase in real wages of industrial workers because sThere is shortage of food supply. The real wages in industrial sector is fixed and equal to real income in agricultural sector. These wages are called institutional wages. in the second stage labor surplus exist where Apl>MPL But it is not equal to institutional wages. If the migration to industrial sector continues, there will be a time from workers produce output that is equal to institutional wages.
The third stage is characterized by self sustained growth where farm workers produce more than the institutional which they get because disguised unemployment has been eliminated. Surplus labor ends and the agricultural sector becomes commercialized sector. MPL here is greater than CIW, disguised unemployment is eliminated. As labor is transferred to industrial sector there will be labor shortage in the agricultural sector so industrial sector cannot get the labor at the same prevailing constant wages therefore the wages in the industrial sector will rise.
From my own point of view the Fei-Ranis model did not take into account the very possible case where a constant transfer of labor from the agricultural sector to the industrial sector causes an extreme shortage of labor in the agricultural sector the model holds that the rate of labor transfer must exceed the rate of population growth. If the largest proportion of the workforce in the country goes to the industrial sector outputs will not be anything close to sufficient to support the whole economy with food and raw materials as Nigeria is facing now. This model is prevalent in Nigeria where labor has been shifted to the industrial sector. Disguised unemployment previously faced by the agricultural sector is now the problem of industrial sector. Shortage of labor in agricultural sector has led to shortage of food supply and raw materials in the economy.

The Harris Todaro Model of Migration
The basic assumption of this model is high expected income in the urban areas than the rural areas. Equilibrium according to this model is reached when expected wage in urban areas is equal to the marginal product of an agricultural worker. It also has the assumption that unemployment is nonexistent in the rural agricultural sector and that rural agricultural products and subsequent market is perfectly competitive which means that agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, rural-urban migration rate is zero since expected rural income equals expected urban income, which is leading to positive unemployment in the urban sector. Expected urban wage rate is equal to urbanwageXemployment rate. Rural urban migration will increase if urban wages increase in the urban sector, increasing the expected urban income and agricultural productivity also decreases, decreasing marginal productivity and wages in the agricultural sector therefore decreasing the expected rural income. This is nothing different to the current Nigerian economy. The expected income in urban areas has caused total neglect to the rural agricultural sector. The rural-urban migration is only rational if equilibrium is achieved, (where expected real wage in urban areas equals marginal product of an agricultural worker). But in the real sense, rural-urban migration is as a result of increase in urban wages in the urban sector which has caused a decrease in expected wages in rural sector.
The neglect to rural agricultural sector caused by rural-urban migration has brought about: shortage of food supply and raw materials, overpopulation and unnecessary competition in the urban sector leading to high crime rates, and a large number of people chasing too few jobs.
This brings an economy back to a state of inadequate development as is seen in Nigeria today.

NAME: EZEH JUDE OBIOMA
REG. NO. 2017/249504
DEPARTMENT: ECONOMICS
EMAIL: judeobioma07@gmail.com

HARRIS – TODARO MODEL OF MIGRATION
INTRODUCTION
The Harris-Todaro model is an economic model developed in 1970 which is being used in development economics and welfare economics in analysing some of the issues of rural-urban migration and unemployment. The key contribution of this model to the field of development economics is by making the migration process a rational choice based on expected earnings, that is, labour migration is as a result of rural-urban differences in average expected wages. Here, the minimum urban wage is substantially higher than the rural wage. Also, if additional employment opportunities are created in the urban sector at the minimum wage, the expected wage shall rise and rural-urban migration on the other hand shall be induced resulting to increasing levels of urban employment.

BASIC ASSUMPTIONS OF THE MODEL
The Harris-Todaro model is based on the following assumptions;
There are two sectors in the economy; the rural or agricultural sector (A) and the urban or manufacturing sector (M).
Migration is primarily an economic decision: Workers rationally compare the expected income to current income to make decision on migration.
There is no unemployment in the rural sector and it is perfectly competitive such that wage is equal to marginal product
The model operates in the short run

MAIN ARGUMENTS OF THE MODEL
The Harris-Todaro (1970) elaborated the basic two sector model of rural-urban labour migration. It takes most of Lewis model’s assumptions as given, such as the rural sector being characterised by subsistence agriculture, and the urban sector being characterised by modernised industries. However, the Harris-Todaro model takes a standard two-sector model and imposes a higher wage in the urban sector which is higher than equilibrium clearing, while wage in the agriculture is flexible. These developing countries are lack good social safety nets such as welfare benefits, unemployment benefits, and old age security. If the migrants were unable to find a job in the urban formal sector, which is the modern industrial sector, they would be forced to work in the informal sector to sustain their lives. The informal sector is very primitive; work in this sector is labour intensive with little or no capital endowment.
The equilibrium condition of the Harris-Todaro model can be described as the wage in rural (agricultural) sector must be equal to the expected wage in the urban sector. The model in its most basic form ignores disutility from not being at home farm, or cost of mobility, but these omissions do not change the essence of the model, the only implication of this is a downward shift of the urban sector’s expected returns. This equilibrium can be defined as,
Wa = (Lf/Lf+Li)Wf + (Li/Lf+Li)Wi
Where;
Wa denote the wage in rural (agricultural) sector
Wf denote the wage in urban formal (industry) sector
Wi denote the wage in urban informal sector
Lf denote the number of workers in the urban formal sector
Li denote the number of workers in the urban informal sector
The left hand side of the equation is simply the agricultural wage. The right hand side, Lf+Li which is the formal sector labour force plus informal sector labour force. Combining these will give the entire labour force in the urban sector.
(Lf/Lf+Li) then is simply the ratio of urban workers in the formal sector, in the (H-T) model, this is what the potential migrant sees as the probability of finding a job in the formal sector.
Similarly, (Li/Lf+Li) is what the potential migrant sees as the probability of ending up in the informal sector.
The probabilities of each sector is then multiplied by that sector’s respective wage, adding the results together yields the right hand side of Harris-Todaro equilibrium, which is the expected wage from moving to the urban sector.
The Harris-Todaro model in essence is an extension of the Lewis model. It simply endogenizes migration decision along with the introduction of a second urban sector. It does not change from the Lewis model in that the fundamental driving force of growth is technological growth.

CONCLUSION
Despite the aforementioned weaknesses of the Harris-Todaro model, the model is said to be more realistic than the other dual economy models because it tries to tackle the problem of rural-urban migration that actually exists in LDCs. We consider one of the assumptions of the model that workers are risk-neutral when in reality, most people are risk-averse. However, the model can be modified to incorporate this. In a risk-averse version of the Todaro Model, less migration occurs, causing the agricultural sector to increase which invariably increases the productivity of the rural sector and improvement on the economic growth. The level of risk-aversion is reflected in the difference between the informal sector wage and the formal sector wage.

APPLYING THE MODEL TO NIGERIA ECONOMY
For the fact that Nigeria is a developing country and the economy being structured into rural and urban sectors, hence the Harris-Todaro model of migration can be successfully applied to the Nigeria economy. Since the beginning of 1980s, the economic position has worsened seriously. The per-capita income fall considerably and wage employment has declined (NISER report, 1993).
In recent times, due to persistent underdevelopment, there has been a noticeable high level of rural-urban migration in search of better standards of living and bigger opportunities for meaningful economic and social activities. This is dysfunctional not only to rural development but retards the overall national development.
In view of the foregoing, various Nigeria governments in the past have initiated rural development programmes targeted at the rural sector. Some of these programmes include;
National Accelerated Food Production Programme (NAFPP)
Agricultural Credit Guarantee Scheme (ACGS)
National Directorate of Employment (NDE)
National Poverty Eradication Programme (NAPEP)
With the effective implementation of these programmes by government, rural-urban migration can be curtailed, thereby increasing the productivity of the rural (agricultural) sector and the overall development of the economy.

LEWIS-FEI-RANIS MODEL OF SURPLUS LABOUR
INTRODUCTION
Lewis model of surplus labour was developed in 1954 and later modified by Fei-Ranis in 1961, 1964 and 1997 respectively. Lewis argued that an economy transits from the first stage, labour-surplus to the second, labour-scarce stage of development. Ranis and Fei (1961) later expanded the Lewis theory and defined three “phases” of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Therefore, the second labour-scarce stage of the Lewis model becomes the phase three of the Ranis-Fei model. The three phases are illustrated with the turning points below;
The breakout point leads to phase one growth with exceeding agricultural labour.
The shortage point leads to phase two growths with false appearance of agricultural unemployment.
The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector.
BASIC ASSUMPTIONS OF THE LEWIS-FEI-RANIS MODEL
The basic assumptions of the model are as follows;
There is rural (agricultural) and urban (manufacturing) sector in an economy.
A developing economy has a surplus of unproductive labour in the agricultural sector.
The wages in the manufacturing sector are more or less fixed.
Higher wages are being offered in the manufacturing sector which attract workers.
An advanced manufacturing sector means an economy has moved from a traditional to an industrialized one.

THE MAIN ARGUMENTS OF THE MODEL
The Lewis-Fei-Ranis model is based on structural change theory which explains the mechanism of changing structure of underdeveloped economic from subsistence agriculture to more modern and more urbanized. The movement of labour from traditional to modern sector bring expansion in both output and employment based on the following;
A. Rate of industrial investment and capital accumulation which ultimately depends on the level of profit. Lewis assumes that all profits are reinvested.
B. Wage difference between the rural and urban sector.
The model is focused on the following points;
There is an abundance of labour in under developed countries and shortage of natural resources.
The population growth rate is very high which results in mass unemployment in the economy.
There is a dynamic industrial sector in the economy.
There are certain non-agrarian sectors in the economy where there is reduced use of capital.
The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labour is zero and negative in agricultural sector. The situation where MPL-0, labour can be transferred to industrial sector without any loss in agricultural output. The real wages in industrial sector remains fixed and it is equal to the initial level of real income in agricultural sector. Such wages are given the name of institutional wages.
CONCLUSION
The Lewis-Fei-Ranis model maintained that in developing countries, surplus labour in the agricultural sector is sufficiently large to give an unlimited supply of labour for industrial expansion, thus labour migration from the agricultural sector to the industrial sector induces more significant structural change in these countries than in the developed countries. The model therefore focuses on the capital accumulation in the modern industrial sector so as to absorb this excess labour from the subsistence agricultural sector.

RELATING THE MODEL TO NIGERIA ECONOMY
As Nigeria being a developing country with a dual economic structure (the rural and urban sectors), and having a massive labour supply from the rural sector to the urban sector, it is therefore pertinent that the government should implement policies that will aid investment in both sectors so that the economy will maintain a balanced growth pattern. This is also a crucial part of the Lewis-Fei-Ranis model to support economic development.

Kalu Emmanuel Chinemerem
2017/249356
Economics philosophy

INTRODUCTION
The surplus model though widely accepted and praised, has been attacked severely after its emergence in 1954. Yet it is hard to conceive development without growth, though there can be growth without development. The model is unclear, and it could not move further, as a result of this. This has prevented its use in empirical research. However, it was important despite it being unclear, as it was the first work ever on economic development, and other works have built on its existence. It was the first time labour in an economy was looked into. It is further accepted generally as ‘the’ contribution for which Lewis was awarded a Noble prize and with this award, he successfully revolutionized the contemporary development thinking (Ranis, 2004).
The Fei–Ranis model of economic growth is a dualism model in developmental economicsor welfare economics that has been develop by Johnc.h.fei and Gaustav Ranis and can be understood as an extension of the Lewis Model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.
According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod-Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries, in this model both primary and secondary sector are both driving force of economic development in developing countries.

HISTORY OF SUPLUS LABOUR THEORY
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.Itrecognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector.Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

COMPARISON WITH OTHER MODELS
Fei and Ranis emphasized strongly on the industry-agriculture interdependency and said that a robust connectivity between the two would encourage and speedup development. If agricultural laborers look for industrial employment, and industrialists employ more workers by use of larger capital good stock and labor-intensive technology, this connectivity can work between the industrial and agricultural sector. Also, if the surplus owner invests in that section of industrial sector that is close to soil and is in known surroundings, he will most probably choose that productivity out of which future savings can be channelized. They took the example of Japan’s dualistic economy in the 19th century and said that connectivity between the two sectors of Japan was heightened due to the presence of a decentralized rural industry which was often linked to urban production. According to them, economic progress is achieved in dualistic economies of underdeveloped countries through the work of a small number of entrepreneurs who have access to land and decision-making powers and use industrial capital and consumer goods for agricultural practices.

THE ASSUMPTIONS
The first assumption of the model was that the modern sector employment creation and labour transfer rate is proportional to the rate of capital accumulation in the modern sector. Marginal productivity of labour, henceforth MPL, is positive in the modern sector. Labour could be transferred from the agricultural sector to the modern sector at zero cost, yielding net profits the industry leading to a higher rate of investment: countries can thus develop rapidly (Todaro and Smith, 2009 ).
The second was the notion that surplus labour exists in the rural areas, while the urban areas were said to have full employment. This, Todaro said, was because there was over-population in the rural area where MPL is zero. Actual output of labour was used to determine their wages (Todaro and Smith, 2009).
ventions.
There was an assumption of diminishing returns in the modern sector, mostly in the industrial areas. But, there is evidence that there is a prevalent increase in returns (Todaro and Smith, 2009 ).
Finally, there was an unreal assumption that if a modern labour sector was competitive, it guaranteed a continuous existence of real urban wages to a point that surplus labour is exhausted in the rural sector (Todaro and Smith, 2009).

CRITICISM
Lewis’ central problem was identifying the major causes of growth and their constraints. According to Lewis, the most important growth constraint in output was the lack of productive capital accumulation. The existing dominant constraint to capital accumulation foe Lewis was the savings rate as, seen by the classical economists (Hunt, 1989). If the savings rate is so small, then enough capital is not saved.
A major criticism of the Lewis model concerns his notion of “surplus labour”. It was interpreted often as zero marginal productivity of agricultural labour. This situation is highly unlikely and was prone to vigorous attack by T. Schultz (1964). He did this by making available; evidence introduced from India which showed that withdrawal of large agricultural population did not result to agricultural output declining (Ranis, 2004).
According to Lewis, surplus labour was thought of in terms of human beings rather than man-hours, thereby defining his surplus labour happening at the given wage rate.
CONCLUSION
The Lewis model, though widely accepted and praised, has been attacked severely after its emergence in 1954. Yet it is hard to conceive development without growth, though there can be growth without development. The model is unclear, and it could not move further, as a result of this. This has prevented its use in empirical research. However, it was important despite it being unclear, as it was the first work ever on economic development, and other works have built on its existence. It was the first time labour in an economy was looked into. It is further accepted generally as ‘the’ contribution for which Lewis was awarded a Noble prize and with this award, he successfully revolutionized the contemporary development thinking (Ranis, 2004).

Obodike Loveth OGADIMMA
2017/249537
obodikeloveth111@gmail.com

AN ESSAY ON THE SUMMARY OF LEWIS AND FEI RANIS MODEL {SURPLUS LABOR THEORY}

INTRODUCTION
William Arthur Lewis, with his most famous published work, Economic Development with Unlimited Supplies of Labour and The Theory of Economic Growth made a great contribution to the theories of economic development. Based on his findings, Ranis and Fei succeeded to extend the initial Lewis model and assessed the changes in the agricultural and industrial labour in more detail. The fei-Ranis model of economic growth is a dualism model in welfare economic that has been developed by JOHN C.H.Fei and Gustav Ranis. It can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. According to this model, the primitive sector consist of the existing agricultural sector in the economy and the modern sector is the rapidly emerging but small industrial sector .This is to say that it recognizes the presence of a dual economy comprising both the modern and the primitive sector and it takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature .both sectors co-exist in the economy ,wherein lies the crux of the development problem .development can be brought about only by a complete shift in the focal point of progress .
HISTORY
Lewis (1954) proposed a seminal theory of dualistic economic development for over-populated and under-developed countries with vast amounts of surplus agricultural labour for which he was later to be awarded the 1979 Nobel Prize in Economics. Economic growth in such an economy can be achieved by rapid capital accumulation in the non-agricultural (industrial and service) sector, facilitated by drawing surplus labour in the agricultural sector. In the Lewis theory, an economy transits from the first, labour-surplus stage to the second, labour-scarce stage of development. Later, Ranis and Fei (1961) formalised the Lewis theory and defined three phases of dualistic economic development by sub-dividing the first stage in the Lewis model into two phases. Thus, the second labour-scarce stage of the Lewis model corresponds to phase three of the Ranis-Fei model. These three phases, are distinguished by the marginal productivity of agricultural labour. The entry into each phase is marked three turning points: The breakout point leads to phase one growth with redundant agricultural labour. The shortage point leads to phase two growth with disguised agricultural unemployment. The commercialisation point leads to phase three of self-sustaining economic growth with the commercialisation of the agricultural sector. The two economists John Fei and Gustav Ranis presented their dual economy model. There was a flaw in Lewis model that it did not pay enough attention to the importance of agricultural sector in promoting industrial growth. But Fei-Ranis model of dual economy explains how the increased productivity in agricultural sector would become helpful in promoting industrial sector. In this respect, it presents three stages whereby underdeveloped countries moves from stagnation to self-sustained economic growth. Thus, this model is treated as an improvement over Lewis model of unlimited supply of labor.
Like in the Harrod-Domar model, savings and investment become the driving forces when it comes to economic development of underdeveloped countries. It has been asserted that Fei and Ranis did not have a clear understanding of the sluggish economic situation prevailing in the developing countries. If they had thoroughly scrutinized the existing nature and causes of it, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed.
ARGUMENT
Fei and Ranis say, “It has been argued that money is not a simple substitute for physical capital in an aggregate production function. Directing majority of my arguments on the analysis by Ranis and Fei in A Theory of Economic Development, The central idea behind the Lewis model is fairly simple. Lewis divided labour force into two differentiated groups subsistence sector and capitalist sector where the former is assumed to contain unlimited supply and consequently, a pool of surplus labour that sets labour-supply conditions for the latter.
There are reasons to believe that the relationship between money and physical capital could be complementary to one another at some stage of economic development, to the extent that credit policies could play an important part in easing bottlenecks on the growth of agriculture and industry.” This indicates that in the process of development they neglect the role of money and prices. They fail to differ between wage labor and household labor, which is a significant distinction for evaluating prices of dualistic development in an underdeveloped economy.Thus we find that whereas Lewis had failed to offer a satisfactory explanation of this subsistence sector and ignored the real impact of population growth on the choice of capital intensity on the process of surplus labor absorption. Moreover, Fei-Ranis model emphasized upon the simultaneous growth of agriculture and industrial sectors. Thus Fei-Ranis model believes in ‘Balanced Growth’ in the take-off stage. It means that there should be a simultaneous investment in both agricultural sector and industrial sector. According to Fei-Ranis model in the beginning the surplus rises; such surplus will be available as a capital in the take-off stage. Some part of this surplus will be used in agricultural development, while some part will be reploughed in industrial development. As a result, both agricultural and industrial sectors will grow under ‘Balanced Growth’ pattern.
Fei-Ranis model argued that surplus can be generated by the investment activities of the land lords and by the fiscal measures of the government. However, leakages could exist because of the cost of transferring the labor from agricultural sector to industrial sector in the form of transport cost and building of schools and hospitals, etc. Moreover, the transference may lead to increased per capita consumption of agricultural output, and a gap may also emerge in case of rural wages and urban wages. Again, if the supply curve of- the labor is backward bending, the peasants may reduce their work effort as their incomes rise.
we refer to the two sectors as agricultural and non-agricultural. Lewis (1954) originally named the two sectors as the subsistence and the capitalistic sectors and later on in Lewis (1979) referred to them as the traditional and modern sectors. Jorgenson (1967, p.291) elaborates further on the distinction between the two sectors and narrows this down to the stylised fact that the two sectors do not share the same production technology, particularly when it comes to capital accumulation. For agricultural labour productivity is very low due to the presence of surplus labour relative to other scarce resources. The agricultural wage rate is lower than the non-agricultural sector.
CRITICISM
i) Marginal Productivity of Labor in Phase I: The FR model is of the view that MFL = 0 in the first phase of growth, and the transfer of labor from agriculture would not reduce output in the agricultural sector in phase I. But the economists like Berry and Soligo are of the view that agricultural output in phase I of Fei-Ranis model will not remain constant and may fell under different systems of land tenure, that is the peasant proprietorship and share cropping etc.
 
(ii) Marginal Productivity of Labor is Not Zero: Prof. Jorgenson who has also presented a model of ‘dual economy’ has object FR model’s contention of zero MP in phase I. He says whether MPL will be zero is an empirical issue. During the seasons of sowing and harvesting the MPL > 0. Jorgenson concluded on the basis of Japanese data even for the pre I world war period the supply of labor was not unlimited. Then how MPL can be zero.
 
(iii) Ignoring The Role of Capital: The FR model concentrated upon land and labor as the determinants of output, ignoring the role of capital. But Profs. Brown, Byres, Frankel, Griffen, Ghatak and Ingersent are of the view that in the underdeveloped countrie there has occurred what is known as ‘Green Revolution’ in agriculture, which has promoted the greater use of capital and technology on lands. Consequently, there has been a greater increase in the agricultural productivity and agricultural incomes.
 
(iv) Open Economy: FR model ignored the role of foreign trade as it assumed a closed economy model. In the 2nd phase when agricultural product decreases, the Terms of trade goes against industrial sector. This would occur in the presence of closed economy. But if the model is made open such would not happen as the goods could be imported in the presence of then-scarcity. This was especially observed in case of Japan which imported cheap farm products to improve her terms of trade .
 
(v) Supply of Land in Long Run: FR model assumed that in the process of economic development the supply of land remained fixed. But it is not true. The supply of land can be increased in case of long run.
 
(vi) Commercialization Of Agriculture And Inflation: According to FR model when 3rd phase starts the agricultural sector becomes commercialized. But it is criticized by saying that this phase does not start so easily The shifting of labor to industrial sector will create labor shortage in agricutural sector. This will create shortage of food stuff leading to increase in their prices. In this way, inflation will generate which may obstruct the process of development.
ASSUMPTIONS
The assumption was that, in the agricultural sector, Fei and Ranis assume constant returns to scale in the industrial sector. The main factors of production are capital and labor.
-There is an abundance of labor in such underdeveloped countries and shortage of natural resources.
 
– The population growth rate is very high which results in mass unemployment in the economy.
 
– The major share of the population is engaged in agriculture. But agricultural sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agricultural sector.
 
– There are certain non-agrarian sectors in the economy where there is reduced use of capital.
 
– There is a dynamic industrial sector in the economy.
One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the FeiRanis dual economy model of three growth stages. They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development In Phase 1 of the FeiRanis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.

COMPARISM WITH THE REAL WORLD
by applying the Labor Reallocation specified by the World Bank (1996). The approach suggest that labor reallocation has a positive impact on Chinas economic growth, accounting for 1 to 2 percent per annum of GDP growth. We find out that the effect of labour reallocation has declined since the mid-1990s because of less absorption of the surplus rural labour in the non-agricultural sector, particularly in industry. Furthermore, we find that the gap of labour productivities between the two sectors is widening, which is at odds with the theoretical expectation. This reflects the effects of market imperfections and government intervention. A critical minimum effort is required for China to release the remaining disguised agricultural unemployment and enter phase three of economic development. Fei and Ranis (1973) analysed the economic development of Taiwan in 1965-1975 and Korea in 1966-1980 by comparing descriptive statistics and their results also supported the Lewis theory. However, Ho (1972) tested the Lewis theory on Taiwan for the period 1951-1965 and found that technological progress played a far more important role on economic growth than sectoral labour migration unlike my country Nigeria where agriculture happen to be the focal point of economic growth, this is to say that Nigeria was not really in support of lewis model of undermining the role of agriculture in boosting the industrial sector even though Nigeria and every other developing countries will still have to pass and benefit from the lewis model.

AN ESSAY ON THE SUMMARY OF HARRIS TODARO MODEL OF MIGRATION
INTRODUCTION
The HarrisTodaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The Harris-Todaro model of the rural-urban migration process is revisited under an agent-based approach. The migration of the workers is interpreted as a process of social learning by imitation, formalized by a computational model. By simulating this model, we observe a transitional dynamics with continuous growth of the urban fraction of overall population toward an equilibrium. Such an equilibrium is characterized by stabilization of rural-urban expected wages differential (generalized Harris-Todaro equilibrium condition), urban concentration and urban unemployment. These classic results obtained originally by Harris and Todaro are emergent properties of our model.incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision. In other words, these authors posit that rural-urban migration will occur while the urban expected wage exceed the rural wage.From this crucial assumption, as denominated by Harris-Todaro, is deduced that the migratory dynamics leads the economic system toward an equilibrium with urban concentration and high urban unemployment.The model was an academic investigation to throw light on the events following Tripartite Agreement in Kenya. The newly independent Kenya in the 1960s was increasingly facing a serious situation of unemployment in the major urban cities. To cope with the situation of unemployment,TripartiteAgreement was signed between the government public sector and theprivate sector. The agreement increased employment in the industrial jobs in exchange for unions agreeing to hold wages at their current levels.
HISTORY
The received theory of rural-urban migration, first set forth in Todaro (1968), has been revised and augmented by Todaro (1969), Harris and Todaro (1970), again by Todaro (1971), and by Johnson (1971). The Harris-Todaro ver￾sion is best known and we shall consider it in that form. The model treats rural-urban migration primarily ~.s an economic phenomenon. In essence, the theory postulates that workers compare the expected incomes in the urban sector with agricultural wage rates and migrate if the former exceeds the latter. Rural-urban migration is thus the equilibrating force which equates rural and urban expected incomes and as such is a disequilibrium phenomenon.The three basic characteristics of their model–that migration occurs largely for economic reasons, that the migration decision depends on expected ralher than nominal wage differentials, and that migration takes place in dis￾equilibrium–suggest that rural-urban migration be given a new emphasis. Rather than considering it as a key phenomenon in its own right, migration could better be regarded as the adjustment mechanism by which workers allocate themselvesbetween different labor markets, some of which are located in urban areas and some in rural areas.The larger number of employment was expected to reduce unemployment, but it appeared that the urban unemployment had increased following the governments agreement. Harris and Todaro subsequently formulated amodelto explain rural-urban economic preferences to migrate. The distinctive concept in the model is that the rate of migration flow from rural (agricultural) areas to urban (industrial) areas is determined by the difference between expected urban wages and rural wages.
COMPARING HARRIS TODARO MODEL WITH LEWIS AND FEI RANIS MODEL
By contrast to the Todarian models, the rural surplus labor models — supporting rural to urban migration — seem to be better founded. What really matters in the Lewis, Ranis and Fei models is not whether there is disguised unemployment in rural areas, but whether the rural sector can massively supply migrants to the urban sector to accompany rapid national growth. The fundamental contribution of Harris and Todaros rural-urban two sector migration model was to build a model that fit the stylized facts of the labour market. On the lines of the theory, developing countries adopted program on integrated rural development which encouraged an increase in the rural traditional sector wage. The theory proves that the higher the unemployment rate, the lower is the probability of new migrants from the countryside actively seeking formal sector employment who are unable to find it. The significant findings of the theory are: first, if the expected urban wage equals rural income, there is no incentive to migrate. Second, if the expected urban wage is greater than rural income, there is a great incentive to move from rural to urban area. Third, if the expected urban wage is less than rural incomes, there would be an incentive to move in other direction. Fourth, the expected urban wage depends on what type of job migrant is engaged in. Therefore, the Harris Todaros model helps policy-makers to avoid two mistakes. One is to assume that development efforts should necessarily be channelled to the sectors where the poor are. The other is to assume that efforts should necessarily be focused on getting the poor out of the sectors in which they presently are. Both the Lewis and Ranis and Fei formalizations describe in a very stylized manner a general mechanism occurring at an initial stage of economic development, which justifies the assumed scarcity of capital and the abundance of labor in these models. The assumption of zero marginal productivity and remuneration at the average product in the agricultural sector is more debatable and has been criticized even though it probably should not be taken at face value: what really matters in the model is that the rural sector can massively provide migrants to the urban sector. In this simple framework, internal migration is desirable to the extent that it accompanies growth. The policy implication of this model is that governments in countries experiencing a transition from a labor-intensive agricultural economy to an economy with significant industrial and services sectors should see to it that migration from rural to urban areas is at least not impeded, and ideally is even facilitated. This type of model also suggests that government should ensure that investments are intense enough for the take-off to ever occur. This would tend to argue in favor of policies favoring investments in modern labor-intensive industries in order to exhaust rural disguised unemployment. It is important, nevertheless, to keep in mind that the Lewis framework applies only to a particular phase of the development process and sheds little light on other contexts. It appears to inadequately describe the urbanization process of many Sub-Saharan African countries, even at the beginning of their urban transition.5In particular, the observation in the late 1960s that urban areas experienced high levels of unemployment suggested that these models might not tell the right story about rural urban interactions. The Todaro (1969) and Harris-Todaro (1970) models also consider the role of internal migration in a dual economy in which the urbansector draws labor force from the rural sector. But the change of focus is radical. In the Lewis model, internal migration removed disguised unemployment from rural areas and enabled the transition to a modern economy. In Todarian models, the focus is on explaining the existence of unemployment in urban areas and its link with internal migration.
ASSUMPTIONS OF THE MODEL
Some of the assumptions of the Harris-Todaros model were judged to be too restrictive.The model also assumesthat potential migrants are risk neutral where the poor migrants will likely be risk averse, as in they are indifferent between a certain expected rural income and an uncertain expected urban income of the same magnitude. The assumption that there exists a perfect competition in rural agriculture sector is not realistic.
Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function: where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a 0 and g > 0 are a parametric constant. g is the elasticity of p with respect to the ratio Ym/Ya. The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:
ARGUMENTS

In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.Rural to urban migration will take place if, With the random matching of workers to available jobs, the ratio of available jobs to total job seekers gives the probability that any person moving from the agricultural sector to the urban sector will be able to find a job. As a result, in equilibrium, the agricultural wage rate is equal to the expected urban wage rate, which is the urban wage multiplied by the employment rate.

Therefore, migration from rural areas to urban areas will increase if: Urban wages (wu) increase in the urban sector (le), increasing the expected urban income. Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income. However, even though this migration creates unemployment and induces informal sector growth, this behaviour is economically rational and utility-maximizing in the context of the HarrisTodaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.
CONCLUSIONS WITH THE REAL WORLD
the conditions for the Todaro paradox to hold. At best empirical tests have provided microeconomic evidence consistent with the migration incentives present in the HarrisTodaro model, measuring for instance how rural dwellers respond to an increase in the wage differential. But this type of evidence does not provide a real test of the link between urban unemployment and migration. In other words, the validity of the model has not been clearly established even though it certainly influenced policies for decades. Many countries have implemented policies aimed at forbidding migration from rural to urban areas. In South Africa, the Apartheid system (1948-1994) used extreme controls to monitor what was meant to be the temporary migration of rural workers to cities

LEWIS FEI-RANIS MODEL
The Lewis Fei-Ranis model is for overpopulated and under developed economy. It is based on dualistic economic development because The theory explains a way the industrial sector and agricultural sector can grow simultaneously without a lapse in the other or in the improvements rather than at its expense. There is always a unique, sole characteristic of surplus agricultural labor found in this kind of economy. The model is an attempt to balance agricultural and industrial growth in these economies. Lewis previously held that Economic growth in such economy can be achieved by investments in the non-agricultural sector by extracting surplus labor in the agricultural sector. But John Fei and Gustav explained how increase in productivity in agricultural sector would be helpful in promoting industrial sector too. The model explains that the complete shift the focus of progress from the agricultural to industrial economy does not mean that agricultural sector should be negligible rather its output should still be sufficient to support the whole economy with food and raw materials. With the assumption that large proportion Of the high population in these countries is engaged in agriculture and still agriculture is stagnant therefore marginal productivity of labor is zero and negative in agricultural sector while there are certain non agrarian sectorsIn the economy where there is reduced use of capital. This model suggests that if this surplus labor in the agricultural sector is transferred to industrial sector where their productivity will increase, economic development will be taking place.
They argue that an economy goes through three phases of development. In phase 1, marginal product of labor is equal to zero. The first phase is where surplus labor Can be withdrawn from agricultural sector without changing agricultural output. In the second phase of the development, additional output due to an increase in labor begins to rise as transfer takes place from agricultural sector to industrial sector, average Product falls showing an increase in real wages of industrial workers because sThere is shortage of food supply. The real wages in industrial sector is fixed and equal to real income in agricultural sector. These wages are called institutional wages. in the second stage labor surplus exist where Apl>MPL But it is not equal to institutional wages. If the migration to industrial sector continues, there will be a time from workers produce output that is equal to institutional wages.
The third stage is characterized by self sustained growth where farm workers produce more than the institutional which they get because disguised unemployment has been eliminated. Surplus labor ends and the agricultural sector becomes commercialized sector. MPL here is greater than CIW, disguised unemployment is eliminated. As labor is transferred to industrial sector there will be labor shortage in the agricultural sector so industrial sector cannot get the labor at the same prevailing constant wages therefore the wages in the industrial sector will rise.
From my own point of view the Fei-Ranis model did not take into account the very possible case where a constant transfer of labor from the agricultural sector to the industrial sector causes an extreme shortage of labor in the agricultural sector the model holds that the rate of labor transfer must exceed the rate of population growth. If the largest proportion of the workforce in the country goes to the industrial sector outputs will not be anything close to sufficient to support the whole economy with food and raw materials as Nigeria is facing now. This model is prevalent in Nigeria where labor has been shifted to the industrial sector. Disguised unemployment previously faced by the agricultural sector is now the problem of industrial sector. Shortage of labor in agricultural sector has led to shortage of food supply and raw materials in the economy.

The Harris Todaro Model of Migration

The basic assumption of this model is high expected income in the urban areas than the rural areas. Equilibrium according to this model is reached when expected wage in urban areas is equal to the marginal product of an agricultural worker. It also has the assumption that unemployment is nonexistent in the rural agricultural sector and that rural agricultural products and subsequent market is perfectly competitive which means that agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, rural-urban migration rate is zero since expected rural income equals expected urban income, which is leading to positive unemployment in the urban sector. Expected urban wage rate is equal to urbanwageXemployment rate. Rural urban migration will increase if urban wages increase in the urban sector, increasing the expected urban income and agricultural productivity also decreases, decreasing marginal productivity and wages in the agricultural sector therefore decreasing the expected rural income. This is nothing different to the current Nigerian economy. The expected income in urban areas has caused total neglect to the rural agricultural sector. The rural-urban migration is only rational if equilibrium is achieved, (where expected real wage in urban areas equals marginal product of an agricultural worker). But in the real sense, rural-urban migration is as a result of increase in urban wages in the urban sector which has caused a decrease in expected wages in rural sector.
The neglect to rural agricultural sector caused by rural-urban migration has brought about: shortage of food supply and raw materials, overpopulation and unnecessary competition in the urban sector leading to high crime rates, and a large number of people chasing too few jobs.
This brings an economy back to a state of inadequate development as is seen in Nigeria today.

Name: Francis Chibuezem David
Reg. No: 2017/241445
E-mail: francischibuezem247@gmail.com

Harris-Todaro model
1. Productive process
The rural sector is specialized in the production of agricultural goods. The productive process of the rural sector can be described by a Cobb-Douglas production function:
where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < f 0 and 0 < a 0 and g > 0 are a parametric constants. g is the elasticity of p with respect to the ratio Ym/Ya.
4. The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:

Summary
The haris todaro model is a dualistic economic model which shows the relationship between the rural and urban areas. It also shows the reason for rural-urban migration and explains that rural production is majorly agricultural goods while urban production is known as manufactured goods. According to this model, individuals migrate from rural areas to urban areas in search of better opportunities and standard of living.
Nigeria is and LDC and so it also has the characteristics of this model which is a dual sector economy. Nigeria also has the characteristics of rural-urban migration of people in search of greener pastures. My only critic of this model is the assumption of full employment in rural areas because rural areas in Nigeria is characterized of large unemployment and underemployment.

Lewis-Fei-ranis model
The Fei-ranis was developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. This model recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account.
They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development. In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.
Phase 1: AL=M
According to Fei and Ranis, AD amount of labor (see figure) can be shifted from the agricultural sector without any fall in output. Hence, it represents surplus labor.
Phase 2: AP>MP
After AD, MP begins to rise, and industrial labor rises from zero to a value equal to AD. AP of agricultural labor is shown by BYZ and we see that this curve falls downward after AD. This fall in AP can be attributed to the fact that as agricultural laborers shift to the industrial sector, the real wage of industrial laborers decreases due to shortage of food supply, since less laborers are now working in the food sector. The decrease in the real wage level decreases the level of profits, and the size of surplus that could have been re-invested for more industrialization. However, as long as surplus exists, growth rate can still be increased without a fall in the rate of industrialization. This re-investment of surplus can be graphically visualized as the shifting of MP curve outwards. In Phase2 the level of disguised unemployment is given by AK. This allows the agricultural sector to give up a part of its labor-force until
Phase 3 begins from the point of commercialization which is at K in the Figure. This is the point where the economy becomes completely commercialized in the absence of disguised unemployment. The supply curve of labor in Phase 3 is steeper and both the sectors start bidding equally for labor.
Phase 3: MP>CIW
The amount of labor that is shifted and the time that this shifting takes depends upon:

The growth of surplus generated within the agricultural sector, and the growth of industrial capital stock dependent on the growth of industrial profits;
The nature of the industry’s technical progress and its associated bias;
Growth rate of population.
The major ideas in this model are:
1. Agricultural growth and industrial growth are both equally important;
2. Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap

Name: UGWOKE, PAUL CHUKWUEBUKA
Red no. 2017/241059
Dept. Edu/eco

INTRODUCTION
Since the wage in cities is higher than one in village people migrate into the cities hoping to get urban job. The probability to get a job depends on the size of unemployment pool in relation to the number employed in industries. Therefore, in many mostly less-developed countries urban unemployment is a big issue. W. Max Corden in his book Trade Policy and Economic Welfare claims that the possible reason for urban unemployment is the wage differential. This coexists with usually high minimum wage in industries and with a marginal product of labor in agriculture less than the urban minimum wage1.
The model presented is derived from Migration, Unemployment and Development: A Two Sector Analysis original article by John R. Harris and Michael P. Todaro (1970)2 and W.M. Corden’s book mentioned above. In our approach we will assume as Harris and Todaro did that the expected urban wage is equal to the average wage of both urban employed and unemployed. Authors’ main claim is that the best policy to improve employment is to protect agricultural sector rather that manufacturing sector of the country. In this paper we will build a Harris-Todaro model of urban unemployment, discuss two cases: 1) subsidizing manufacturing, and 2) subsidizing agriculture, and test Harris and Todaro’s claim. For that purpose, we will run simulations for both cases in MS Excel, and try to analyze outcomes and suggest possible policies. The approach of the project will be comparative static.

GENERAL ASSUMPTIONS OF THE MODEL

• Two sectors: urban (manufacture) and rural (agriculture)
• Rural-urban migration condition: when urban real wage exceeds real agricultural product
• No migration cost
• Perfect competition
• Cobb-Douglas production function
• Static approach
• Low risk aversion

J. R. HARRIS AND M. P. TODARO MODEL OF LABOUR MIGRATION AND REALLOCATION. Employment policy in developing countries like Nigeria cannot be formulated and implemented without answering a basic question, such as, how can underutilised labour be used in a develop¬ment strategy? Ragnar Nurkse and W. A. Lewis asserted that large numbers of people remain engaged in work which adds nothing to national output. Nurkse saw the reallocation of a sur¬plus labour to more productive uses, especially labour-intensive construction projects, as a major source of capital formation and economic growth.
Lewis conceived a similar reallocation process but he focused on the ‘capitalist sector’, essentially industry, as the main employer of surplus labour. Both theories regarded the labour reallocation process as nearly costless but they worried about how to capture from the agricultural sector the food necessary to feed the transferred workers.
While criticising the Lewis model, J. R. Harris and M. P. Todaro have developed a new model of economic development which is relevant for labour surplus countries like Nigeria. It is the best known model of internal migration in the context of present-day developing countries. The model has focused mainly on migration of labour from rural to urban areas caused by certain incentives. J. R. Harris and M. P. Todaro have referred to two types of migration—induced migration and internal mi¬gration.
According to this model migrating workers are essentially participants in a lottery of rela-tively high-paid jobs in the towns. When new urban jobs are created the lottery becomes more attractive to potential migrants. Depending on their responsiveness to this improved opportu¬nity, more than one worker is likely to migrate for each job created.
If so, the output foregone may be that of two or more agricultural workers, not just one. This is because those in the rural areas are primarily farmers. If the migrants bring some of their family members to urban areas more output will be lost. The reason is that the wife and children of migrants find fewer employment opportunities in towns than in the rural areas because they do not have land in the towns on which to grow food. This also leads to food shortage as the farm produce is drastically reduced.
Internal Migration:
According to J. R. Harris and M. P. Todaro, most of the internal labour migration which occurs in the course of economic development is from rural to urban areas. The model try to explain why the observed high rates of small- urban migration found in most developing countries is quite natural from an economic view point.
In this model the expected real wage-differential between urban and rural areas is the main motivating force behind migration or the main determinant of the migration decision. The potential migrant first calculates the real income which he would get in the urban area for a job with his present effort. He next makes a personal judgement of the probability of obtain-ing such a job.
He then compares the expected income with that which he hopes so obtain in the rural area. His migration decision is based on the difference. For example, suppose the ex¬pected rural income is N1000 per Month, and that real income of an urban job which is commensurate with his qualification is N2000.
However, this information alone is not suffi¬cient to make the migration decision. If the subjective probability of getting the urban job was 0.4, than the expected income would be N800 and no migration would take place on this case expected urban wage = actual urban wage x the probability of getting a job
800 = 0.4 x N2000
If the probability were 0.8 the expected income would be Rs 1600 (= 0.8 x N2000) and the worker would migrate. (To this one may, of course, add the cost of transfer.) Thus the model brings into consideration the role of economic incentive in the migration decision.
The Basic Model:
The Harris-Todaro model assumes that migration from rural to urban areas depends majorly on the difference in wages between the rural and urban labour markets.
That is:

Where: Mt is the number of rural to urban migrants in time t, is response function, Wu is the urban wage and W is the rural wage. Since there is unemployment in the town (and it is as-sumed that there is no unemployment in rural areas), and every migrant cannot expect to find a job there, the model postulates that the expected urban wage with the rural wage. The expected urban wage is the actual urban wage times the probability of getting a job, or

Where Weu = expected urban wage and p = probability of getting a job Here p is expressed as

Where Eu is urban employment, Uu is urban unemployment and L is total urban work force. Harris and Todaro assume that all members of the urban labour force have equal chances of obtaining the jobs available. So Weubecomes simply the urban wage times the urban em-ployment rate.

Migration in any given time then depends on these three factors:
(a) The urban-rural wage gap,
(b) The urban employment rate and
(c) The responsiveness of potential migrants to the resulting opportunities.
Thus

Where Mt = migration in period t and h = the response rate of potential migrants
As long as Weu > Wr the rural-urban migration will continue. It will stop only when migra¬tion has forced down the urban wage or forced up urban unemployment so much that expected urban wage (Weu) is covated to existing rural wage (Wr). If Wr > Weu there will be a flow of disappointed urban jobseekers back to the rural areas. This is known as reverse migration.

Theoretical Implication of the Model:
There is no need to deny the fact that any development project can be evaluated using social cost- benefit analysis. An important part of the social cost of any input is opportunity cost, its value in its next best alternative use. Labour hired for an urban formal-sector project might well be drawn from the urban informal sector also.
The worker who moves out of the urban informal sector may, in turn, be replaced by someone from the rural sector. In this case, the output lost is that of the worker who was formerly in the rural sector, i.e., the worker at the end of the em¬ployment chain. For this reason, some analysts believe that the wage paid to casual agricultural labourers provides a good measure of the social cost of unskilled labour.
However, this measure, although a good indicator of output foregone through labour reallo-cation, probably understates the true social cost of employing labour, which has other compo¬nents that are likely to be significant. One such component is induced migration. No doubt there are both pull and push factors behind internal labour migration that occurs in the course of economic development from rural to urban areas.
Such migration can result either from favourable economic developments in the towns or from adverse developments in the rural areas. The Harris-Todaro model integrates these two sets of forces in their analysis of the proc¬ess of labour reallocation that is likely to occur during economic development. This is why the model was sort of innovation in the literature of development economics when it appeared for the first time in 1970′.
The Policy Implications of the Model:
The H-T model has far-reaching implications from the policy point of view. For example, if the government of the country concerned were successful in fostering industrial development in an urban area, employment would increase there.
• The effect would be to increase the subjective productivity of getting urban employment in the minds of rural inhabitants. Migration would increase and the eventual effect of the new industrial development could be that urban unem-ployment becomes higher that the level prevailing before the new development took place.
• There will be some level of urban employment which ensures equilibrium in the sense that no further migration takes place. Potential migrants may take a long-term view in arriving at a decision. They may consider that their desireness of obtaining an urban job will be higher after a waiting period of some months. Thus they will compare the present value of the sum of expected urban earnings with that of expected rural earnings.
• They may be content to accept a low wage in the urban informal sector for some time. This might be a rational decision on a long-term basis. The root of the problem is the large difference between earnings in the modern industrial sector and those in the rural areas.
• The former are well above the market clear¬ing levels for varies reasory. The long-term solution to the problem lies in adopting policies for both urban and rural areas which reduces the real income differences between the two areas.
Comparisons between Harris-Todaro and Lewis models
The Lewis model and Harris-Todaro model have similar outcomes in the sense of labour moving from rural agricultural areas into urban areas in search of modern industrial work as an approach to earn more money and leave poverty. However, the assumptions of the two models are very different and maybe this is why each model has had different impacts in terms of economic development history. The Lewis model is an early traditional model. which in practical situations does not work properly because of the assumptions. Therefore, the extent of the model is rarely realised. Although, this model does provide a good general theory on labour transiting in developing economies. The Harris-Todaro model, on the other hand, even with its problems with the assumptions, has lead to policy implications such as ways to reduce inequalities and bias between rural areas and urban cities as an attempt to reduce this migration problem.
Overall, both models have increased awareness of the growing issues surrounding rural-urban migration. As many countries like India, Singapore and China act as success stories of this type of migration and economic transition as a catalyst towards leaving poverty, there are many developing nations who have not had the same success, but have suffered from a rise in urban poverty, unemployment and fall in living standards
CONCLUSION
Harris Todaro model explains some issues of rural-urban migration. This migration happens in case when expected rural income is higher than rural wages. In this case economy may have high rates of unemployment. The equilibrium condition of this model is when expected rural wage is equal to rural wage.
When government subsidize manufacturing sector Harris Todaro paradox may happen. According to the authors job creation instead of dealing with unemployment problem actually may cause increase of unemployment. This happens when urban-rural wage differential is high enough, so rural workers move to the cities hoping to find a job with high wage. Obviously, not all these workers succeed in finding jobs which leads to unemployment.
Another issue is that inducing minimum wages creates labor market distortions. Therefore, policy makers should not set the minimum wage rates.
In addition, simulations showed that different policies’ outcomes depend on elasticity of labor demand in different sectors and on marginal product of labor.
Reference
Warner Max Corden, Trade Policy and Economic Welfare, 1997.
Migration, Unemployment and Development: A Two Sector Analysis, John R. Harris and Michael P. Todaro, 1970.

ASSIGNMENT TWO
Lewis Ranis and Fei model
Introduction
Current literature on growth and development continues to be influenced by the one-sector Solow-type models or the two-sector Uzawa-type models, both of which have now been complemented by endogenous growth. While these endogenous growth models have recently begun to confront such issues as poverty traps at a theoretical level, they generally share the neoclassical feature of full employment and market clearing. In contrast, the surplus labor models advanced by Lewis (1954), and expanded upon by Ranis and Fei (1961, 1964, 1997), described a two-sector economy depicting an initially large traditional sector and a relatively small commercialized sector, with the key feature that the traditional sector does not adhere to the neoclassical full employment labor market clearing assumption. While various micro foundations can be constructed to detail why this might be so, at the macro level, which was the focus of these early dual economy models, it was sufficient to posit that labor was in excess supply relative to cooperating factors at the prevailing wage and technology, and thus that the commercialized sector faced an essentially infinitely elastic labor supply at any moment in time.
With unskilled rural labor the abundant resource in many developing countries, especially at an early stage of their development, what determines the price of labor has continued to be a controversial issue, although it is clear that, in recent years, the neoclassical model and market clearing approaches have enjoyed increasing popularity in not only the theoretical but also the applied literature. The notion of an institutional or bargaining wage not based on marginal productivity fundamentals has been especially repugnant to orthodox economists. The rejection of the labor surplus model has, in part, been due to some confusion as to which of its assumptions are necessary as opposed to which are sufficient.
The Lewis-Ranis-Fei model
The Lewis (1954) theory of dualistic economic development provides the seminal contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to followthe sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent (Lewis, 1954, p.150). Thenon-agricultural sector accumulates capital by drawing surplus labour out of the agricultural sector. The expansion of the non-agricultural sector takes advantage of the infinitely elastic supply of labour from the agricultural sector due to its labour surplus. When the surplus labour is exhausted, the labour supply curve in the non-agricultural sector becomes upward-sloping.
CONCEPT OF SURPLUS LABOUR
The concept of surplus labour is widely discussed among development economics but its specific meaning needs to be defined, especially in technical terms, as many neoclassical economists still doubt the existence of surplus labour in an economy.
Defining the source and the extent of surplus labour is then a prerequisite for further discussion. This section considers the various definitions of surplus labour and clarifies them.
The simple definition of surplus labour implies the existence of a point at which the marginal product of labour becomes zero and labour can be transferred out of the traditional sector without reducing the quantity of output, as noted by Wellisz (1968: 22): The (disguised-unemployment or the Unlimited Supply of Labour) hypothesis claims that in poor, densely populated countries, more people are employed than needed to produce the prevailing output with the existing techniques and the existing supply of non-labour inputs. The ‘surplus’ labour constitutes ‘hidden’ or ‘disguised’ unemployment. Many of the proponents of the hypothesis make the further claim that agricultural output will not decrease, and industrial output will increase, if measures are taken to re-allocate labour from subsistence agriculture (where the surplus is supposed to exist) to industry (where there is no surplus labour). Since
labour can be removed from agriculture at no social cost, its supply to industry is, in a sense, ‘unlimited’ as long as disguised unemployment prevails. However, Ranis (2004b) does not agree with this definition of ‘surplus labour’, preferring to regard those whose marginal product lies below their consumption or income share as ‘surplus labour’, or more specifically, as ‘disguised unemployed’ or ‘underemployed’. Ranis defines surplus labour as follows: The basic premise is that there exist some sectors or sub-sectors in which, in the presence of a large endowment of unskilled labour and the absence of sufficient cooperating land or capital, with a given technology and a wage level bounded from below, labour markets cannot clear. A full employment, neoclassical ‘wage equals marginal product’ solution would drive remuneration below socially acceptable, possibly subsistence, levels of consumption. Consequently, a labour surplus exists in the sense that a substantial portion of the labour force contributes less to output than it requires, i.e., its marginal product falls below its remuneration, set by bargaining. (Ranis, 2004b: 1) Lewis (1954: 141) provides a general definition that: an unlimited supply of labour may be said to exist in those countries where population is so large relatively to capital and natural resources, that there are large sectors of the economy where the marginal productivity of labour is negligible, zero, or even negative.
This paper agrees with Lewis that both these circumstances exist, but we distinguish these two types of surplus labour: the labourers with positive but ‘negligible’ marginal because they have different implications in the wage determination in the modern sector, which will be discussed later. If w is the real wage of a labourer, we have:
Definition 1: Type I surplus labour (or Absolute Surplus Labour, ASL): Labour is defined as Absolute Surplus Labour if the MPL is equal to or less than zero, that is,
whenMPL ≤ 0 < ws ≤ w. Type II surplus labour (Relative Surplus Labour, RSL): Labour is defined as Relative Surplus Labour if the MPL is greater than zero but lower than the actual wage received, that is, when 0 < MPL < w . ASL is a narrow definition and RSL a more general one. The definition of RSL means that, as long as 0 < MPL < w holds, it does not matter if MPL is lower or higher than the subsistence level (whether s MPL w ), though normally it is assumed to be lower than the subsistence level ( s MPL < w ).
Having defined the concept, let us now examine the micro-foundations of surplus labour to see how it operates in reality. Surplus labour also includes unutilised labour, including those who do not participate in production in the neoclassical way. People can be considered to be ‘surplus labour’ even if they do not work. That is, were they to work, their MPL would be small, zero or even negative. In reality, these people may stay idle, doing nothing, rather than participate in work and contribute non-positively. Of course, as discussed previously, they have to be supported by their families to survive. Their marginal utility of leisure is also zero. They want to work but there is no job for them. In such a situation, these people either do not work or work less than any reasonable conception of full time, and they could readily be put to work at subsistence level wages.
For example, in the traditional agricultural economy, a certain amount of field work (e.g. ploughing a certain piece of land) may need either all family members to work one-fifth of their time, or only one-fifth of the members to work full-time while the rest are idle. Surplus labour exists in this sense.

Conclusion
For economies in the early stages of development, the rural agricultural sector consists of family farming units, with a hiring principle that is different from that of the firm. Family members work together and share the value of their output. They are paid not the marginal product but the average product of labour. Thus, it is possible that there exists surplus labour in many developing countries. The notions of surplus labour and disguised unemployment have been a central part of development economics since Lewis (1954).
With the presence of surplus labour in the traditional sector, the modern sector can expand without increasing labour costs. This process will continue until the surplus labour in the traditional sector is used up. After this point is reached, wages begin to rise consistent with rising marginal productivity, in which the workers in the traditional sector would also be paid in accordance with their marginal product rather than the subsistence wage. At this stage, the dualistic economic structure disappears, replaced by acompetitive one-sector economy that can be explained by the neoclassical model.
This paper contributes to the literature by clarifying some of the ambiguities in the discussions following Lewis’ model. There has long been a debate about the precise definition of surplus labour. This paper first identified the problem and defined two typesof surplus labour, with type I (absolute) surplus labour being defined to be when the marginal product of labour is equal to or even lower than zero, and type II (relative) surplus labour being when the marginal product of labour is higher than zero but lower than the wage level, which is set at the subsistence level in the long run. This seemingly simple distinction resolves much of the misunderstanding. Based on this classification of two types of surplus labour, we define two turning points: the type I turning point, when type I surplus labour is used up; and the type II turning point, when type II surplus labour is used up. The wage is constant before the type I turning point, increases slowly after it,,and the dual economy merges with the neoclassical one-sector economy after the type II turning point is passed.

UNIVERSITY OF NIGERIA, NSUKKA
FACULTY OF SOCIAL SCIENCE
DEPARTMENT OF ECONOMICS

AN ASSIGNMENT WRITTEN IN THE PARTIAL FUFUILMENT OF THE COURSE: DEVELOPMENT ECONOMICS 1 (ECO 361).
TOPIC:
LEWIS-FEI-RANIS MODEL OF ECONOMIC GROWTH

BY:
ABIAZIA RUFUS CHIDIEBUBE
2017/243371

LECTURER:
DR. OLISAEMEKA ACHIME

MARCH, 2021

LEWIS-FEI-RANIS MODEL
INTRODUCTION
BRIEF HISTORY OF THE LEWIS MODEL:
The Lewis Model of economic development was developed by Sir. W. Arthur Lewis ( 1915-1991) in 1954. He was a political economics tutor in different universities and the 1950’s he worked with the United Nations. He won a Noble Prize for Economics in 1979.
Lewis most famous and influential contribution to Economics is undoubtedly the 1954 paper on ” Economic development with unlimited supply of labour”. He called it a “Dual-sector model” by categorising an economy into two, as a traditional and as a modern sector. The traditional sector provided surplus labour to the modern sector and this process led to development stability. He focused mainly on labour reallocation and an organisational dualism, but less on product dualism.

BRIEF HISTORY OF FEI-RANIS MODEL:
The model is a dualism model in development economics or welfare economics that has been developed by John. C.H. Fei and Gustave Ranis, it is understood as a extension and modification of the Lewis Model, it is also known as the surplus labour model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes into account the economic situation of unemployment and underdevelopment of resources into account.
Both sectors coexist in the economy. Development can be obtained by a complete shift in the focal point of progress from the agricultural to the industrial economy. This is done by transfer of labour from the agricultural to industrial sector. Showing that underdeveloped countries do not suffer from constraints of labour supply.
Surplus labour is the central element in the LEWIS-FEI-RANIS MODEL which based on a “capitalist and a subsistence sector” and it is grouped into three main instruments; labour force, capital accumulation and integration to the world economy.
The main focus in Lewis Model was on the reallocation of labour until a turning point is reached, economy become fully commercialized.

COMPARISON WITH OTHER MODELS
i) Other growth model considers underdeveloped countries to be homogeneous in nature.
ii) Keynesian (1936) model, focusing on advanced economy cyclical issues. He focused on the temporary unemployment of both capital and labor in the advanced economy, not the secular underemployment of labor in the developing world. Clearly, savings-oriented one-sector models were all the vogue, incorporated in both approaches,
iii) Lewis rejected the neoclassical assumptions of full employment, market clearance and perfect competition.
CORE DISCUSSIONS AND THE MAIN ARGUMENT OF THE MODEL:
This theory is concerned with a poor economy which has following properties:
(i) There is an abundance of labor in such underdeveloped country and shortage of natural resources.
(ii) The population growth rate is very high which results in mass unemployment in the economy.
(iii) The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agriculture sector.
(iv) There are certain non-agrarian sectors in the economy where there is reduced use of capital.
(v) There is a dynamic industrial sector in the economy.
THUS THE MODEL SUGGESTS THAT:
“Economic development would be taking place if agricultural laborers are transferred to industrial sector where their productivity will increase”.
STAGES OF FEI-RANIS MODEL:
Fei and Ranis develop their dual economy model with the help of three stages of economic growth. They are presented as:
Diagram/Figure:

In the (a) part of the Fig., the labor supply curve is perfectly elastic, as between S and T. In phase (I) as shown in (c) part of Fig., the MPL = 0. In other words AL = MPL = 0. But here APL = AB.
Following Lewis the FR model argues that AD units of labor are the surplus amount of labor in agricultural sector which is prey to disguised unemployment.
In phase (II) APL > MPL, but after AD, MPL begins to rise (c part of Fig). The growth of labor force in industrial sector increases from zero to OG (a part of Fig). The APL in agri. sector is shown by BYZ curve (c part of Fig).
The first stage of FR model is very similar to Lewis. Disguised unemployment comes into being because the supply of labor is perfectly elastic and MPL = 0. Therefore, such disguised unemployed are to be transferred to industrial sector at the constant institutional wage.
In the second stage of FR model (phase) agri. workers add to agri. output but they produce less than institutional wage they get. In other words, in the second stage the labor surplus exists where APL > MPL, but it is not equal to subsistence (institutional) wages.
Accordingly, such disguised unemployed also have to be transferred to industrial sector
In the third stage of FR model the take-off situation comes to an end and there begins the era of self-sustained growth where the farm workers produce more than the institutional wage they get. In this stage of economic growth the surplus labor comes to an end and the agri. sector becomes commercialized sector. All such is explained with the Fig.
Accordingly, they have to be shifted to industrial sector. As labor is transferred to industrial sector a shortage of labor will develop in agri. sector. As a result, the wages in the industrial sector will rise as from T to Q in (a) part of Fig.
After point T the turn which occurs in the SZ curve is known as “Lewis Turning Point”. In the 3rd phase the agri. laborers produce more than CIW. (As here MPL > CIW shown in (c) part of Fig). In this phase the take off comes to an end and self-sustained growth starts. This is also known as point of commercialization (of agri.) in FR model.
The Amount And Time To Re-Allocate Labor Will Depend Upon:
(i) The rate of growth of industrial capital which depends upon the growth of profits in industrial sector and growth of surplus generated within the agri. sector.
(ii) The nature and bias of technical progress in industry.
(iii) The rate of growth of population. It means that the rate of labor transfer must be in excess of the rate of growth of population.
The Three Phases Of Labor Transfer Are Summarized As:
In phase I: MPL = 0 and there exists the surplus labor equal to AD.
In phase II: CIW > MPL > 0 and there exists the open and disguised unemployment equal to AK.
In phase III: MPL > CIW and the economy is fully commercialized and disguised unemployment is exhausted.
Criticism:
(i) According to prof.Jorgenson, he says whether MPL will be zero is an empirical issue. During the seasons of sowing and harvesting the MPL > 0. Jorgenson concluded on the basis of Japanese data even for the pre I world war period the supply of labor was not unlimited.
(ii) Ignoring the Role of Capital: The FR model concentrated upon land and labor as the determinants of output, ignoring the role of capital.
(iii) Open Economy: FR model ignored the role of foreign trade as it assumed a closed economy model.
(iv) Supply of Land in Long Run: FR model assumed that in the process of economic development the supply of land remained fixed. But it is not true. The supply of land can be increased in case of long run.
(v) Low Productivity in Agricultural Sector: According to Jorgenson it has been observed that there has been a very slow rise in the productivity of agricultural sector. Consequently, the surplus will hardly be created in agricultural.
Conclusion/Comparison with Real World/Opinion:
Thus we find that whereas Lewis had failed to offer a satisfactory explanation of this subsistence sector and ignored the real impact of population growth on the choice of capital intensity on the process of surplus labor absorption. Moreover, FR model emphasized upon the simultaneous growth of agricultural and industrial sectors. Thus FR model believes in ‘Balanced Growth’ in the take-off stage. It means that there should be a simultaneous investment in both agricultural sector and industrial sector. According to FR model in the beginning the surplus rises; such surpluses will be available as a capital in the take-offstage. Some part of this surplus will be used in agri. development, while some part will be reploughed in industrial development. As a result, both agri. and industrial sectors will grow under ‘Balanced Growth’ pattern.
Apparently, Niegeria as case study, the model has fail because the model focuses only on surplus labour and its reallocation to the industrial sector without considering institution-political factors, and effect cause by migration to industrial, agricultural output will decrease which increase price and lead to inflation at the longrun. As such balance growth or equilibrium will be obtained in the economy.
Thus, three major opinions are highlighted in the FR mode:
(i) Growth of agriculture is as important as the growth of industry.
(ii) There should be a balanced growth of agriculture and industrial sectors.
(iii) Balance growth can be obtain in the economy by equitable distribution of resources ( labour and capital) to both sectors.

HARRIS-TODARO MODEL
INTRODUCTION:
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in
development economics and welfare economics to explain some of the issues concerning rural-urban migration . The main assumption of the model is that the migration.
BASIC ARGUMENTS:
decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
It has long been realized that in order for an economy to develop or grow, a large amount of labor has to be transferred from the traditional (or backward) agricultural sector in rural areas, where the productivity of labor is low (or negligible, or zero, or even negative) to the modern manufacturing sector where the productivity of labor is higher and rising due to capital accumulation in that sector.
The model treats rural-urban migration primarily is an economic phenomenon. In essence, the theory postulates that workers compare the expected incomes in the urban sector with agricultural wage rates and migrate if the former exceeds the latter. Rural-urban migration is thus the equilibrating force which equates rural and urban expected incomes and as such is a disequilibrium phenomenon.o The three basic characteristics of their model–that migration occurs largely for economic reasons, that the migration decision depends on expected ralher than nominal wage differentials, and that migration takes place in dis-equilibrium–suggest that rural-urban migration be given a new emphasis. Rather than considering it as a key phenomenon in its own right, migration could better be regarded as the adjustment mechanism by which workers allocate themselves between different labor markets, some of which are located in urban areas and some in rural areas.
The structure of the HT model is based on the premise that a fixed wage leads to
an outbreak of distortion and urban unemployment. By introducing the concept ofexpected wage in the urban sector.

ASSUMPTIONS OF THE MODEL
I. The model assumes that unemployment is non-existent in the rural agricultural sector
ii. There are two sectors, and the rural prices are wholly flexible, which implies that there is full employment in the rural labour market.
iii. It also assumed that in the urban sector, minimum wage is assumed to be fixed institutionally in a level above equilibrium in it’s lbour market.
iv. It also assumed that rural agricultural production and the subsequent labour market is perfectly competitive.
v. The model also assumes that potential migrants are risk neutral where the poor migrants will likely be risk aversive in that they are indifferent between a certain a certain expected rural income and an uncertain expected urban income.
Conclusion:
Harris-Todaro model postulated rural-urban labour migration, which it also stipulate that employment on the rural sector is at full employment level. Migration been determined by expected wage differential in urban.
In Nigeria, rural-urban labour migration is at high speed, as many graduate leaves there rural agricultural sector and migrate to urban industrial sector in search of white collar Jobs over the years. Thus, it have but negative and positive effect in both sectors.
Negative impact in rural agricultural sector:
It reduces labour (man power) in the rural areas.
It reduces production of agricultural products
It increases cost of agricultural products.
Positive impact in the rural sector:
It helps in the introduction of technology in the agricultural sector
Negative impact in Urban Sector:
It increases the population of the urban area.
It increases cost of living.
It causes job scarcity–many people chasing few job
It lead to the reduction of wages
Positive Impact in Urban Sector
It increases labour supply ( labour force)
It increases production .

NAME: Likibe Gita Cassandra
REG NO: 2017/241429
DEPARTMENT: ECONOMICS
EMAIL ADDRESS: likibegitacassy@gmail.com

FEI-RANIS MODEL OF ECONOMICS GROWTH
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model.[1] It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.[2] According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector.[3] Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
According to Fei and Ranis, AD amount of labor can be shifted from the agricultural sector without any fall in output. Hence, it represents surplus labor.
After AD, MP begins to rise, and industrial labor rises from zero to a value equal to AD. AP of agricultural labor is shown by BYZ and we see that this curve falls downward after AD. This fall in AP can be attributed to the fact that as agricultural laborers shift to the industrial sector.

HARRIS-TODARO MODEL OF MIGRATION
Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income. In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.

Therefore, migration from rural areas to urban areas will increase if:

Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

Name: Oji Samuel Nkemakolam
Reg no: 2017/249548
Department: Economics

Lewis-Fei-Ranis Model (Surplus labour theory)
Two economists, by name, John Fei and Gustav Ranis presented their dual economy model which is an improvement on Lewis model. Fei-Ranis (FR) model of dual economy explains how the increased productivity in the agricultural sector would become helpful in promoting the industrial sector in the evonomy.Thus, this model is treated as an improvement over Lewis model of unlimited supply of labor. They observed the Lewis model by reading it from left to right and assessed the changes in the output and wage as more people moved from agriculture to the industry. A new concept was added – namely, disguised unemployment, which appears in the traditional subsistence sector (primitive sector). It acknowledges the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account. Some of the basic thesis of the model are:
I. The growth rate of population is high which results in mass unemployment.
II. The industrial sector is dynamic.
IV. Natural resources are scarce and there is an abundance of labour.
V. There are certain non-agrarian sectors in the economy where there is reduced use of capital.
There are three stages in this model which are:
Stage one: The first stage of the FR model is very similar to Lewis. Disguised unemployment comes into being because the supply of labor is perfectly elastic and MPL = 0. Therefore, such disguised unemployment are to be transferred to industrial sector at the constant institutional wage.
Stage two: In the second stage of the FR model, agricultural workers add to agricultural output but they produce less than the institutional wage they get. In other words, the labor surplus exists where APL > MPL, but it is not equal to subsistence (institutional) wages. Accordingly, such disguised unemployed also have to be transferred to industrial sector. If the migration to industrial sector continues a situation is eventually reached where the farm workers produce output equal to institutional wages. This would mean that productivity in agricultural sector has gone up. With this, the third phase starts.
Stage three: In the third stage of the FR model, the take-off situation comes to an end and there begins the era of self-sustained growth where the farm workers produce more than the institutional wage they get. In this stage of economic growth the surplus labor comes to an end and the agricultural sector becomes a commercialized sector.
Some of the criticisms of the Lewis-fei-Ranis model includes:
I. The model ignored the role of foreign trade as it assumed a closed economy model.
II. MPL is zero in the model but Prof. Jorgenson who has also presented a dual economy model says that the MPL is an empirical issue. During good farming seasons, the MPL > 0.
III.The model holds that MPL is zero in the first phase of growth and the transfer of labor from agriculture would not reduce output in the agricultural sector in phase I but some other economists like Berry insists that agricultural output in phase I will not remain constant and can be affected by different land conditions.
IV. The model assumed that in the process of economic development, the supply of land remains fixed but this is not so. Land supply can be increased in the long run.
In conclusion, the Fei-Ranis Model is one of dualism. The model believes in the simultaneous growth of the agricultural and investment sector because it accelerates economic development in the economy. In real life, this model is significant amd realistic, the two sectors of the model, agricultural and industrial sector, exists real life and efforts are normally made to speed up development of the two sectors. Labour also move from the agricultural sector into the industrial sector without the agricultural sector being ignored.

HARRIS-TODARO model of migration
The Harris–Todaro model was named after John R. Harris and Michael Todaro. It is an economic model of migration developed in the year 1970 and used in development economics to explain the concept of rural-urban migration. The main hypothesis of Harris and Todaro are that migrants react mainly to economic incentives, earnings differentials, and the probability of getting a job at the destination have influence on the migraton decision.
Rural to urban migration does not equate the wage differences between the two labor markets as designated by demand and supply fundamentals. The reason is the lack of full employment in urban areas. The probability of finding a job in an urban area is never 100%. In other words, the urban labor market never fully clears due to institutionally determined urban wages; there will always be unemployment. This provides a technical rational to the reason why there is rural to urban migration amidst unemployment.
The model assumes the following:
I. A two sector economy (urban and rural also seen as manufacturing and agricultural sectors respectively).
II. To move from one sector to another, there is little or no marginal cost.
III. The two sectors are perfectly competitive.
The following are the critiques of the Harris Todaro model
I. The Harris-Todaro model is a static model describing migration, which is a dynamic phenomenon by nature.
II. The assumption that urban workers are either employed in the manufacturing sector or unemployed has been criticized as too simplistic even though, it was implicit that unemployment could also be interpreted as underemployment in the informal sector.
III. The influence on decision making of risk and risk attitudes on the part of the potential immigrants is not included;
IV. Differences in skill levels among the migrants are not accounted for.
In conclusion, the model examines the concept rural-urban migration. This migration occurs as a result of rational decision makers comparing urban expected income with wage in rural areas. The equilibrium condition of this model is when expected rural wage is equal to rural wage. It is also explains the idea of urban unemployment which is referred to as the Todaro Paradox. This model, which seem incomplete at first, has been advanced and improved upon by latter economists increasing its analytic, predictive and prescriptive power.

NAME: Uwode Joy Ogheneyonle
DEPARTMENT: Economics
REG NO: 2017/241451
EMAIL: yonlejoyuwode@gmail.com

Harris_todaro Model of Migration
The Harris_Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural_urban migration. The main assumption of the model is that the migration decision is based on expected income differentials. This implies that rural_urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.

Lewis_Fei_Ranis Model of Economic Growth

The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

Name: Okwuchie Amos
Reg. Number: 2017/249562
Email: Okwuchieamos@gmail.com

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR)
The Lewis (1954) Model was the first model to explicitly focus on dualist economic development. The original Lewis model was simple yet genius with the clarity he expressed his ideas, nearly every development model is some way related to the roots of the Lewis Model. The Lewis model understood that in most LDC’s, most workers are in the rural/agricultural sector. Agricultural sector in these nations are not endowed with capital with high productivity like agricultural sectors in the developed nations. Agricultural sector in the LDC’s are mostly family farms characterized by low productivity and uncertain output. This assumption made by Arthur Lewis is valid in most LDC’s; every development model after the Lewis model has used some form of the assumptions made by
Arthur Lewis
ASSUMPTIONS OF LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR)
1. There is traditional and urban sector.
2. Labour are perfectly mobile.
3. Markets are perfectly competitive.
4. Diminishing returns of factors
5. There is downward rigid wage
SUMMARY OF THE MODEL
The Lewis Dual Sector model of development
This is based on structural change theory which explains the mechanism of changing structure of underdeveloped economic from subsistence agriculture to more modern and more urbanized.
This model became the general theory of development process for surplus labour nation during 1960s and early 1970s.
Lewis model consist of two sectors which are traditional sector and modern sector and modern sector.
TRADITIONAL SECTOR: This sector is the overpopulated subsistent sector where marginal marginal productivity of labour is zero. Due to zero marginal productivity, it is possible to withdraw labour from this sector without affecting the level of output. This is why it is classified as the surplus labour sector.
MODERN SECTOR: This sector is urban, industrial sector. Productivity is high in this sector. Labour is gradually transferred into this sector from traditional sector.
The movement of labour from traditional to modern sector bring expansion in both output and employment. The speed of this expansion depends on
1. Rate of industrial investment and capital accumulation which ultimately depends on the level of profit. Lewis assume that all profit are reinvested.
2. Wage difference between the rural and urban sector.
According to Lewis, there should be at least 30 percent higher wage rate in the urban sector than rural sector in order to transfer labour automatically from rural to urban sector.
Lewis assume that there is perfectly competitive labour market in modern sector giving fixed wage rate and horizontal supply of labour. In other hand wage rate in traditional sector is given average productivity of labour (w = APPL = TP/L).
On the other hand, the labour surplus theory is concerned with poor economy that is the under developing countries. The main argument of the model is focused on the following backgrounds.
There is an abundance of labour in under developed countries and shortage of natural resources.
The population growth rate is very high which results in mass unemployment in the economy.
There is a dynamic industrial sector in the economy.
There are certain non-agrarian sectors in the economy where there is reduced use of capital.
The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labour is zero and negative in agricultural sector. The situation where MPL-0, labour can be transferred to industrial sector without any loss in agricultural output. The real wages in industrial sector remains fixed and it is equal to the initial level of real income in agricultural sector. Such wages are given the name of institutional wages.
From the focal point above, the Lewis-Fei-Ranis theory of dualistic economic development provides the primary contribution to theories of economic development particularly for labour-surplus and resource for poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow the sharing rule and be equal to average productivity, which is also known as the institutional wage. While the non-agricultural seems to be the obverse of the agricultural sector
HOW THE LEWIS-RANIS-FEI MODEL OF SURPLUS LABOUR RELATE TO NIGERIA ECONOMY.
Mr President, it should interest you to know that Nigeria is operating under the above model, since the model applies to developing countries. Hence Nigeria happens to be one of the developing countries.
In sum, Nigeria has two sector economy, the urban and rural sector. These two sectors have their labour. But there is excess or surplus labour in the rural area. It therefore needs that the surplus labour be transferred to the urban area. The urban area is the industrialized and can absorb the excess labour. Checking the existing scenario in Nigeria economy, we can observe that we are operating on this model. But we need to invest in both sectors so as to speed up development.
To conclude, I have shown the main ideas behind the Lewis-Ranis-Fei model and used the consecutive analysis of the model to explain why it is important to invest in both sectors in order to remain on the balanced growth path and maintain the rate of industrialization. The existence of surplus labour in agriculture allows the industry to continue to pay the institutional wage and therefore enjoy further profits and continued investment. At the same time, as more and more people are moving away from agriculture, there will be some amount of agricultural surplus that can be used up to fuel further development. This process continues until the surplus labour is absorbed. Hence, saving and investment are a crucial part in the Lewis-Ranis-Fei to support economic development.

HARRIS – TODARO MODEL OF MIGRATION
The Harris-Todaro (H-T) model is based on the experiences of Less Developed Countries (LCDs) facing the problems of rural-urban migration and urban unemployment.
The key contribution of this model to the field of development economics is by making the migration process a rational choice based on expected earnings, that is, labour migration is as a result of rural-urban differences in average expected wages. Here, the minimum urban wage is substantially higher than the rural wage. Also, if additional employment opportunities are created in the urban sector at the minimum wage, the expected wage shall rise and rural-urban migration on the other hand shall be induced resulting to increasing levels of urban employment. Harris and Todaro suggest a subsidised minimum wage through a lumpsum tax.
BASIC ASSUMPTIONS OF HARRIS-TODARO MODEL
The Harris-Todaro model is based on the following assumptions;
There are two sectors in the economy; the rural or agricultural sector (A) and the urban or manufacturing sector (M).
The model operates in the short run
Capital is available in fixed quantities (K-) in the two sectors.
There are N workers in the economy with NA and NM numbers employed in the rural and urban sectors respectively.
The urban wage if fixed at WM and the rural wage at WA, such that WM > WA.
The rural wage equals the rural marginal product of labour, and the urban wage is exogenously determined.
Rural-urban migration continues as long as the expected urban real income is more than the real agricultural income (by making rational decision)
There is perfect competition among producers in both sector
The price of the agricultural good is determined directly by the relative quantity of the two goods produced in both the sectors.
SUMMARRY OF THE MODEL
The Harris-Todaro (1970) elaborated the basic two sector model of rural-urban labour migration. It takes most of Lewis model’s assumptions as given, such as the rural sector being characterised by subsistence agriculture, and the urban sector being characterised by modernised industries. However, the Harris-Todaro model takes a standard two-sector model and imposes a higher wage in the urban sector which is higher than equilibrium clearing, while wage in the agriculture is flexible. The equilibrium clearing is simply when wage across both sectors equalize, minus movements costs or natural advantages (such as better living environment) in one of the sectors. By imposing this higher wage in the urban sector, we no longer have market clearing wage which gives the workers in the rural sector an incentive to migrate to the urban sector. These migrant workers are not guaranteed to find a job in the urban sector. There is a probability that they will end being unemployed or in the informal sector.
Less Developed Countries (LDCs) are unlikely to have good social safety nets such as welfare benefits, unemployment benefits, and old age security. If the migrants were unable to find a job in the urban formal sector, which is the modern industrial sector, they would be forced to work in the informal sector to themselves alive. The informal sector is very primitive; work in this sector is labour intensive with little or no capital endowment.
The equilibrium condition of the Harris-Todaro model can be described as the wage in rural (agricultural) sector must be equal to the expected wage in the urban sector. The model in its most basic form ignores disutility from not being at home farm, or cost of mobility, but these omissions do not change the essence of the model, the only implication of this is a downward shift of the urban sector’s expected returns.
HOW THE MODEL RELATE TO NIGERIAN ECONOMY.
Mr president, the Harris-Todaro model of migration is a typical scenario obtained in the Nigerian economy where those in the rural area migrate to the urban area for greener pasture where the wages are higher than as obtained in the rural agricultural sector.
Consequently, there is high unemployment in the urban area in Nigeria today because of the perceived better life in the city (urban area). But the cost of living in the urban area leads to balance in the cost of living in the rural area when the high cost of living in the urban area is accounted for.

Due to excess labour in subsistence sectors whose marginal productivity is zero, it is necessary for these labour to be put to productive use, there’s need for utilization of these labour or human capital i.e moving them from where they are under-utilized to where there’re effectively utilized.
According to Harris-Todaro’s model developed in 1970, which is used to explain some of the issue concerning rural-urban migration, it is necessary for mobility of labour to exist. This model believes migration is based on expected income difference between rural and urban areas. The model interprets the transitional dynamics with continuous growth of the urban fraction of overall population toward an equilibrium. This model focuses on rural-urban migration.
The Harris-Todaro’s model is mostly relevant for labour surplus countries like India, Nigeria, China, Pakistan, etc. This is because, there’s an assumption that lives in the rural areas will improve greatly if they migrate to urban areas rather than I’m the rural environment, unless the workers are comfortable in the rural areas.
The expected real wage difference between Urban and rural areas is the main determinant of migration decision. The urban market is according to H-T is imperfect cause it is assumed there’s a fixed wage rate.
Migration from rural to urban is inevitable as the Urban sector is seen as a lucrative sector where opportunities are open for better standard of living condition compared to the rural sectors.
The Lewis Fei-Ranis model developed in 1954 divides the economy into two sectors namely the subsistence or agricultural sector and the capitalist or manufacturing sector. This model believes in a dual sector where the unemployed and underemployed resources are taking into consideration. The model emphasized strongly on the industry and agricultural interdependency and encourages partnership between these sectors as one is the producer of raw materials and the other is the manufacturer of finished goods by transforming the raw materials into utilities.
The main assumption of this model is that there exist surplus labour in the subsistence sector. The surplus labour in the subsistence or agricultural sector acts as a source of unlimited supply of labour for the manufacturing sector. Lewis believes supply of labour is perfectly elastic at a particular wage which in most cases is higher than the wage each worker in the agricultural sector gets.
Lewis also made an assumption based on savings, he believed the capitalist invests all it’s savings for it’s further expansion while those in the agricultural sector squander away their savings. The propensity to save is low in the agricultural sector compared to the capitalist. Lewis even advocated for a transfer of income from the agricultural sector to the capitalist sector. The additional savings will not only help the capitalist to invest more but also improve the quality of capital invested leading to more employment from the agricultural sector which will bring more Cash for the capitalist which can re-invested leading to more employment of surplus labour.
Though Lewis model was criticized by experts, as some argued that he didn’t include the cost of training the unskilled labour transferred from the agricultural sector to the capitalist sector. This model assumes besides labour, there’s unlimited supply of manufacturers which is not true as seen in some developing countries. The experts also argued that it is wrong to assume the capitalist will re-invest while the agricultural worker squanders all his savings, cause propensity to save is an individual ideology. Also it is wrong to assume there’s an already existing market for the industrial products in the country. The experts believed not all underdeveloped country have surplus labour as some surplus labour depend on the size of the population.
Both models are emphasized on savings and investment, as the driving forces for economic development of underdeveloped countries.
The HT model is very applicable in Nigeria due to the low infrastructural facilities and low standard of living that is very high in rural areas. the labour force in the rural areas has to move so as to improve their lives and access better living standards.

NAME: IFETAYO KOSI ANWOLUWA
REG NO: 2017/249343
DEPARTMENT: ECONOMICS

THE LEWIS FEI RANIS MODEL ( SURPLUS LABOUR THEORY)
One of the best-known early theoretical models of development that focused on the structural transformation of a primarily subsistence economy was that formulated by Nobel laureate W. Arthur Lewis in the mid-1950s and later modified, formalized, and extended by John Fei and Gustav Ranis. It is a dualism model in development and welfare economics. It is also known as the Surplus Labour Model. The Lewis two-sector model became the general theory of the development process in surplus-labor developing nations during most of the 1960s and early 1970s, and it is sometimes still applied, particularly to study the recent growth experience in China and labor markets in other developing countries. There was a flaw in Lewis model that it did not pay enough attention to the importance of the agricultural sector in promoting industrial growth. But Fei-Ranis (FR) model of dual economy explains how the increased productivity in agricultural sector would become helpful in promoting industrial sector. In this respect, it presents three stages whereby a underdeveloped country moves from stagnation to self-sustained economic growth. Thus, this model is treated as an improvement over Lewis model of unlimited supply of labor. This is because the assumption of unlimited supply of labour is unrealistic. Since Fei-Ranis model builds on the proponents of Lewis two-sector model, both are generally referred to as Lewis-Fei-Ranis model. Therefore, it is a matter of necessity to first define the Lewis two-sector model.
tries. In the Lewis model, the underdeveloped economy consists of two sectors:a traditional, overpopulated rural subsistence sector characterized by zero marginal labor productivity ( a situation that permits Lewis to classify this as surplus labor in the sense that it can be withdrawn from the traditional agricultural sector without any loss of output) and a high-productivity modern urban industrial sector into which labor from the subsistence sector is gradually transferred.The Lewis two-sector theory of development in which surplus labor from the traditional agricultural sector is transferred to the modern industrial sector, the growth of which absorbs the surplus labor, promotes industrialization, and stimulates sustained development. Here, Surplus Labour means the excess supply of labor over and above the quantity demanded at the going free-market wage rate. In the Lewis two-sector model of economic development, surplus labor refers to the portion of the rural labor force whose marginal productivity is zero or negative
In this line with this mode of thinking, the Lewis-Fei-Ranis model recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
Like most economic theories, the Lewis-Fei-Ranis model relies on various assumptions:
(i) There is an abundance of labor in such underdeveloped countries and shortage of natural resources.
(ii) The population growth rate is very high which results in mass unemployment in the economy.
(iii) The major share of population is engaged in agriculture. But agriculture sector is stagnant. Hence, the marginal productivity of labor is zero and negative in agriculture
sector.
(iv) There are certain non-agrarian sectors in the economy where there is reduced use of capital.
(v) There is a dynamic industrial sector in the economy.
These assumptions are necessary for the justifications of the various conclusions reach in the model. That is, it is necessary for restating the model. The model suggests that if agricultural labourers are transferred to industrial sector, there will be economic development since the labour force in the economy will become more productive. This model is classified under the structural change theory (The hypothesis that undevelopment is due to underutilization of resources arising from structural or institutional factors that have their origins in both domestic and international dualism) and their solution to this problem is transfer of surplus labour from agricultural sector ,where it is less utilised, to industrial sector for better productivity. The model divided into three phases:
– Breaking Point: The first stage of Fei-Ranis model is very similar to Lewis. Disguised unemployment comes into being because the supply of labor is perfectly elastic and MPL(Marginal Productivity of Labour) = 0. Therefore, such disguised unemployed are to be transferred to industrial sector at the constant institutional wage. That is, there is redundant agricultural labour.
– Shortage Point: In the second stage of Fei-Ranis model (phase) agricultural sector workers add to agricultural output but they produce less than institutional wage they get. In other words, in the second stage the labor surplus exists where APL(average productivity of labour) > MPL, but it is not equal to subsistence (institutional) wages. That is, at this point, the constitutional institutional wage(CIW)>MP>AP. This means there is disguised agricultural unemployment. This, such disguised unemployed also have to be transferred to industrial sector. If the migration to industrial sector continues a situation is eventually reached where the farm workers produce output equal to institutional wages. This would mean that productivity in agricultural sector has gone up. With this the third phase (stage) starts.
– The Lewis turning point or Commercialization Point: In the third stage of FR model , the take-off situation comes to an end and there begins the era of self-sustained growth where the farm workers produce more than the institutional wage they get. In this stage of economic growth the surplus labor comes to an end and the agricultural sector becomes commercialized sector. Accordingly, they have to be shifted to industrial sector. As labor are transferred to industrial sector a shortage of labor will develop in agricultural sector. In other words, it will be difficult for the industrial sector to get the labor at same prevailing constant wages. That is, there is self-sustaining agricultural growth with commercialization of agricultural sector. This is because MPL>CIW. Here, the economy is fully commercialized in the absence of disguised unemployment. Such commercialization took place at the cost of absorption of disguised unemployment in industrial sector. Lewis was a great proponent of balanced growth strategy and it is only natural that this theory will be of the above policy impications. And this has influenced various policies in developing countries. For empirical analysis has shown that China development miracles was as a result of it going through this stages systematically. China’s economic growth is mainly attributable to the development of the non-agricultural (industrial and service) sector, driven by rapid labor migration and capital accumulation. It was found that the sectoral reallocation of labor plays a significant role inpromoting China’s economic growth. Further, it was found that in China marginal productivity of agricultural labor stopped stagnating in 1978, which indicates that China entered quickly into phase two of economic development with the initiation of market reforms. Moreover, by 2009, the marginal productivity of labor has likely exceeded the institutional wage, as defined by the initially low average labor productivity, indicating that China may be now in th The same cannot be said for Japan.
Although the Lewis two-sector development model is simple and roughly reflects the historical experience of economic growth in the West, four of its key assumptions do not fit the institutional and economic realities of most contemporary developing countries. This, it has been subjected to various criticism:
(i) Marginal Productivity of Labor in Phase I: The FR model is of the view that MFL = 0 in the first phase of growth, and the transfer of labor from agriculture would not reduce output in the agri. sector in phase I. Various economists are of the view that agri. output in phase I of Fei-Ranis model will not remain constant and may fell under different systems of land tenure, i.e., the peasant proprietorship and share cropping etc.
(ii) Marginal Productivity of Labor is Not Zero: Prof. Jorgenson, a development economist, who has also presented a model of ‘dual economy’ has object FR model’s contention of zero MP in phase I. He says whether MPL will be zero is an empirical issue. During the seasons of sowing and harvesting the MPL > 0. Jorgenson concluded on the basis of Japanese data even for the pre I world war period the supply of labor was not unlimited. Then how MPL can be zero.
(iii) Ignoring The Role of Capital: The Fei-Ranis model concentrated upon land and labor as the determinants of output, ignoring the role of capital. But Profs. Brown, Byres, Frankel, Griffen, Ghatak and Ingersent are of the view that in the UDCs there has occurred what is known as ‘Green Revolution’ in agri. which has promoted the greater use of capital and technology on lands. Consequently, there has been a greater increase in the agri. productivity and agrcultural incomes.
(iv) Open Economy: FR model ignored the role of foreign trade as it assumed a closed economy model. In the 2nd phase when agri. product decreases the Terms of Trade goes against industrial sector. This would occur in the presence of closed economy. But if the model is made open such would not happen as the goods could be imported in the presence of then-scarcity. This was especially observed in case of Japan which imported cheap farm products to improve her Terms of Trade.
(v) Supply of Land in Long Run: Fei-Ranis model assumed that in the process of economic development the supply of land remained fixed. But it is not true. The supply of land can be increased in case of long run.
(vi) Commercialization Of Agriculture And Inflation: According to FR model when 3rd phase starts the agri. sector becomes commercialized. But it is criticized by saying that this phase does not start so easily The shifting of labor to industrial sector will create labor shortage in agri. sector. This will create shortage of food stuff leading to increase their prices. In this way, the inflation will generate which may obstruct the process of development.
(vii) Low Productivity in Agricultural Sector: According to Jorgenson it has been observed that there has been a very slow rise in the productivity of agri. sector. Consequently, the surplus will hardly be created in agri. sector. Accordingly, agri. sector will not contribute to development Thus the growth requires that the surplus must be generated and it should persist.

THE HARRIS-TODARO MODEL OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration.Harris and Todaro subsequently formulated amodelto explain rural-urban economic preferences to migrate. The distinctive concept in the model is that the rate of migration flow from rural (agricultural) areas to urban (industrial) areas is determined by the difference between expected urban wages and rural wages.In the Harris–Todaro model, the rising urban wage pushes up the expected wage in the urban sector and consequently encourages workers to migrate from the rural sector to the urban sector. This phenomenon is referred to as Todaro paradox.The Harris-Todaro model assumes that migration from rural to urban areas depends primarily on the difference in wages between the rural and urban labour markets. where Eu is urban employment, Uu is urban unemployment and L is total urban work force. … So Weu becomes simply the urban wage times the urban employment rate.

THEORETICAL IMPLICATIONS OF THE MODEL
There is no denying the fact that any development project can be evaluated using social cost- benefit analysis. An important part of the social cost of any input is opportunity cost, its value in its next best alternative use. Labour hired for an urban formal-sector project might well be drawn from the urban informal sector also.

The worker who moves out of the urban informal sector may, in turn, be replaced by someone from the rural sector. In this case, the output lost is that of the worker who was formerly in the rural sector, i.e., the worker at the end of the em­ployment chain. For this reason, some analysts believe that the wage paid to casual agricultural labourers provides a good measure of the social cost of unskilled labour.

However, this measure, although a good indicator of output foregone through labour reallo­cation, probably understates the true social cost of employing labour, which has other compo­nents that are likely to be significant. One such component is induced migration. No doubt there are both pull and push factors behind internal labour migration that occurs in the course of economic development from rural to urban areas.

Such migration can result either from favourable economic developments in the towns or from adverse developments in the rural areas. The Harris-Todaro model integrates these two sets of forces in their analysis of the proc­ess of labour reallocation that is likely to occur during economic development. This is why the model was sort of innovation in the literature of development economics when it appeared for the first time in 1970′. The H-T model has far-reaching implications from the policy point of view. For example, if the government of the country concerned were successful in fostering industrial development in an urban area, employment would increase there.

The effect would be to increase the subjective productivity of getting urban employment in the minds of rural inhabitants. Migration would increase and the eventual effect of the new industrial development could be that urban unem­ployment becomes higher that the level prevailing before the new development took place.

There will be some level of urban employment which ensures equilibrium in the sense that no further migration takes place. Potential migrants may take a long-term view in arriving at a decision. They may consider that their desireness of obtaining an urban job will be higher after a waiting period of some months. Thus they will compare the present value of the sum of expected urban earnings with that of expected rural earnings.

They may be content to accept a low wage in the urban informal sector for some time. This might be a rational decision on a long-term basis. The root of the problem is the large difference between earnings in the modern industrial sector and those in the rural areas.

Often the former are well above the market clear­ing levels for varies reasory. The long-term solution to the problem lies in adopting policies for both urban and rural areas which reduces the real income differences between the two areas. In any case, the Harris Todaro model suffers from theoretic oversimplification, among which several are likely to overestimate the link. The critiques revolve around the three major points;
1. The model framework is only a static model describing migration, which is a dynamic phenomenon by nature. Even though the model can be thought of as representing a steady state equilibrium,this is a limitation. Furthermore, the formalization is made in a partial equilibrium context which greatly weakens the justification for policy recommendations.
2. The assumptions that urban workers are either employed in the manufacturing sector or unemployed has been criticized as too simplistic even though, in the authors’ minds, it was implicit that unemployment could also be interpreted as underemployment in the informal sector.
3. The Harris-Todaro model assumes that the urban wage is exogenously set above the endogenous rural wage . The assumption that wages are high find several explanations ranging from the existence of trade unions to the agglomeration of economic activities. It is confirmed in practice,since wages are often reported three to four times higher in urban areas than in rural areas (Todaro, 2000). What is more problematic, however, is the assumption that the urban wage is fixed, especially in the presence of an informal sector as typical of many developing economies. In fact, the argument of a minimum wage should only hold for low wages in the formal sector, unless remunerations in the informal sector align themselves with those in the formal sector (due to the competition for labor between employers)In addition, the wage in the Harris-Todaro model is not related to unemployment in any manner. If the urban wage tends to decrease with an increase in the unemployment rate as argued by Hoddinott (1996) in his study on urban African labor markets, then this would tend to reduce the expected earnings differential in the transition towards the equilibrium in the model. This gives another reason why migration flows could be overestimated, making the Todaro paradox even less likely to occur. Migration in any given time then depends on three factors:

(a) The urban-rural wage gap,

(b) The urban employment rate and

(c) The responsiveness of potential migrants to the resulting opportunities.

Ezeamaku chukwuemeka victor
2017/243370
Victorezeamaku76@gmail.com

The Lewis Fei-Ranis model

The model know as the Fei–Ranis model of economic growth is a dualism model in developmental economics, it was developed by John C. H. Fei and Gustav Ranis and is viewed to be an extension of the model developed by lewis. It is also known as the Surplus Labor model.

It recognizes the presence of two economy that consists of both the modern & the primitive sector and takes the economic situation of unemployment & underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature.
As postulated by this theory, the primitive sector consists of the already existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the major focus of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.

One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages.[4] They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development In Phase 1 of the Fei–Ranis model, the elasticity of the agricultural labor work-force is infinite and as a result, suffers from disguised unemployment. Also, the marginal product of labor is zero. This phase is similar to the Lewis model. In Phase 2 of the model, the agricultural sector sees a rise in productivity and this leads to increased industrial growth such that a base for the next phase is prepared. In Phase 2, agricultural surplus may exist as the increasing average product (AP), higher than the marginal product (MP) and not equal to the subsistence level of wages.
This model again stresses the importance of Nigeria making a shift in the amount of labour availability for agriculture to labour available for industrialization, which goes against the current economic policy being pursued by the present Nigerian government, which is an insistence on labour migration to agriculture, this move my the Nigerian government goes against the generally accepted principle for developing nation’s that the more the rate of reallocation from agriculture, the faster the growth of that economy.

The Harris-Todaro model

The Harris–Todaro model was developed in the 1970s and is named after two economists, John R. Harris and Michael Todaro, it is an economic model used in development economics to explain some of the issues concerning rural-urban migration.
The main assumption of the model is that the migration decision is based on expected difference in income between the rural and urban areas rather than just differences in wages.
It has long been realized that in order for an economy to develop or grow, a large amount of labor has to be transferred from the traditional (or backward) agricultural sector in rural areas, where the productivity of labor is low (or negligible, or zero, or even negative) to the modern manufacturing sector where the productivity of labor is higher and rising due to capital accumulation in that sector.
It should not be surprising, therefore, that, in the literature of development economics, dualistic models gained popularity over the single-commodity or single-sector theories
in the 1950’s. A typical dualistic model in development economics contains two sectors, a traditional or agricultural sector in the rural area and a modern or manufacturing sector in the urban area and there is large scale migration from the traditional sectors to the modern sector
In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector.

Therefore, migration from rural areas to urban areas will increase if:
Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

Name: Ugorji Ijeoma Judith
Reg no: 2017/243088
Department: ECONOMICS
Email: peppyhijay@gmail.com
Blog: peppyxperience.blogspot.com

INTRODUCTION
In times past, various economists have come up with different approaches and models of economic growth in a bid to explain and possibly proffer solution(s) to the patterns and problems of economic growth of developing countries. This approaches ranges from the linear stages of growth model to the structural change models down to the traditional neoclassical growth theories.

Various types of growth models include the Harrod-Domar growth model which highlights the mobilization of domestic and foreign savings to generate investment and hence economic growth. The Solow growth model also known as the exogenous growth model analyses the changes in the levels of economic growth (output) over time as a result of the changes in the population growth rate and the rate of technological process. The endogenous growth model is another model placing more emphasis on internal factors which brings about economic growth than external factors. These internal factors according to the model includes improvement in innovation, knowledge, and human capital. There is the Lewis growth model which divided the economy of an underdeveloped nation into subsistence sector and the capitalist sector and then the Harris- Todaro growth model of migration. These models however have their strength and weaknesses.

Harris -Todaro model of migration
The model is named after two economists John R. Harris and Micheal Todaro who developed it in the year 1970. The model is used in development and welfare economics to explain some of the phenomena concerning rural-urban migration as it affects economic growth of developing countries. Harris-Todaro model just like Lewis model divided the economy into two sectors(region);
The rural region (agricultural) and the urban region (industrial) in order to explain the influence or rural-urban migration and critical urban unemployment problems in developing countries.

The model tries to answer the question “why rural-urban migration is still taking place despite high unemployment in urban areas. The model sees migration as an economic decision. People migrate on the basis of wages and probability of unemployment. Migrants take into account present value of urban expected income or it’s equivalent and then move if it exceeds average rural income.
The model assumes that the urban minimum wage is set to be higher than the wage rate paid to rural labour. This results in a wage differential between the two sectors. Rural workers have an incentive to migrate to the urban areas despite of increasing level of urban unemployment, because of the potential of higher earnings in the urban sector brought about by a high concentration of Industries in the cities.
Such migration will continue as long as there is a possibility for migrants to increase their income by moving to a city. Some migrants will have arranged employment before leaving the countryside. Others will begin job search only once they have arrived at their destination, while some still will join the pool of urban unemployed with the hope of finding a meaningful and sustaining means if livelihood in the future. This explains why there is a continuous flow of migrants observed in developing countries irrespective of the high unemployment rates.

BASIC ASSUMPTIONS OF HARRIS-TODARO GROWTH MODEL
Migration is primarily an economic phenomenon based on private rational economic decisions.
Wage difference (wage gap) between the two sectors of the economy. Migration proceeds in response to urban-rural differences in expected earnings rather than actual earnings and the urban employment rate acting as an equilibrating force on such migration.
The model also assumes that potential migrants are risk neutral where the poor migrants will likely be risk aversive in that they are indifferent between a certain a certain expected rural income and an uncertain expected urban income.
They also assume that there is a perfect competition and there is no unemployed in rural agricultural sector. Although this was countered as unrealistic.

Harris-Todaro two sectors model is characterised by the following;
Real wages (adjusted for cost of living difference) were higher in urban sector jobs than in the rural traditional sector jobs.
To be hired for a formal sector job, it was necessary to be physically present in the urban areas where the jobs were located.
More workers searched for the industrial sector jobs than were hired leaving the many others to join the league of the unemployed.
To maintain the equality between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower paying rural job, the equilibrium arising in such a setting would be characterised by urban unemployment.
Any temporary difference in the expected wage between one sector and another would be eroded as workers migrate from the low expected wage labour market to the high expected wage labour market.

A graphical illustration of the Harris-Todaro two sector model of migration.
Fig 1. Harris-Todaro model.

The graph above explains the Harris-Todaro two sector model where there is declining marginal productivity in both sectors. Hence, the higher the wage is, the lower the demand for workers in both sectors (according to law of demand for labour).
Total labour force is represented by L, and it does not depend on wages. There are LA workers in agricultural sector and LM workers in the mirdern sector and the remaining Lu are unemployed. If we assume a flexible wage in both sectors then we get equal wages in both agricultural and modern sector and no unemployment. The situation is depicted in the diagram above, where AA curve is the demand for labour in agricultural sector and MM curve is the demand for labour in the modern sector.

COMPARISON OF THE HARRIS-TODARO MODEL OF MIGRATION WITH THE LEWIS MODEL OF MIGRATION
The Harris-Todaro model of migration has a basic similarity with the Lewis model if migration in that both models adopted the system of two sector model in their analysis. While Harris-Todaro two sector model is divided into the rural (agricultural sector) and urban (modern/industrial sector), Lewis two sector model on the other hand comprises of the subsistence sector and the capitalist sector. Lewis mentioned that of the two sectors, the capitalist sector is predominant. He defined the capitalist sector as “that part of the economy which uses reproducible capital, pays capitalists for the use thereof and employs wages labour for profit making purpose”.

The distinguishing feature of a capitalist sector is that it hires labour from the subsistence sector at a given wage rate and sells output to earn profit. The subsistence sector on the other hand is that part of the economy which does not use reproducible capital. Labour is abundant and disguised unemployment is the result. The Lewis model auggests that the capitalist sector to be expanded by transferring labour from the subsistence (rural) sector to the capitalist sector because he assumes that the supply of labour is perfectly elastic at the subsistence wage. However this was a major criticism of the model. The model assumes a constant wage rate in the capitalist sector until the supply of labour is exhausted from the subsistence sector. This is unrealistic as a result of the continuous increase in the wage rate overtime in the industrial sector of an underdeveloped economy even when there is open unemployment in it’s rural sector. From this , the following deductions can be made on comparison of the two models;
Both models adopts two sector model in their analysis.
Harris-Todaro model tries to explain why there is continuous increase in rural-urban migration despite increasing rate of unemployment in the urban sector while Lewis model suggest for migration of labour from subsistence sector to the capitalist sector.
Lewis model is interested in the expansion of the capitalist sector at the expense of the subsistence sector.
Harris-Todaro model assumes no unemployment in the rural area, Lewis on the other hand assumes a disguised unemployment in the rural (substantence sector).
Harris-Todaro model operates in the short run while Lewis model operates in the long run.
Both assumes fixed wage rate in the urban sector.
Significance of thE HARRIS-TODARO MODEL OF MIGRATION.
The fundamental contribution if Harris and Todaro’s two sector model of migration was to build a model that fits the stylized facts of the labour market. On the lines if the theory, developing nations adopted program on integrated rural development which encouraged an increase in the rural traditional sector wage. The theory proves that the higher the unemployment rate in the urban area, the lower is the probability of migrants from the rural to the rural area actively seeking formal sector employment who are unable to find it. The significant findings of the model are;
Firstly, if expected urban wage equals rural income, there is no incentive to migrate.
Secondly, if the expected urban wages is greater than the rural income, there is great incentive to move from rural to urban migration.
Thirdly, if the expected urban wages is less than rural income, there would be an incentive to move in other direction.
Lastly, the expected urban wage depends on what type of job migrants are engaged in.
LIMITATIONS OF THE MODEL
Some of the assumption of the Harris-Todar’s model were judges to be too restricted. The model also assumes that’s the potential migrants are risk neutral where the poor migrants will likely be risk averse as in they are indifferent between a certain expected rural income of the same magnitude. The assumption that there exists a perfect competition in rural agricultural sector is not realistic.
Implications and conclusion
The migration of labour from rural to urban area is an important part of urbanisation in the developing nations. Infact, it is the major source of labour for industries mostly concentrated in the modern sector. The question is, to what extent is internal migration a desirable phenomenon and under what circumstances?. There is need for government of developing nations to encourage programs that would boost the rural sector economy and encourage more people to stay back. This would reduce the increasing rate of unemployment in the urban area.
Considering developing nations of Africa and taking Nigeria as a case study, the migration of labour from rural sector to urban sector is evident in the over population, increase in crime rate and unemployment that characterizes the industrialised urban area. Young people tend to leave the rural areas which are majorly villages and small towns characterised by majorly subsistence agriculture and other menial jobs as blacksmith, carpentery, craftsmanship, petty trades to mention a few with little or no industries in search of “greener pastures” in forms of better paying jobs with good working conditions that would eventually lead to a better or higher standard of living. The rural sector is therefore left to the weak and aged who are mostly farmer and could produce little that would sustain them to say nothing of any surplus to sell to the urban area. This leads to reduction in production of agricultural sector.
LEWIS-FEI-RANIS MODEL OF SURPLUS THEORY.
The Lewis model of surplus labour is an example of structural-change theory which focuses on the mechanism and strategies by which underdeveloped economies transform their domestic economic structure from a more dominant rural agricultural sector to a more urbanised industrial economy.
The surplus labour theory one of the best known early models of development was developed by Nobel laureate W. Arthur Lewis in the 1950s and was later modified and extended by John Fei and Gustav Ranis. The Lewis-Fei-Ranis model of surplus theory was named after these there men.
The surplus labour theory uses the analysis of two sector model in explaining growth experiences of developing nations. These two sectors are the traditional rural subsistence sector characterised by surplus labour (the excess supply of labour over and above the quantity demanded at the going free market wage rate). And the modern urban sector with high industrialization. This the Lewis model also calls the capitalist sector. The surplus theory assuming zero marginal productivity of labour in the rural sector posits that surplus labour should be transferred from the overpopulated rural sector to the high productive industrial sector. The model focuses on the movement/transfer of surplus labour from the rural to the urban sector and also the growth of the industrial urban sector in terms of output and employment. It is majorly interested in the growth and expansion of the modern sector.

Assumptions of the model
The model assumes the economy is divided into two sector, traditional rural sector and urban industrial sector( the capitalist sector).
There exists surplus labour in the traditional rural sector
There is mobility of labour from the rural to urban area.
The model assumes there is a perfectly competitive labour market in the modern sector given fixed wage rate and horizontal supply of labour.

Explaining the Lewis model
Given the subsistence and capitalist sector where the subsistence sector is identified with agriculture and considered labour intensive. Poor technices of production are employed Which leads to low productivity. It does not use reproducible capital. The capital sector on the other hand implies mainly the manufacturing sector of the economy where hired labour is required for the purpose of mass production and which can be private or public in nature.
The model opined that if a wage higher than the institutional wage prevailing in the subsistence sector by a certain proportion of the institutional wage is fixed in the capitalist sector. that is, if the labour wage in the capitalist sector is higher than what is obtained in the rural area then the capitalist sector have an an incentive to obtain more labour force from the rural area.
By so doing, the manufacturing sector is expanded and growth is experienced. More wealth is created and hence savings is increased. This increase in savings leads to capital accumulation. Investment is increased. More investment therefore means more employment of labour from the subsistence rural sector.
This process of capitalist (modern sector ) self sustaining growth and employment expansion is assumed to continue until the surplus rural labour is absorbed in the new modern sector, there after additional can be withdrawn from the subsistence sector only at a higher cost of food production because the declining labour to land production means that the marginal product of rural labour is no longer zero.
Criticism of the model
Even though the Lewis two sector model of development to a large extent relects the growth experiences of many developing countries, some of it’s basic assumptions has been brought under questioning and is considered invlid. These criticism include but not limited to;
The Lewis model is of the notion that surplus labour exists in the rural areas while there is full employment in the urban sector. However, most recent development economists are of the opinion that this notion not always true although there is seasonal and geographical exception to this. Labour availability varies by geographical and seasonal conditions.
Another criticism of the model is its assumption of a perfectly competitive modern market which guarantees continues existence of constant real urban wages up to the point where the supply of rural labour is exhausted. This assumption is considered not to hold as wages in modern sector are not constant but rises substantially over time birh in absolute terms and in relation to average rural wages. Institutional factors such as trade union bargaining power , civil service wage scales tends to oppose competitive forces in modern sector labour market in developing countries.
The model was also criticized for assuming diminishing returns in modern industrial sector when infact increasing returns are evidenced as prevailing in industrial sector.

IMPLICATION OF THE MODEL AND CONCLUSION.
The Lewis model analysis is obviously expressed in the growth experience of developing countries, Nigeria inclusive and most expecially China in recent times. It is common for labour to be shifted from the rural agricultural sector to the urban industrialised sector of the economy for the purpose of hiring in the manufacturing and service sectors to boost production.
This leads to expansion of the modern sector at the expense of the agricultural rural sector. An extreme effect would result in decline in agricultural productivity and eventually rise in price of essential goods such as food which is a major product of agriculture. This would also lead to increase in the price of industrial inputs such as raw materials from agriculture. In the long run, unemployment rate would increase in the modern sector.

Name: Ojigwe Shalom Chinaza
Department: Economics
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Harris-Todaro Model of Migration
This model was named after John R Harris and Michael Todaro in 1970, it was used to address development and welfare economics to explain certain issue that arose due to rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income. This simply means that people migrate to urban areas because they feel that there is a higher tendency to receive more income in the urban area than in rural areas
A simplified Harris-Todaro Model is given below:
• Let Wr be the wage rate (marginal productivity of labor) in the rural agricultural sector.
• Let Le be the total number of jobs available in the urban sector, which should be equal to the number of employed urban workers.
• Let Lus be the total number of job seekers, employed and unemployed, in the urban sector.
• Let Wu be the wage rate in the urban sector, which could possibly be set by government with a minimum wage law.
According to Harris-Todaro, Rural- Urban migration will take place if:
Wr (Le/Lus) * Wu
At equilibrium,
Wr=(Le/Lus) * Wu

With the random matching of workers to available jobs, the ratio of available jobs to total job seekers gives the probability that any person moving from the agricultural sector to the urban sector will be able to find a job. As a result, in equilibrium, the agricultural wage rate is equal to the expected urban wage rate, which is the urban wage multiplied by the employment rate.
Looking at the situation of Nigeria, people actually move to the urban regions because they believe that they will be able to make it in those places. They refer to the urban regions as “greener pastures”, but unfortunately, they ignore the fact that they could be worse-off in the cities because jobs are not being created to accommodate the new migrants. Also, certain jobs require specificities, in that it could be academic, intellectual and so on which often times these labourers from the rural area might not possess.
Also, an increase in inflow of labour to the urban area would have a negative impact on the wage rate.

Lewis-Fei Ranis model( Surplus Labour Theory)

The Lewis -Fei Ranis model is one of the best-known early theoretical models of development that focused on the structural transformation of a primarily subsistence economy was that formulated by Nobel laureate W. Arthur Lewis in the mid-1950s and later modified, formalized, and extended by John Fei and Gustav Ranis. The Lewis-Fei Ranis model is an improved version of the Lewis method of economic development. In 1954, Sir Arthur Lewis published a paper, “Economic Development with unlimited supplies of Labour”(The Manchester School), which was an elaborate discussion of the labour surplus economy. This model concentrated on a dual sector economy. A central theme of that article was that, labour in dual economies is available to the urban, industrialized sector at a constant wage determined by minimum levels of existence in traditional family farming because of ‘disguised unemployment in agriculture, there is practically unlimited supply of labour and available of industrialization, at least in the early stages of development. The basic assumption of the model is that there exists surplus labour in the subsistence sectors. It includes labour whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. According to Lewis model, this surplus labour is common in the rural areas and it’s basically agricultural. Lewis talks of an institutional wage, which he refers to as the wage which is as a result of institutional arrangements. The surplus labour in the agriculture sector acts as a source of unlimited supply of labour for the manufacturing sector.
The Lewis model is really simple. Sir Arthur Lewis feels that if a wage higher than the institutional wage prevailing in the subsistence sector by a certain proportion of the institutional wage is fixed in the capitalist sector the capitalist sector will be able to attract an unlimited quantity, the labour from subsistence sector. This will enable the capitalist sector to expand. It will, in turn lead to the generation of more savings in the capitalists sector.
The additional saving, will not only help the entrepreneurs to invest more but also to improve the quality of capital invested. This will result in more employment of labour from the subsistence sector. This will lead to generation of more savings in the Capitalist sector which can be further invested leading to employment of more surplus labour and so on. One of the biggest drawbacks of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. Arthur Lewis saw the agricultural sector as just a source of labour (surplus labour) to the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages. Fei-Ranis believed that labour could be transferred from the subsistence sector without a change in output. This simply implies that Fei-Ranis did not view the agricultural sector as just a source of labour for the industrial sector.Fei and Ranis emphasized strongly on the industry-agriculture interdependency and said that a robust connectivity between the two would encourage and speedup development. If agricultural laborers look for industrial employment, and industrialists employ more workers by use of larger capital good stock and labor-intensive technology, this connectivity can work between the industrial and agricultural sector. Also, if the surplus owner invests in that section of industrial sector that is close to soil and is in known surroundings, he will most probably choose that productivity out of which future savings can be channelized
Fei–Ranis model goes a step beyond and states that agriculture has a very major role to play in the expansion of the industrial sector. In fact, it says that the rate of growth of the industrial sector depends on the amount of total agricultural surplus and on the amount of profits that are earned in the industrial sector. So, larger the amount of surplus and the amount of surplus put into productive investment and larger the amount of industrial profits earned, the larger will be the rate of growth of the industrial economy. As the model focuses on the shifting of the focal point of progress from the agricultural to the industrial sector, Fei and Ranis believe that the ideal shifting takes place when the investment funds from surplus and industrial profits are sufficiently large so as to purchase industrial capital goods like plants and machinery. These capital goods are needed for the creation of employment opportunities. Hence, the condition put by Fei and Ranis for a successful transformation is that:Rate of increase of capital stock & rate of employment opportunities > Rate of population growth

In Nigeria, the assumption that labour employment must be higher than the population is highly impossible. The Fei-Ranis model ignored the aspect of population distribution, this is because there could be a case of the dependent population being higher than the independent population. In this situation, the population rate would be higher than those employed and the economy would not grow. Also, the concept of an institutional wage is quite far-fetched, it might not always be fair because there are other externalities that could affect the institutional wage. For example, In Nigeria today, politics, nepotism and corruption affects the institutional wage or rather the minimum wage.

Moreover, both models ignored the aspect of international trade, foreign direct investment and comparative advantage which in reality has a major role to play in labour supply, production of goods and services and economic growth.

LEWIS FEI RANIS MODEL
INTRODUCTION
The Fei Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be seen as the extention of the Lewis model. It is often also known as the Surplus Labour Model. It recognizes the presence of a dual economy or the existence of two separate economic sectors within a country which in this case comprises of the Modern and the Primitive sectors.
In the Lewis Fei Ranis model, the model takes into account the economic situation or economic problems of unemployment or underemployment of the various economic resources unlike many other models that retain that underdeveloped or developing countries are homogeneous in nature.
According to the assumption of the dual economy of the primitive and the modern economic sectors, the Primitive sectors comprises of the existing agricultural sectors in the economy while the modern sector is the fast growing but small industrial sector. The two sectors coexist in the economy. The model is quite unique in its own right but it agrees with the Harrod Domar model that both savings and investments becomes strong driving forces when it comes to the economic development of developing or underdeveloped countries.

THE MODEL

The Fei Ranis model assumed two sectors in the economy; the Primitive and the Modern economic sectors. These two sectors were believed to coexist in the economy together and this is where the crux of the development problem is. In this model, development can only brought about by a complete shift in the focal point of progress or a complete change of attention from the agricultural sector(primitive sector) to the industrial (modern) sector such that there is an augmentation of industrial output.
This is done by transfer of Labour from the agricultural sector to the industrial sector showing that underdeveloped or developing countries do not suffer from a shortage of labour or constraints of labour supply.
One of the biggest drawbacks or flaws of the Lewis model was the undermining or neglect of the role of agriculture in the in the boosting or in the aiding of growth of the industrial sector. In addition to that he (Lewis) did not acknowledge that the increase in productivity of labour was to take place prior or before the shift or movement of labour from the agricultural sector to the industrial sector. These two flaws were however was taken into account in the Fei Ranis dual economy model of three growth stages. They also argues that the model lacks in proper application of concentrated analysis to the change that takes place with agricultural sector.
In phase 1 of the Fei Ranis model, the elasticity of the agricultural labour work force is infinite and from this as a result suffers from hidden or disguised unemployment. Also the marginal product of labour is zero. This phase is similar to the Lewis model. In phase two of the Fei Ranis model, the agricultural sector of the dual economy sees a rise in productivity and this leads to an increase in the productivity of the industrial sector or an increase in the growth of the industrial sector. Here (phase 2), the agricultural Surplus may exist as the increasing average product (AP) higher than the marginal product (MP) but regardless not equal to the subsistence level of wages.
fig 1.1

According to the Fei and Ranis, AD amount of labour (from the figure above) can be shifted from the agricultural sector without any fall in output, hence it shows or represents “Surplus Labour”.
PHASE 1 : AL (from figure fig 1.1) = MP= 0, and AB = AP
After AP, MP begins to rise and industrial labour rises from zero to a value equal to AD. AP of agriculture labour is shown as BYZ a. D we see that the curve falls downward after AD. This fall in AP can be attributed or it is because of the fact that as agricultural laborers shift to the industrial sector, the real wage of labour decreased due to shortage of food also due to reduced productivity from the agricultural sector since compared to before the shift, there are now less labour or less workers in the agricultural sector. The decrease in wage rate also results in decrease in profits and the size of surplus that could have been reinvested for more industrialisation.
PHASE 2 = AP greater than MP
However, as long as surplus exists, growth rate can still be increased without a fall in the rate of industrialisation. This re-investment can be graphically realised in fig 1.1 as the outward shifting of the curve of the MP. In Phase 2, the disguised unemployment is represented as AK. This allows the industrial sector to give up some or part of its own labour force until MP equals Real wages
MP = REAL Wages = AB = Constant Institutional Wages(CIW).
Phase 3 begins at the point where the economy becomes conpletely and totally commercialized in the absence of the disguised unemployment. It (phase 3) starts at the point of commercialization which is “k” in the fig 1.1. The supply curve of labour in phase 3 is steeper and both the two sectors starts bidding or building for equity or equality in labour force
PHASE 3 = MP greater than CIW.
We know that there would be shifts in labour from the primitive or agricultural sector to the industrial or modern sector. The amount labour that is being shifted from the agricultural sector to the industrial sector and also the time that this shifting takes depends on;
1. The growth of surplus gotten or generated from or within agricultural sector and the growth of the capital stock gotten from the industrial sector dependent on the growth of industrial profits.
2. The nature of the industry’s technical progress and its associated bias
3. Growth rate of population.
Therefore the three main and fundamental ideas used in this model are;
1. The growth of the agricultural or primitive sector and the growth of the industrial sector or modern sector are both very important.
2. The growth of the industrial sector and also the agricultural sector is balanced.
3. Only if the rate at which labour is shifted from the agricultural sector or primitive sector to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the the Malthusian population trap which occur when the growth of the population becomes so much compared to the growth of agricultural products which would lead to famine or war causing poverty and de -population.
This shifting of labour can take place by landlord’s investments and also by the government’s fiscal policies or measures. However, the cost of the shifting of labour work force in terms of both private cost or social cost may be high for example transportation cost or the cost of buildings. Furthermore, per capita agricultural consumption can be increased or there can be a wide gap between the wages earned by the urban people and the wages earned by the rural workers.
These three occurences; High cost, High consumption and High gap in wages are known as “Leakages” and unfortunately leakage prevent the production or creation of agricultural Surplus. In fact surplus generation might be prevented due to a backward sloping supply curve of labour as well which happens when high income levels are not consumed. This would invariably mean that the productivity of labourers will not rise with a rise in income this however the case of backward sloping supply curves is clearly unpractical.
Fei and Ranis emphasized strongly on the agricultural-industrial interdependence and said that a large relationship between the two would speed up and encourage development. If agricultural laborers look for industrial employment and industrialists employ more workers by use of larger capital good stock and labour intensive technology, this connectivity can work between the agricultural and the industrial sector. Also if the Surplus owner invests in that section of industrial sector that is close to soil and is in known surroundings he would basically choose that productivity out of which future savings can be channeled.
AGRICULTURAL SECTOR
Fig 1.2
From fig 1.2 above, in land A land is measured in the vertical axis while labour is measured in the horizontal axis. OU and OV represent two ridged lines and the
production contour lines or curves are depicted by M, M1 and M2. The region or the area enclose by the ridge lines depict the region of factor substitutability or the area where factors can easily be substituted. The repercussion of this is that if the total amount of labour is the total labour in the agricultural sector, the intersection of the ridge line OV with the production curve M1 at point S renders M1 perfectly horizontal under or below OV. The horizontal behavior of the production line implies that outside the region of factor substitutability, output stops and labour becomes redundant once land is fixed and labour is increased.
If Ot is the total land in the agricultural sector, “ts” amount of labour can be employed without it being redundant and “es” is the redundant agricultural labour force. This led Fei and Ranis to develop the concept of LABOUR UTILIZATION RATIO (R) which they defined as the units of labour that can be productively employed without redundancy per unit of the land in use.
R=ts/Ot
They also built the concept of ENDOWNMENT RATIO (S) which is the measure of the relative availability of the two factors of production. From the figure above if Ot represents agricultural land and tE represents agricultural labour, then the endowment ratio is given as
S=tE/Ot
Which is equal to the inverted slope OE. The actual point of endownment is given by E
The third concept that Fei and Ranis came up with was that of the NON REDUNDANCY RATIO (T) which is measured by
T=ts/te.
These three concepts helped them in formulation a relationship between T, R and S given mathematically as
T= R/S
N/B
This mathematical relation shows that or proves that the non redundancy coefficient is directly proportional to labour utilization ratio and inversely to the endowment ratio.
Land B shows the total physical productivity of labour (TPPl) curve. The curve increases at a decreasing rate as more units of labour are added to a fixed amount of land. At point N, the curve shapes horizontally and this point N conforms to the point G in graph C which shows the marginal productivity of labour (MPPl) curve and with point S on the ridge line OV in graph A.

INDUSTRIAL SECTOR
Fig 1.3

Like in the agricultural sector, Fei and Ranis assumed a constant return to scale in the industrial sector. However, the main factors of production are labour and capital. In the graph A, we see that the production functions have plotted taking labour on the horizontal axis while capital is on the vertical axis. The expansion path or the road to development of the industrial sector is shown in the line 0A0A1A3. As capital increases from K0 to K1 to K2 and labour increases from L0 to L1 to L2, the industrial output represented by the production contour A0, A1 and A3 increases accordingly.
As earlier stated this model assumes the prime labour supply source of the industrial sector is the agricultural sector. Graph B shows the labour supply curve of the industrial sector S. PP2 represents the straight line part of the curve and is a measure of the redundant agricultural labour force on a graph with industrial labour force on the horizontal axis and output or real wages on the vertical axis. Due to the redundant agricultural labour force, the real wages remain constant. But once the curve starts going upwards from P2, the upward sloping indicates that additional labour would be supplied only with a corresponding rise in the real wages level. Total industrial activity rises with or due to the increase in the supply of investment funds, leading to more or increased industrial employment.

CONLUSION
The model has strong theoretical and policy implications on the underdeveloped countries’ efforts towards development. However the model has been criticized on many grounds. One of the criticisms is that Fei and Ranis did not have a clear understanding of the slow economic situation in the developing countries. If they had done more research, they would have found that the existing agricultural backwardness was due to the institutional structure, primarily the system of feudalism that prevailed. Another criticism is that Fei and Ranis assumed the MPPl to be zero during the early phases of economic development which was criticized by Harry T Oshima on the grounds that MPPl of labour is zero if only the agricultural population is very large. And if it is very large, some of that labour would rather shift to cities in search of work. Although in the short run, these labour that moved to the city would be unemployed but in the long run they would be absorbed by the informal sector. Fei and Ranis also assumed a closed economy leaving no room for foreign trade which is not only wrong but also unrealistic as goods can not be imported. Also foreign exchange is very vital for development especially for the developing countries.
Stagnation also was not taken into account and no distinction or difference was made between labour through family and labour through wages. There is also no explanation of the process of self sustained growth or of the investment function. There is a complete neglegence of the terms of trade between agriculture and industrial when the shift is to be made, foreign exchange, money and price.

HARRIS TODARO MODEL OF MIGRATION
The Harris TODARO model named after John R Harris and Micheal TODARO is an economic model that was developed in the early 1970s. This model is readily used in development economics and welfare economics to explain many problems or factors that relate to rural – urban migration. The model assumes primarily that the real reason why people would migrate from the rural to the urban areas is because of the expected wage rate, meaning that they believe that they would see or get a better income when they work. This means that tbe people would only migrate when the urban wage rate exceeds with a significant difference, the rural wage rate. This is mostly seen in developing countries as the move from less developed areas like their villages in search of “greener pastures”.

NAME: OMADA DORATHY AMARACHUKWU
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DEPARTMENT: ECONOMICS EDUCATION
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THE LEWIS- FEI-RANIS MODEL OF ECONOMIC GROWTH
INTRODUCTION
The Lewis (1954) theory of dualistic economic development provides the seminal contribution to theories of economic development particularly for labour-surplus and resource-poor developing countries. In the Lewis theory, the economy is assumed to comprise the agricultural and non-agricultural sectors. The agricultural sector is assumed to have vast amounts of surplus labour that result in an extremely low, close to zero, marginal productivity of labour. The agricultural wage rate is presumed to follow the sharing rule and be equal to average productivity, which is also known as the institutional wage. The non-agricultural sector has an abundance capital and resources relative to labour. It pursues profit and employs labour at a wage rate higher than the agricultural institutional wage by approximately 30 percent. The non agricultural sector accumulates capital by drawing surplus labour out of the agricultural sector. The expansion of the non-agricultural sector takes advantage of the infinitely elastic supply of labour from the agricultural sector due to its labour surplus. When the surplus labour is exhausted, the labour supply curve in the non-agricultural sector becomes upward-sloping. Ranis and Fei (1961) formalised Lewis’s theory by combining it with Rostow’s (1956) three “linear-stages-of-growth” theory. They disassembled Lewis’s two-stage economic development into three phases, defined by the marginal productivity of agricultural labour. They assume the economy to be stagnant in its pre-conditioning stage. The breakout point marks the creation of an infant non-agricultural sector and the entry into phase one. Agricultural labour starts to be reallocated to the non-agricultural sector. Due to the abundance of surplus agricultural labour, its marginal productivity is extremely low and average labour productivity defines the agricultural institutional wage. When the redundant agricultural labour force has been reallocated, the agricultural marginal productivity of labour starts to rise but is still lower than the institutional wage. This marks the shortage point at which the economy enters phase two of development. During phase two the remaining agricultural unemployment is gradually absorbed. At the end of this process the economy reaches the commercialisation point and enters phase three where the agricultural labour market is fully commercialised.
THE FEI- RANIS MODEL
The Fei –Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been develop by Johnc.h.fei and Gaustav Ranis and can be understood as an extension of the Lewis Model. It is also known as the The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod-Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries, in this model both primary and secondary sector are both driving force of economic development in developing countries.
COMPARISON BETWEEN THE TWO MODELS
Like Lewis model, Fei-Ranis model is also based on the Nurkse’s model of Economic Development. Fei-Ranis model tries to overcome the limitations of the Lewis model by incorporating certain major departures from it due to which Fei-Ranis model is seen as an improvement over the Lewis model. These departures are as under:
1. Lewis model invariably underscores the significance of the agriculture sector, it talks about a model of growth in which there is no interaction between the capitalist sector and agriculture sector, except that the surplus labour force moves from agriculture sector to the capitalist sector. In this model, one sector continues to grow while the other to lag behind, i.e. capitalist sector grows at the expense of the agriculture sector. However, Fei-Ranis model emphasize that the interaction between K sector and agriculture sector is significant and this interaction accelerates the process of overall economic development in the economy.
2. Fei-Ranis model is closer to reality prevailing in the LDC as it takes into account the impact of population growth on labour force. This feature is completely missing in Lewis model.
3. Lewis model does not assign any role to the landlord i.e. landlord is a passive factor and does not have any important role to play. But in Fei-Ranis model landlord plays an important role in the sense that he may be prompted to introduce innovation and technological progress in the agriculture sector under two circumstances:
(a) if the price of agriculture sector products is allowed to rise
(b) In case of subsidization of input cost
4. In Lewis model, the speed of transfer of labour force from agriculture to capitalist sector depends upon the growth of profits of the capitalist sector only. In Fei-Ranis model, it depends upon rate of growth of population, nature of technological progress and growth of industrial capital. Industrial capital depends upon growth of profits of industries and surplus generated in agriculture sector.
5. In the Lewis model, the end result is a lopsided pattern of development because capitalist sector grows at the expense of agriculture sector. The two cannot grow simultaneously and the gap tends to increase overtime. In the Fei-Ranis model on the other hand, balanced growth of capitalist and agriculture sector is necessary because otherwise the end product will be stagnation.
6. In Fei-Ranis model when the surplus labour force is exhausted, the supply of labour curve turns upward implying thereby that higher wage rate must be paid to the workers if more labourers are to be employed. In Lewis model, the supply curve is perfectly elastic.
Assumptions of Fei-Ranis Model
1. There is a presence of dual economy. Traditional or agriculture sector is passive and stagnant in nature while the capitalist sector is active and progressive in nature.
2. Supply of land is fixed, and both A sector and K sector makes use of the land.
3. Population is an exogenous factor i.e. it is determined by factors other than those present in the model.
4. Real wage rate in the industrial sector is fixed. This wage rate is equal to initial level productivity and is also called constant institutional wage rate.
5. There are constant returns to scale with respect to labour where labour acts as a variable factor in both A Sr and K Sr.
IMPACT OF THIS THEORY ON THE ECONOMY
The Lewis model of dualism also has some relevance to contemporary mainstream development models at the micro level. For example, the “informal insurance mechanism” of Townsend (1994) by which farmers smooth consumption by insuring each other across space is not radically different from the aforementioned “moral peasant” of Scott (1976) who is concerned with supporting others over time as well as space. Whether all this can be forced into a comforting neoclassical model or comes close to institutional altruism remains a point of contention, and one would hope that the current emphasis on the new institutional economics could potentially be an ally of the revival of the concept of dualism as an important guide to development theory and policy. In Townsend’s world, income is reallocated expost, i.e., after neoclassical distribution rules have been observed, while in the Lewis world, income is divided exante among members of the extended family or wider community. The policy implications for achieving a successful transition to modern economic growth probably don’t differ fundamentally depending on which of the concepts is deployed. But what remains relevant is which model fits better the basic empirical reality in successful labor abundant countries: which is better suited to analyze agricultural neglect in failure cases; which provides a better explanation of the marked early rise in the system’s savings rate; which is more capable of explaining discontinuities in income distribution and technical choice and the direction of technology change, a model that assumes full employment and smooth neoclassical equilibrium everywhere or one that recognizes initial underemployment and disequilibrium en route to a one sector modern economic growth epoch.
Lewis was basically a macro-economist, deeply immersed in economic history and the history of thought, both neglected subjects today. He always chose a general equilibrium approach, not only with respect to working within a domestic two-sector world but also with respect to the relationship of the typical developing country to the world economy, as indicated by his Wicksell and Janeway lectures (1969 and 1977). His notion of dualism, especially that focused on the labor market dimension, rural and urban, continues to offer a theoretically valid, empirically relevant and practically useful framework for dealing with some fundamental real world issues of development.

THE HARRIS- TODARO MODEL OF MIGRATION
INTRODUCTION

The model was an academic investigation to throw light on the events following ‘Tripartite Agreement’ in Kenya. The newly independent Kenya in the 1960s was increasingly facing a serious situation of unemployment in the major urban cities. To cope with the situation of unemployment, Tripartite Agreement was signed between the government public sector and the private sector. The agreement increased employment in the industrial jobs in exchange for unions agreeing to hold wages at their current levels. The larger number of employment was expected to reduce unemployment, but it appeared that the urban unemployment had increased following the government’s agreement. Harris and Todaro subsequently formulated a model to explain rural-urban economic preferences to migrate. The distinctive concept in the model is that the rate of migration flow from rural (agricultural) areas to urban (industrial) areas is determined by the difference between expected urban wages and rural wages.
The rural-urban two-sector model centrally holds the following futures:
1) Real wages (adjusted for cost-of-living differences) were higher in urban formal sector jobs than in rural traditional sector jobs.
2) To be hired for a formal sector job, it was necessary to be physically present in the urban areas where the formal sector jobs were located.
3) Consequently, from the first two features, more workers searched for formal sector jobs than were actually hired. Employers hired some of the searchers but not all of them.
4) To maintain equality between the expected wage associated with searching for an urban job and the expected wage associated with taking up a lower-paying rural job, the equilibrium arising in such a setting would be characterized by urban unemployment.
5) Any temporary difference in the expected wages between one sector and another would be eroded as workers migrate from the low expected wage labour market to the high expected wage one.
There are two regions: rural (agricultural) and urban (industrial) in two sector economic model. The crucial assumption of the Harris and Todaro’s model is that workers base their migration decision on their expected incomes at urban (industrial) areas. As the basic model is static, the expected income is just the weighted average of the urban wage and the unemployment benefit, the weights being the probabilities to find and not to find an urban job.
The fundamental contribution of Harris and Todaro’s rural-urban two sector migration model was to build a model that fit the stylized facts of the labour market. On the lines of the theory, developing countries adopted program on integrated rural development which encouraged an increase in the rural traditional sector wage. The theory proves that the higher the unemployment rate, the lower is the probability of new migrants from the countryside actively seeking formal sector employment who are unable to find it. The significant findings of the theory are: first, if the expected urban wage equals rural income, there is no incentive to migrate. Second, if the expected urban wage is greater than rural income, there is a great incentive to move from rural to urban area. Third, if the expected urban wage is less than rural incomes, there would be an incentive to move in other direction. Fourth, the expected urban wage depends on what type of job migrant is engaged in. Therefore, the Harris Todaro model helps policy-makers to avoid two mistakes. One is to assume that development efforts should necessarily be channeled to the sectors where the poor are. The other is to assume that efforts should necessarily be focused on getting the poor out of the sectors in which they presently are.

ASSUMPTIONS OF THE HARRIS- TODARO MODEL OF MIGRATION
Harris and Todaro studied the migration of workers in a two-sector economic system,
Namely, rural sector and urban sector. The differences between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function:
Ya = AaNa (1)
Where Ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa > 0 and 0 < _ 0 and 0 < _ 0 and > 0 are a parametric constants. Is the elasticity of p with respect to the ratio Ym/Ya. The overall population of workers in the economy is N, which is kept constant during the whole period of analysis. By assumption there are only two sectors and rural prices are wholly flexible, which implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period. Then at any period the following equality is verified:
Na + Nu = N.

CONCLUSION AND POLICY RECOMMENDATION
In this work we developed various assumptions model which formalizes the rural-urban allocation of workers as a process of social learning by imitation. We analyze a two-sectorial economy composed by adaptative agents, i.e., individuals that grope over time for best location in terms of earnings. This search is a process of imitation of successful neighbor agents. The dispersed and non-coordinated individual migration decisions, made based on local information, generate aggregate regularities. Firstly, the crucial assumption of Harris and Todaro, the principle that rural-urban migration will occur while the urban expected wage exceed the rural wage, comes out as spontaneous upshot of interaction among adaptative agents.
Secondly, the migratory dynamics generated by agents that seek to adapt to the economic environment that they concrete leads the economy toward a long run equilibrium characterized by urban concentration with urban unemployment. When this long run equilibrium is reached, the generalized Harris-Todaro condition is satisfied, i.e., there is a stabilization of the rural-urban expected wage differential. Thirdly, the impact of the minimum wage and elasticity of terms of trade in a long run equilibrium obtained by simulations are in agreement with the predictions of the original Harris-Todaro model with Cobb-Douglas technology. Finally, the simulations showed an aggregated pattern not found in the original Harris-Todaro model. There is the possibility of small fluctuations of the urban share around an average value. This phenomenon is known as reverse migration.

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LEWIS FEI RANIS MODEL OF ECONOMIC GROWTH
The perturbing question of “how to revive the failing economy of underdeveloped countries?” has continued to prevail over time, since the early post world war II era. Theories upon theories emerge, based on varieties of assumptions. However, some of these assumptions, which end up as unrealistic, make these theories inapplicable in so many underdeveloped countries. Fully called the Lewis-Ranis-Fei theory of dualistic economic development, the model provides a suitable theoretical framework for studying the growth path of labor-surplus in developing countries. In the theory, the economy is assumed to be divided into agricultural and industrial (also called non-agricultural) sectors. Whilst the agricultural sector is abundant in labor which leads to close to zero marginal productivity of labor, the industrial or non-agricultural sector has an abundance capital and resources relative to labor.
The Lewis Fei Ranis model is a pure extension of the Lewis model of 1954. Lewis in his model of “Development with Unlimited Supplies of Labor” represented a growth model of early industrialization in developing countries over the long run, which is now regarded as canonical to development economics (Fitzgerald, 2004). The model assumes a dual economy, of which there are two sectors, hereinafter called ‘modern’ and ‘traditional’, such that the modern sector grows by recruiting labor from the traditional. On a second note, unskilled labor is [aid less in the traditional sector compared to the modern sector. Additionally, unskilled labor is at inception more abundant such that at the current wage, much more labor is offered to the modern sector than that sector wishes to hire.

Lewis argued that the driver of capital accumulation was a sectoral movement of the factor of production abundant in developing countries, labor, from the ‘traditional’ or ‘noncapitalist’ sector (of low productivity, low wage, priced to average product not marginal product, and thus with widespread disguised unemployment) to the ‘modern’ or ‘capitalist’ sector (of higher productivity and where wages are set by productivity in the ‘subsistence sector’). (Andy, 2018)
The Lewis model emerged as a criticism of the neoclassical approach. This is in tandem to its tenets that labor is available to the modern or capitalist sector of an economy, not in a perfectly elastic supply but upward sloping rather than flat, and with a distinction between surplus-producing labor and subsistence labor. Conversely, the neoclassicals believe that the supply of labor is inelastic. Lewis equally criticized the assumptions of neoclassical economists of perfect competition, market clearing and full employment. Generally, in the Lewis model, growth is sustained by the transition of labor from traditional to modern sectors and this from low productivity to higher productivity sectors.

It was on this ground that Ranis and Fei (1964) modified the theory by combing the famous Rostow’s (1956) three “linear-stages-of-growth” theory. They formalized Lewis’s two-stage
economic development model into three phases, defined by the marginal productivity of
agricultural labor.

The following are the key assumptions of the Lewis Fei Ranis model. They include:
Surplus labor in subsistence sectors
Disguised unemployment exists in the agricultural sector
The capitalist sector invests all its savings for its expansion.
Besides labor, there is unlimited supply of entrepreneurs in the capitalist sector.
Capitalists will always reinvest their profit.
Landlords will always squander their savings.

APPLICATION OF THE LEWIS FEI RANIS MODEL IN THE NIGERIAN ECONOMY
As aforementioned, the Lewis Fei Rani’s model focuses on structural transformation. Structural transformation in this case is the process of transforming an economy in such a way that the contribution to the national income by the manufacturing sector exceeds the contribution by the agricultural sector. Just like Lewis connoted, it is obvious that the two sectors, traditional/agricultural and modern/industrial, are dominant in the Nigerian economy. However, several assumptions outlined by the model do not hold water in Nigeria.
There’s no doubt the country has a population of over 200 million, with a good number living in the rural areas. However, majority of this population do not engage in agriculture. In tandem with this, it is very important to understand that living in the rural area does not entail engaging in agricultural activities. In other words, the assumption that surplus labour exist in the agricultural sector does not fully apply to Nigeria. Take a look around and you’ll be amazed at the rate of agricultural import. Goods like coconut, cashew, raw sugar, wheat e.t.c, are imported. These goods would have been cultivated or better still, exported had the giant of Africa utilised it’s advantageous population.
Additionally, the model denoted that with labour transfer, growth is expanded in the modern sector. This growth is propelled and determined by the rate of industrial investment and capital accumulation in the modern sector. If this be the case, then there is little chances for the Lewis model. Taking the first determinant, the rate of industrial investment. Over time, the rate of investment in the country has been on the decline. This is as a result of the ever increasing political unrest coupled with insurgency of all size and shape. Also included is the increasing level of insecurity ravaging the economy and scaring away investors. All these put together will drastically reduce the level of capital accumulation, which is the second determinant.

HARRIS-TODARO MODEL OF MIGRATION
The Harris-Todaro model was developed in 1970 to explain imperative issues relating to rural-urban migration. The model was named after John R. Harris and Michael P. Todaro. The front line tenet of the model is that the decision to migrate is based on expected income differentials between rural and urban areas rather than just wage differences. According to the proponents of the model, unemployment is non existent in the rural agricultural sector. It further assumes perfect competition in the rural agricultural production and labour market.
MAJOR ARGUMENTS OF THE MODEL
The model propose that the sole purpose of the model is to explain the urban unemployment problem in developing countries. As described, the economic incentives, earning differentials and the probability of getting a job at a destination have influence on the migration decision. Harris and Todaro built this model in a bid to fit the stylized facts of the labour market. The theory clearly proves that with a higher unemployment rate, there is a lower probability of new immigrants seeking for employment. In other words, if the expected urban wage equals rural income, then there is no incentive to migrate.
APPLICATION OF THE HARRIS-TODARO MODEL TO THE NIGERIAN ECONOMY
As a third-world country, Nigeria is characterized by a very high population. One that is not necessarily common in other world countries. The analysis by Harris and Todaro is unrealistic in the Nigerian context especially with the nature of migration that the country is facing. It’s true that majority of the Nigerian populace are located in the rural area, but one flaw of the model is the assumption that the migration decision is determined by wage expectation. It is important to note that migration decision in Nigeria is not only determined by the wage differentials between the rural and urban sectors. Several other factors affect individuals decision during migration including traditional beliefs. So, migrants do not really expect to become employed on arrival. Finally, with increased migration from rural to urban areas, it is possible for quick adjustments to occur in the general employment level.

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THE LEWIS FEI RANIS MODEL (SURPLUS LABOUR THEORY)
In 1954, in his model Lewis divides the economy in an underdeveloped country in two sectors namely the subsistence sector and the capitalist sector. The subsistence is identified into agricultural sector while the capitalist was identified under the manufacturing sector of the economy.
The FEI RANIS model of Economic growth is a dualism model in developmental Economics or welfare Economics that has been developed by John C.H Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the surplus labour model. It recognises the presence of a dual economy comprising both the modern and the primitive sector and takes the Economic situation of unemployment and underemployment of resources into account, unlike other growth models that consider underdeveloped countries to the homogeneous in nature. One of the biggest drawback of the Lewis model was the undermining of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labour should take place prior to the labour shift between the two sectors. However, these two ideas were taken into account in the Fei Ranis dual economy model of three growth stages. They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place in the agricultural development.
The three fundamental ideas used in this model are: 1. Agricultural growth and industrial growth are both equally important.
2. Agricultural growth and industrial growth are balanced.
3. Only if the rate at which labour is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusium population trap.
THE ASSUMPTIONS OF THE LEWIS MODEL
* Surplus labour in the subsistence sectors – The basic assumptions of the model is that there exists surplus labour in the subsistence sectors. It include labour whose marginal productivity is positive but is less than the institutional wage. This labour comprises farmers, agricultural labourer and so on.
* Importance of Saving – Another important assumptions of Lewis model is about the savings generated in the capitalist sector and in the subsistence sector. The capitalist sector invests all its savings for its further expansion those in subsistence sector, on the other hand squander away their savings, if any in purchase of jewellery and for construction of temples. The propensity to save of the people in subsistence sector is lower when compared with that of those in the capitalist sector.
The Lewis model assumptions are:
1. There is surplus labour in the subsistence sectors.
2. Population growth is an exogenous phenomenon.
3. Land has no rule as a factor of production.
4. Industrial sector is a function of capital and land alone.
5. Supply of labour is fixed.
The model of Economic growth has been criticized on multiple grounds, although if the model is accepted then it will have a significant theoritical and policy implications on the underdeveloped countries efforts towards development and on the persisting controversial statements regarding the balanced and unbalanced growth debate.
1. The assumptions that disguised unemployment exists in the agriculture sector has not been accepted by many Economists like Schultz, Viner and so on. According to them, production in subsistence sector will be affected when labour is withdrawn from it.
2. Lewis ignored the cost involved in training the unskilled worker transferred from the subsistence sector. Even if it is obtained at a constant wage rate, so far as it’s transfer from the subsistence sector is concerned, the supply curve may slope upwards so far as the capitalist.
3. The model assumes that, besides labour, there is unlimited supply of entrepreneurs in the capitalist sector. This is not true in the case of many of the underdeveloped countries.
4. It is wrong to assume that a capitalist will always re-invest their profits they can indulge in unproductive pursuits. They can use their profits for speculative purposes.
5. The model assumes that there already exists a market for the industrial products in the country. This is wrong people of an underdeveloped country may not be able to purchase the products perturbed by the expanding capitalist sector. Foreign markets, too may not be available to capitalist sector in the beginning.
6. It is not easy to transfer labour from the subsistence sector to the capitalist sector by offering them an incentive of a little higher wage. Mobility of labour is very low. Many factors like family affection, difference in language, caste, religion etc. affect it adversely.
In conclusion, although Lewis FEI RANIS MODEL is flawed in multiple direction, it is still instrumental in explaining the stages of development in various cases.

THE HARRIS-TODARO MODEL OF MIGRATION
The Harris–Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.In the model, an equilibrium is reached when the expected wage in urban areas (actual wage adjusted for the unemployment rate), is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in China as the regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local governments’ main concern in many cities.
The formal statement of the equilibrium condition of the Harris–Todaro model is as follows:

1. Let wr be the wage rate (marginal productivity of labor) in the rural agricultural sector.
2. Let le be the total number of jobs available in the urban sector, which should be equal to the number of employed urban workers.
3. Let lus be the total number of job seekers, employed and unemployed, in the urban sector.
4. Let wu be the wage rate in the urban sector, which could possibly be set by government with a minimum wage law.
Rural to urban migration will take place if:

Wrle/Lus Wu

At equilibrium,

Wr=le/Lus Wu

With the random matching of workers to available jobs, the ratio of available jobs to total job seekers gives the probability that any person moving from the agricultural sector to the urban sector will be able to find a job. As a result, in equilibrium, the agricultural wage rate is equal to the expected urban wage rate, which is the urban wage multiplied by the employment rate.Therefore, migration from rural areas to urban areas will increase if:

Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

Todaro (1969) and Harris and Todaro (1970), the problem of underemployment and unemployment in the urban sector has long been a major focus in the economic analyses of LDCs. The Harris–Todaro model (hereafter, HT model), proposed in the two papers mentioned above, provides an interesting short-run analysis of labor migration between rural and urban areas and urban unemployment and underemployment in the urban informal sector.

In the HT model, workers determine migration between the sectors based on their expected wages. Thus, the workers decide to migrate to the urban sector when their expected wages there are higher than those in the rural sector. It is assumed in the HT model that the urban wage is institutionally and legally fixed, so that as a result of the migration of workers, if there are more workers than the number of new jobs, some workers would necessarily be unemployed. They have to enter the urban informal sector and be unemployed or underemployed there.

In general, capital accumulation in the urban sector is indispensable for economic development in LDCs. Although they all might be lumped together as “capital”, there are a lot of types and features. From the micro-perspective of a firm, machinery and equipment for production are one of the capital, capital stock such as internal reserves is also a capital. On the other hand, from the macro-perspective of an economy, social infrastructure such as airports, loading and port facilities, is also included in the capital. In this sense, industrial parks including the special economic zones (hereafter, SEZs) are one of the most important social capital. Accumulated capital, such as the SEZs in the urban industrial parks creates new job opportunities. In particular, construction of the SEZs invites many foreign companies, since in the SEZs the corporation tax is treated well. Therefore, through the exemption or discount from the corporation tax, the companies operating in the SEZs can reduce their operation costs and could become profitable.

In the process of economic development in LDCs, it has been repeatedly observed that as foreign capital creates new employment opportunities, there is an increase in worker flow from rural areas to urban areas with a concomitant decrease in per-capita income in the urban area. This phenomenon is generally referred to as the “Todaro paradox” in the field of development economics

The most significant feature of this model is that it made it possible for analysts to deal with unemployment, within the framework of general equilibrium, by including still unemployed workers who were waiting for job opportunities in the urban sector, a factor that had previously been difficult to assess. It gave rise to a more realistic description of developing economies and helped to explain migration between urban and rural areas theoretically.

The HT model is a specific form of the “neo-classical two sectors model”, represented by the “Heckscher, Ohlin and Samuelson model” (hereafter HOS model), and it can be understood as a “specific factor model” (hereafter SF model), proposed by Jones (1971). In the SF model, each sector has its own specific production factor which cannot move between sectors, and the specific factor endowments are also fixed. The HT model is a short-run model with fixed specific capital endowment in each sector. In this paper, however, we examine the effects that the urban capital is exogenously increased by such as economic supports or development aid by advanced foreign countries. The Harris-Todaro model of the rural-urban migration process is revisited under an agent-based approach. The migration of the workers is interpreted as a process of social learning by imitation, formalized by a computational model. By simulating this model, we observe a transitional dynamics with continuous growth of the urban fraction of overall population toward an equilibrium. Such an equilibrium is characterized by stabilization of rural-urban expected wages differential (generalized Harris-Todaro equilibrium condition), urban concentration and urban unemployment. These classic results obtained originally by Harris and Todaro are emergent properties of our model.

ARGUMENTS AND ASSUMPTIONS OF THE HARRIS-TODARO MODEL OF MIGRATION
Harris Todaro model explains some issues of rural-urban migration. ThisHarris Todaro model explains some issues of rural-urban migration. This migration happens in case when expected rural income is higher than rural wages. In this case economy may have high rates of unemployment. The equilibrium condition of this model is when expected rural wage is equal to rural wage. migration happens in case when expected rural income is higher than rural wages. In this case economy may have high rates of unemployment. The equilibrium condition of this model is when expected rural wage is equal to rural wage.The model assumes that unemployment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The difference between these sectors are the type of goods produced, the technology of production and the process of wage determination. The rural sector is specialized in the production of agricultural goods. The productive process of this sector can be described by a Cobb-Douglas production function.
The rate of population growth is the rate of natural increase combined with the effects of migration. Thus a high rate of natural increase can be offset by a large net out-migration, and a low rate of natural increase can be countered by a high level of net in-migration.
The assumptions of the Harris Todaro model of migration include;
1. Two sectors: Urban(manufacturer) and rural(agriculture).
2. Rural – Urban migration condition when urban real wage exceeds real agricultural product.
3. Perfect competition.
4. Cobb-Douglas production function.
5. Low risk aversion.
6. Static approach.
7. No migration cost.
In any case, the Harris Todaro model suffers from theoretic oversimplification, among which several are likely to overestimate the link. The critiques revolve around the three major points;
1. The model framework is only a static model describing migration, which is a dynamic phenomenon by nature. Even though the model can be thought of as representing a steady state equilibrium,this is a limitation. Furthermore, the formalization is made in a partial equilibrium context which greatly weakens the justification for policy recommendations.
2. The assumptions that urban workers are either employed in the manufacturing sector or unemployed has been criticized as too simplistic even though, in the authors’ minds, it was implicit that unemployment could also be interpreted as underemployment in the informal sector.
3. The Harris-Todaro model assumes that the urban wage is exogenously set above the endogenous rural wage . The assumption that wages are high find several explanations ranging from the existence of trade unions to the agglomeration of economic activities. It is confirmed in practice,since wages are often reported three to four times higher in urban areas than in rural areas (Todaro, 2000). What is more problematic, however, is the assumption that the urban wage is fixed, especially in the presence of an informal sector as typical of many developing economies. In fact, the argument of a minimum wage should only hold for low wages in the formal sector, unless remunerations in the informal sector align themselves with those in the formal sector (due to the competition for labor between employers)In addition, the wage in the Harris-Todaro model is not related to unemployment in any manner. If the urban wage tends to decrease with an increase in the unemployment rate as argued by Hoddinott (1996) in his study on urban African labor markets, then this would tend to reduce the expected earnings differential in the transition towards the equilibrium in the model. This gives another reason why migration flows could be overestimated, making the Todaro paradox even less likely to occur.
In concluion, The model explains some issues of the rural urban migration. The migration happens in case when expected rural income is higher than rural wage. In this case economy may have high rates of unemployment. The equilibrium condition of this model is expected when rural wage is equal to rural wage.
Therefore, migration from rural areas to urban areas will increase if:

Urban wages (wu) increase in the urban sector (le), increasing the expected urban income.
Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector (wr), decreasing the expected rural income.
However, even though this migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility-maximizing in the context of the Harris–Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income-maximizing decision.

Name: Egbo Chiinemelum Chinonso
Reg no: 2017/249493
Email: egboemecs@gmail.com
Answer:
Harris-Todaro Migration Model

The Harris-Todaro model, named after John R. Harris and Michael Todaro, is an economic model developed in 1970 and used in development economics and welfare economics to explain some of the issues concerning rural-urban migration. The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. This implies that rural-urban migration in a context of high urban unemployment can be economically rational if expected urban income exceeds expected rural income.
Todaro accepts the logistics of Lewis-Fei-Ranis model of rural-urban migration but only with reservations. According to him, this theory may correspond to the historical scenario of migration in the western socio-economic milieu but does not explain the trends of rural-urban migration in less developed countries.
Starting from the assumption that migration is primarily an economic phenomenon, which for the individual migrant can be a quite rational decision despite the existence of urban unemployment, the Todaro model postulates that migration proceeds in response to urban-rural differences in expected income rather than actual earnings. The fundamental premise is that migrants consider the various labor market opportunities available to them in the rural and urban sectors and choose the one that maximizes their expected gains from migration.
Todaro migration model: A theory that explains rural-urban migration as an economically rational process despite high urban unemployment. Migrants calculate (present value of) urban expected income (or its equivalent) and move if this exceeds average rural income.
Harris-Todaro model: An equilibrium version of the Todaro migration model that predicts that expected incomes will be equated across rural and urban sectors when taking into account informal sector activities and outright unemployment.
The Harris-Todaro equation is
wa= βwm
Where wa is the flexible wage in the agricultural sector which is equated to the value of the marginal product in that sector, β is the probability of employment, depending on the number of newly created jobs and the size of the population of the urban unemployed, and wm is the wage in the manufacturing sector and is assumed to be fixed institutionally (either because of union activities or a friendly government towards to the workers in the modern sector) above the competitive level.

Migration and how it affects the Real World

Migration worsens rural-urban structural imbalances in two direct ways.
First, on the supply side, internal migration disproportionately increases the growth rate of urban job seekers relative to urban population growth, which itself is at historically unprecedented levels because of the high proportion of well-educated young people in the migrant system. Their presence tends to swell the urban labor supply while depleting the rural countryside of valuable human capital. Second, on the demand side, urban job creation is generally more difficult and costly to accomplish than rural job creation because of the need for substantial complementary resource inputs for most jobs in the industrial sector. Moreover, the pressures of rising urban wages and compulsory employee fringe benefits in combination with the unavailability of appropriate, more labor-intensive production technologies means that a rising share of modern-sector output growth is accounted for by increases in labor productivity. Together this rapid supply increase and lagging demand growth tend to convert a short-run problem of resource imbalances into a long-run situation of chronic and rising urban surplus labor.
But the impact of migration on the development process is much more pervasive than its exacerbation of urban unemployment and underemployment. In fact, the significance of the migration phenomenon in most developing countries is not necessarily in the process itself or even in its impact on the sectoral allocation of human resources. Rather, its significance lies in its implications for economic growth in general and for the character of that growth, particularly its distributional manifestations. We must therefore recognize that migration in excess of job opportunities is both a symptom of and a contributor to underdevelopment. Understanding the causes, determinants, and consequences of internal rural-urban labor migration is thus central to understanding the nature and character of the development process and to formulating policies to influence this process in socially desirable ways. A simple yet crucial step in underlining the centrality of the migration phenomenon is to recognize that any economic and social policy that affects rural and urban real incomes will directly or indirectly influence the migration process. This process will in turn itself tend to alter the pattern of sectoral and geographic economic activity, income distribution, and even population growth. Because all economic policies have direct and indirect effects on the level and growth of urban or rural incomes or both, they all will have a tendency to influence the nature and magnitude of the migration stream. Although some policies may have a more direct and immediate impact (e.g., wages and income policies and employment promotion programs), there are many others that, though less obvious, may in the long run be no less important. Included among these policies, for example, would be land tenure arrangements; commodity pricing; credit allocation; taxation; export promotion; import substitution; commercial and exchange-rate policies; the geographic distribution of social services; the nature of public investment programs; attitudes toward private foreign investors; the organization of population and family planning programs; the structure, content, and orientation of the educational system; the functioning of labor markets; and the nature of public policies toward international technology transfer and the location of new industries. There is thus a clear need to recognize the central importance of internal and, for many countries, even international migration and to integrate the two-way relationship between migration and population distribution on the one hand and economic variables on the other into a more comprehensive framework designed to improve development policy formulation.
In addition, we need to understand better not only why people move and what factors are most important in their decision-making process but also what the consequences of migration are for rural and urban economic and social development. If all development policies affect migration and are affected by it, which are the most significant, and why? What are the policy options and trade-offs among different and sometimes competing objectives (e.g., curtailing internal migration and expanding educational opportunities in rural areas)?
Part of our task in the following sections will be to seek answers to these and other questions relating to migration, unemployment, and development. Migration patterns are complex. The most important type of migration from the standpoint of long-run development is rural-urban migration, but a great deal of rural-rural, urban-urban, and even urban-rural migration also takes place. Rural-urban migration is most important because the population share of cities is growing, despite the fact that fertility is much lower in urban areas, and the difference is accounted for by rural-urban migration. It is also important because of the potential development benefits of economic activity of cities, due to agglomeration economies and other factors. However, urban-rural migration is important to understand because it usually occurs when hard times in cities coincide with increases in output prices from the country’s cash crops, as occurred in Ghana not long ago. Thus the overall picture is one of a remarkable amount of “churning,” or continuous movements of people within developing countries, especially over short distances.

Critiques of the Todaro Model by Williamson (1988)

1. The lottery style job allocation excludes investment in job search on the part of the immigrants;
2. The informal sector is not explicitly modelled;
3. There is not enough evidence to support the assumption of a rigid wage in the modern sector. Moreover, besides trade union pressure or minimum wage legislation, the wage differentials among sectors could be explained as well by, say, firm-specific training costs;
4. The issue of discount rates and rational migrants is ignored;
5. The influence on decision making of risk and risk attitudes on the part of the potential immigrants is not included; and
6. Differentials in skill levels among the migrants are not accounted for.

Basic Characteristics of the Todaro Migration Model

1. Migration is stimulated primarily by rational economic consideration of relative benefits and costs, mostly financial but also psychological.
2. Migration is decided on the basis of expected, rather than actual, urban-rural wage differentials where the expected differential is determined by the interaction of two variables, the actual urban-rural wage differential and the probability of successfully obtaining employment in the urban sector.
3. Probability of obtaining urban job is inversely related to the urban unemployment rate and thus inversely related to the urban unemployment rate.
4. Migration rates in excess of urban job opportunity growth rates are not only possible but also rational and even likely in the face of wide urban-rural expected income differentials.

Implications of the Todaro Migration Model

First, imbalances in urban-rural employment opportunities caused by the urban bias, particularly first-city bias, of development strategies must be reduced. Because migrants are assumed to respond to differentials in expected incomes, it is vitally important that imbalances between economic opportunities in rural and urban sectors be minimized. When urban wage rates rise faster than average rural incomes, they stimulate further rural-urban migration in spite of rising levels of urban unemployment.
Second, urban job creation is an insufficient solution for the urban unemployment problem. The traditional (Keynesian) economic solution to urban unemployment (the creation of more urban modern-sector jobs without simultaneous attempts to improve rural incomes and employment opportunities) can result in the paradoxical situation where more urban employment leads to higher levels of urban unemployment! Once again, the imbalance in expected income-earning opportunities is the crucial concept. Because migration rates are assumed to respond positively to both higher urban wages and higher urban employment opportunities (or probabilities), it follows that for any given positive urban-rural wage differential (in most developing countries, urban wages are typically three to four times as large as rural wages), higher urban employment rates will widen the expected differential and induce even higher rates of rural-urban migration. For every new job created, two or three migrants who were productively occupied in rural areas may come to the city.
Finally, programs of integrated rural development should be encouraged. Policies that operate only on the demand side of the urban employment picture, such as wage subsidies, direct government hiring, elimination of factor price distortions, and employer tax incentives, are probably far less effective in the long run in alleviating the unemployment problem than policies designed directly to regulate the supply of labor to urban areas. Clearly, however, some combination of both kinds of policies is most desirable.

Solutions to the Rural-Urban Migration Problem

1. Creating an appropriate rural-urban economic balance. A more appropriate balance between rural and urban economic opportunities appears to be indispensable to ameliorating both urban and rural unemployment problems and to slowing the pace of rural-urban migration. The main thrust of this activity should be in the integrated development of the rural sector, the spread of rural nonfarm employment opportunities, improved credit access, better agricultural training, the reorientation of social investments toward rural areas, improving rural infrastructure, and addressing shortcomings of rural institutions (including corruption, discrimination, and stratification), the presence of which has the effect of raising the cost of delaying out-migration.
2. Eliminating factor price distortions. There is ample evidence to demonstrate that correcting factor price distortions-primarily by eliminating various capital subsidies and curtailing the growth of urban wages through market-based pricing-would increase employment opportunities and make better use of scarce capital resources. But by how much or how quickly these policies would work is not clear. Moreover, their migration implications would have to be ascertained. Correct pricing policies by themselves are insufficient to fundamentally alter the present employment situation.
3. Reducing population growth. This is most efficiently accomplished through reductions in absolute poverty and inequality, particularly for women, along with the expanded provision of family-planning and rural health services. The labor force size for the next two decades is already determined by today’s birth rates, and hidden momentum of population growth applies as well to labor force growth.

Egbo Chiinemelum Chinonso

The Lewis-Fei- Ramis Model

One of the best-known early theoretical models of development that focused on the structural transformation of a primarily subsistence economy was that formulated by Nobel laureate W. Arthur Lewis in the mid-1950s and later modified, formalized, and extended by John Fei and Gustav Ranis. The Lewis two-sector model became the general theory of the development process in surplus-labor developing nations during most of the 1960s and early 1970s, and it is sometimes still applied, particularly to study the recent growth experience in China and labor markets in other developing countries. In the Lewis model, the underdeveloped economy consists of two sectors: a traditional, overpopulated rural subsistence sector characterized by zero marginal labor productivity—a situation that permits Lewis to classify this as surplus labor in the sense that it can be withdrawn from the traditional agricultural sector without any loss of output—and a high-productivity modern urban industrial sector into which labor from the subsistence sector is gradually transferred. The primary focus of the model is on both the process of labor transfer and the growth of output and employment in the modern sector. (The modern sector could include modern agriculture, but we will call the sector “industrial” as a shorthand). Both labor transfer and modern-sector employment growth are brought about by output expansion in that sector. The speed with which this expansion occurs is determined by the rate of industrial investment and capital accumulation in the modern sector. Such investment is made possible by the excess of modern-sector profits over wages on the assumption that capitalists reinvest all their profits. Finally, Lewis assumed that the level of wages in the urban industrial sector was constant, determined as a given premium over a fixed average subsistence level of wages in the traditional agricultural sector. At the constant urban wage, the supply curve of rural labor to the modern sector is considered to be perfectly elastic.
Lewis two-sector model: A theory of development in which surplus labor from the traditional agricultural sector is transferred to the modern industrial sector, the growth of which absorbs the surplus labor, promotes industrialization, and stimulates sustained development.
Surplus labor: The excess supply of labor over and above the quantity demanded at the going free-market wage rate. In the Lewis two-sector model of economic development, surplus labor refers to the portion of the rural labor force whose marginal productivity is zero or negative.
Production function: A technological or engineering relationship between the quantity of a good produced and the quantity of inputs required to produce it.
Average product (AP): Total output or product divided by total factor input (e.g., the average product of labor is equal to total output divided by the total amount of labor used to produce that output).
Marginal product (MP): The increase in total output resulting from the use of one additional unit of a variable factor of production (such as labor or capital). In the Lewis two sector model, surplus labor is defined as workers whose marginal product is zero.

Criticisms of the Lewis Model

First, the model implicitly assumes that the rate of labor transfer and employment creation in the modern sector is proportional to the rate of modern sector capital accumulation. The faster the rate of capital accumulation, the higher the growth rate of the modern sector and the faster the rate of new job creation. But what if capitalist profits are reinvested in more sophisticated laborsaving capital equipment rather than just duplicating the existing capital, as is implicitly assumed in the Lewis model? (We are, of course, here accepting the debatable assumption that capitalist profits are in fact reinvested in the local economy and not sent abroad as a form of “capital flight” to be added to the deposits of Western banks.)
The second questionable assumption of the Lewis model is the notion that surplus labor exists in rural areas while there is full employment in the urban areas. Most contemporary research indicates that there is little surplus labor in rural locations. True, there are both seasonal and geographic exceptions to this rule (e.g., at least until recently in parts of China and the Asian subcontinent, some Caribbean islands, and isolated regions of Latin America where land ownership is very unequal), but by and large, development economists today agree that Lewis’s assumption of rural surplus labor is generally not valid.
The third dubious assumption is the notion of a competitive modern sector labor market that guarantees the continued existence of constant real urban wages up to the point where the supply of rural surplus labor is exhausted. Prior to the 1980s, a striking feature of urban labor markets and wage determination in almost all developing countries was the tendency for these wages to rise substantially over time, both in absolute terms and relative to average rural incomes, even in the presence of rising levels of open modern-sector unemployment and low or zero marginal productivity in agriculture. Institutional factors such as union bargaining power, civil service wage scales, and multinational corporations’ hiring practices tend to negate competitive forces in modern-sector labor markets in developing countries.
A final concern with the Lewis model is its assumption of diminishing returns in the modern industrial sector.

Okoye Felix Onyekachi 2017/241446
Felix.okoye.241447@unn.edu.ng

THE LEWIS-FEI-RANIS MODEL OF ECONOMIC GROWTH
This model was originally proposed by W. Arthur Lewis in 1954 and was later expanded upon by two Economists, John C. H. Fei and Gustav Ranis in 1961. It was drawn out from the Lewis model, and it is as well known as the Surplus labour model.
Unlike many development theories, theLewis- Fei-Ranis models takes into account a situation of unemployment and underemployment of Labour. The theory begins with the assumption of a two-sector economy comprising the primitive sector and the modern sector. The primitive sector is primarily agrarian in nature constituting the agricultural sector whilst the modern sector is made up of the industrial sector.
The central thesis of the model is that an economy can only achieve economic development by prioritising the development and expansion of the modern sector so as to increase industrial output. This can be achieved by channeling labour from the agricultural sector to the industrial sector. This does not mean however that the agricultural sector should be totally neglected. The agricultural sector should be competitive enough to supply the economy with food and the industrial sector with raw mmaterials.
In the Lewis theory an economy transits from ‘labour Surplus’ to the ‘labour scarce’ stage but in the Fei-Ranis Model the first stage in the Lewis model is split into two stages, thereby having three growth stages . This three growth stages are explained thus:
The first growth stage is characterised by superfluos labour and thus has a marginal productivity of zero due to the excess supply of labour.The second growth stage is characterised by disguised unemployment which arises as a result of regallocation of the Surplus labour from the agricultural sector to the industrial sector. In this stage, the marginal productivity of labour in the agricultural sector is rising but is still below the institutional wage they earn. This implies that APL<MPL and there's still room for further re-allocation of labour from the agricultural sector to the industrial sector.
The third stage describes an economy in which MPL is greater than the institutional wage received and this stage kick-starts the era of self-sustainable economic growth wherein there is a complete commercialisation of the agricultural sector and the Surplus labour no longer exist.
Unlike many growth models which propose for a complete neglect of the agricultural sector in the process of advancing the industrial sector, the Lewis-Fei-Ranis Model still recognises the importance of the agricultural sector to economic development. This can be seen in the assumption of Surplus agricultural labour which they argue should be transferred to the industrial sector for a sustained economic growth.
Bringing it to the Nigerian economy, Nigerian economy is still primarily agrarian in nature as the bulk of the country's foreign exchange earnings come from the sale of raw materials and agricultural products. In comparison with the Lewis-Fei-Ranis Model, Nigeria seems to be lying either in the first stage, the stage of Surplus labour where the marginal productivity of labour is zero or the second stage, the stage of disguised unemployment, wherein the marginal productivity of labour is rising but is still below the institutional wage rate. Following the argument of the Lewis-Fei-Ranis Model, more Surplus labour had to be re-allocated to the industrial sector for the Nigerian economy to achieve the the third stage i.e the stage of sustainable economic growth. But in reality, what the Nigerian economy needs to take off is not further re-allocation of Surplus agricultural labour to the urban sector. This is because the Nigerian urban sector is already saturated with labour Surplus to requirement thus leading to a situation of great underemployment and unemployment. Nigeria has to devise a way of solving her urban unemployment problem by expanding the industrial sector so as to increase the industrial output.

THE HARRIS-TODARO MODEL OF MIGRATION
INTRODUCTION
John Harris and Michael Todaro formulated the Harris-Todaro model to explain the high unemployment rate besetting the economies of the less developed countries in the 1960's.
The Harris-Todaro model studied in particular the economy of Kenya.Shortly after independence, Kenya's economy experienced a high rate of unemployment in their major cities . In an effort to overturn this problem, the Kenyan government implemented some policies that aimed at increasing employment in the urban areas.
However, while this policy indeed increased the number of jobs in the urban sector, the rate of urban unemployment increased rather than reduced.The Harris-Todaro model was an attempt to explain this paradox.
The Harris-Todaro hypothesis sharply contrasts with the structural change models, particularly the Lewis theory of labour transfer which postulates that for developing countries to experience a significant growth, they need to transfer a significant proportion of their labour force from the agricultural sector to the industrial sector through rural-urban migration.
The main argument of the Harris and Todaro's theory of migration is that economic incentives, earning differetials and the probability of getting a job at the new destination are the major factors influencing migration decisions of individuals.
ASSUMPTIONS
The Harris-Todaro's theory is built on the following underlying assumptions:
(i)Emphasis is laid on two sectors of the economy, the rural sector and the urban sector.The two sectors differ from each other on th type of goods produced, the technology employed in its production and th proces of wage determination.The rural sector specializes in the production of agricultural goods and uses labour as the only input factor.The rural sector on the other hand specializes in the production of industrial goods and like the rural sector uses labour as the only input factor.
(ii)Migration decisions are based on expected income differentials between the rural and urban sectors rather than just wage differentials.This assumption implies that migration is primarily an economic phenomenon, which for the individual migrant can be a quite rational decision despite the existence of urban unemployment, the Harris-Todaro's model postulates that migration proceeds in response to urban-rural differences in expected income rather than actual earnings. The fundamental premise is that migrants consider the various labor market opportunities available to them in the rural and urban sectors and choose the one that maximizes their expected gains from migration.
(iii)Both goods and labor markets are perfectly competitive.This implies that the agricultural wage is equal to the agricultural marginal productivity.Although both the goods and labour markets are perfectly competitive, there is a segmentation in the labor market due to a high minimum urban wage politically determined.
(iv)Unemployment is nonexistent in the rural sector.This implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period.
It is also assumed that equilibrium is reached when the expected wage in the urban sector is equal to the marginal product of the rural worker.In equilibrium, the rural-urban migration will be zero since the expected rural income equals the expected urban income.
Analysing the Assumptions:
In a full-employment environment,the decision to migrate can be based solely on the desire to secure the highest-paid job wherever it becomes available. Simple economic theory would then indicate that such migration should lead to a reduction in wage differentials through the interaction of the forces of supply and demand .
Sadly, such an assumption is not realistic in the context of the institutional and economic framework of most developing nations.This is because, these countries are faced with a high unemployment problem, which implies that a typical migrant cannot expect to gain a high-paying urban job immediately.In reality, most migrants who do not have high educational qualifications or those who are not highly skilled often find themselves doing manual jobs. In the case of migrants with considerable human capital in the form of a secondary or university certificate, opportunities are much brighter, and a lot will find formal-sector jobs relatively fast. But they make up only a tiny fraction of the total migration. As a result of this, in deciding to migrate, the migrant must balance the probabilities and risks of being unemployed or underemployed for a considerable period of time against the positive urban-rural real income differential.
The fact that a typical migrant who gains an urban sector job can expect to earn double the yearly real income in an urban area than in a rural area may not really be an issue of great importance if the chances of his securing the higher-paying job within a particular period is one chance in eight and the urban wage is $80 against rural wage of $40.Thus the actual probability of his being successful in securing the higher-paying urban job is 10%, and thus his expected urban income for that period is in fact 10 units and not the 80 units that an urban worker in a full-employment environment would expect to receive. Note that we are assuming that his rural income is 40 units. So it would not be rational for this particular migrant to seek urban employment despite the fact he will earn double of his rural income if he migrated .
However, if the chances of success were 70% and the expected urban income thus 56 units, pursuing an urban employment will be a rational decision even though urban unemployment might be high.If we approach this analysis using a longer time frame, then the decision to migrate will still be rational because the chances of the migrant securing urban job gets brighter as he stays in the city.As long as the expected urban income is higher than the expected rural income over a longer time horizon, migration decisions will always be rational. Thus instead of equating urban and rural wage rates, we see that rural-urban migration in the Harris-Todaro model equates rural and urban expected incomes.
Thus, equilibrium is reached in the Harris-Todaro model when the agricultural wage equals the the ratio of urban employment and urban Labour force multiplied by the urban wage. In this equilibrium, there will be no tendency to migrate since the expected rural income equals the expected urban income. Hence migration will be zero.

CONCLUSION
We observed that even though migrants respond sharply to differences in economic opportunities between the two sectors as postulated by Harris and Todaro, in reality, all urban migrants are not the same in terms of human capital endowments. The more educated ones tend to migrate more because they have brighter chances of securing urban job.
Migrants create positive externalities for future potential migrants by providing them with information about job availabilities. In reality, this lowers their unemployment probabilities.
The Harris-Todaro model contends that migration is determined mainly by rational economic considerations of relative benefits and costs. The actual urban-rural wage differentials and the probability of successfully obtaining employment in the urban sector are the major determinants of migration decisions. While we agree with this postulation, it is important to point out that in the real world, migration is not purely an economic phenomenon. Other factors such as psychological factors affect migration as well.
The probability of getting an urban employment is directly proportional to the urban environment rate and indirectly proportional to the urban unemployment rate.
Wide imbalances in economic opportunities between the the urban and rural sectors is the reason for urban unemployment. This economic imbalance is in form of wage differences but in the real world, it could include other economic opportunities such as the chances of accessing a better health care and education. Moreover, migration in the face of high urban unemployment is not only possible but rational due to the wide margin between the two sectors with respect to economic opportunities.
Governments should not place greater priority to the cities in terms of development strategies. This is because, developing the urban sector while neglecting the rural sector creates a huge economic imbalances, and as we pointed earlier, this scenario creates further rural-urban migration despite the rising urban unemployment rate, thereby causing a lot of socioeconomic problems like the increase in crime wave in the cities and shortage of food due to the shortage of agricultural workers. Reducing the economic imbalances between the rural sector and the urban sector is key to solving the rural-urban migration and its associated negative repercussions.
Creating more urban employment with the purpose of solving the urban unemployment problem without cuncurrently developing the rural sector is a mistaken policy.This could worsen the unemployment situation in the urban sector. This is because, in the face of a sharp contrast between the two sectors in terms of economic opportunities, any increase in urban employment rate will result to a tripple increase in rural-urban migration rate.
Therefore, any policy that will reduce urban unemployment will aim to develope the rural sector so as to reduce or minimize the rate of rural-urban migration.

Okoye Felix Onyekachi
2017/241446
Felix.okoye.241447@unn.edu.ng

THE LEWIS-FEI-RANIS MODEL OF ECONOMIC GROWTH
This model was originally proposed by W. Arthur Lewis in 1954 and was later expanded upon by two Economists, John C. H. Fei and Gustav Ranis in 1961. It was drawn out from the Lewis model, and it is as well known as the Surplus labour model.
Unlike many development theories, the Lewis- Fei-Ranis models takes into account a situation of unemployment and underemployment of Labour. The theory begins with the assumption of a two-sector economy comprising the primitive sector and the modern sector. The primitive sector is primarily agrarian in nature constituting the agricultural sector whilst the modern sector is made up of the industrial sector.
The central thesis of the model is that an economy can only achieve economic development by prioritising the development and expansion of the modern sector so as to increase industrial output. This can be achieved by channeling labour from the agricultural sector to the industrial sector. This does not mean however that the agricultural sector should be totally neglected. The agricultural sector should be competitive enough to supply the economy with food and the industrial sector with raw materials.
In the Lewis theory an economy transits from ‘labour Surplus’ to the ‘labour scarce’ stage but in the Fei-Ranis Model the first stage in the Lewis model is split into two stages, thereby having three growth stages . This three growth stages are explained thus:
The first growth stage is characterised by superfluous labour and thus has a marginal productivity of zero due to the excess supply of labour.The second growth stage is characterised by disguised unemployment which arises as a result of re-allocation of the Surplus labour from the agricultural sector to the industrial sector. In this stage, the marginal productivity of labour in the agricultural sector is rising but is still below the institutional wage they earn. This implies that APL< MPL and there's still room for further re-allocation of labour from the agricultural sector to the industrial sector.
The third stage describes an economy in which MPL is greater than the institutional wage received and this stage kick-starts the era of self-sustainable economic growth wherein there is a complete commercialisation of the agricultural sector and the Surplus labour no longer exist.
Unlike many growth models which propose for a complete neglect of the agricultural sector in the process of advancing the industrial sector, the Lewis-Fei-Ranis Model still recognises the importance of the agricultural sector to economic development. This can be seen in the assumption of Surplus agricultural labour which they argue should be transferred to the industrial sector for a sustained economic growth.
Bringing it to the Nigerian economy, Nigerian economy is still primarily agrarian in nature as the bulk of the country's foreign exchange earnings come from the sale of raw materials and agricultural products. In comparison with the Lewis-Fei-Ranis Model, Nigeria seems to be lying either in the first stage, the stage of Surplus labour where the marginal productivity of labour is zero or the second stage, the stage of disguised unemployment, wherein the marginal productivity of labour is rising but is still below the institutional wage rate. Following the argument of the Lewis-Fei-Ranis Model, more Surplus labour had to be re-allocated to the industrial sector for the Nigerian economy to achieve the the third stage i.e the stage of sustainable economic growth. But in reality, what the Nigerian economy needs to take off is not further re-allocation of Surplus agricultural labour to the urban sector. This is because the Nigerian urban sector is already saturated with labour Surplus to requirement thus leading to a situation of great underemployment and unemployment. Nigeria has to devise a way of solving her urban unemployment problem by expanding the industrial sector so as to increase the industrial output.

THE HARRIS-TODARO MODEL OF MIGRATION
INTRODUCTION
John Harris and Michael Todaro formulated the Harris-Todaro model to explain the high unemployment rate besetting the economies of the less developed countries in the 1960's.
The Harris-Todaro model studied in particular the economy of Kenya.Shortly after independence, Kenya's economy experienced a high rate of unemployment in their major cities . In an effort to overturn this problem, the Kenyan government implemented some policies that aimed at increasing employment in the urban areas.
However, while this policy indeed increased the number of jobs in the urban sector, the rate of urban unemployment increased rather than reduced.The Harris-Todaro model was an attempt to explain this paradox.
The Harris-Todaro hypothesis sharply contrasts with the structural change models, particularly the Lewis theory of labour transfer which postulates that for developing countries to experience a significant growth, they need to transfer a significant proportion of their labour force from the agricultural sector to the industrial sector through rural-urban migration.
The main argument of the Harris and Todaro's theory of migration is that economic incentives, earning differetials and the probability of getting a job at the new destination are the major factors influencing migration decisions of individuals.
ASSUMPTIONS
The Harris-Todaro's theory is built on the following underlying assumptions:
(i)Emphasis is laid on two sectors of the economy, the rural sector and the urban sector.The two sectors differ from each other on the type of goods produced, the technology employed in its production and the process of wage determination.The rural sector specializes in the production of agricultural goods and uses labour as the only input factor.The rural sector on the other hand specializes in the production of industrial goods and like the rural sector uses labour as the only input factor.
(ii)Migration decisions are based on expected income differentials between the rural and urban sectors rather than just wage differentials.This assumption implies that migration is primarily an economic phenomenon, which for the individual migrant can be a quite rational decision despite the existence of urban unemployment, the Harris-Todaro's model postulates that migration proceeds in response to urban-rural differences in expected income rather than actual earnings. The fundamental premise is that migrants consider the various labor market opportunities available to them in the rural and urban sectors and choose the one that maximises their expected gains from migration.
(iii)Both goods and labor markets are perfectly competitive.This implies that the agricultural wage is equal to the agricultural marginal productivity.Although both the goods and labour markets are perfectly competitive, there is a segmentation in the labor market due to a high minimum urban wage politically determined.
(iv)Unemployment is nonexistent in the rural sector.This implies that there is full employment in the rural area, i.e., all workers living at the rural sector are employed at any period.
It is also assumed that equilibrium is reached when the expected wage in the urban sector is equal to the marginal product of the rural worker.In equilibrium, the rural-urban migration will be zero since the expected rural income equals the expected urban income.
Analysing the Assumptions:
In a full-employment environment,the decision to migrate can be based solely on the desire to secure the highest-paid job wherever it becomes available. Simple economic theory would then indicate that such migration should lead to a reduction in wage differentials through the interaction of the forces of supply and demand .
Sadly, such an assumption is not realistic in the context of the institutional and economic framework of most developing nations.This is because, these countries are faced with a high unemployment problem, which implies that a typical migrant cannot expect to gain a high-paying urban job immediately.In reality, most migrants who do not have high educational qualifications or those who are not highly skilled often find themselves doing manual jobs. In the case of migrants with considerable human capital in the form of a secondary or university certificate, opportunities are much brighter, and a lot will find formal-sector jobs relatively fast. But they make up only a tiny fraction of the total migration. As a result of this, in deciding to migrate, the migrant must balance the probabilities and risks of being unemployed or underemployed for a considerable period of time against the positive urban-rural real income differential.
The fact that a typical migrant who gains an urban sector job can expect to earn double the yearly real income in an urban area than in a rural area may not really be an issue of great importance if the chances of his securing the higher-paying job within a particular period is one chance in eight and the urban wage is $80 against rural wage of $40.Thus the actual probability of his being successful in securing the higher-paying urban job is 10%, and thus his expected urban income for that period is in fact 10 units and not the 80 units that an urban worker in a full-employment environment would expect to receive. Note that we are assuming that his rural income is 40 units. So it would not be rational for this particular migrant to seek urban employment despite the fact he will earn double of his rural income if he migrated .
However, if the chances of success were 70% and the expected urban income thus 56 units, pursuing an urban employment will be a rational decision even though urban unemployment might be high.If we approach this analysis using a longer time frame, then the decision to migrate will still be rational because the chances of the migrant securing urban job gets brighter as he stays in the city.As long as the expected urban income is higher than the expected rural income over a longer time horizon, migration decisions will always be rational. Thus instead of equating urban and rural wage rates, we see that rural-urban migration in the Harris-Todaro model equates rural and urban expected incomes.
Thus, equilibrium is reached in the Harris-Todaro model when the agricultural wage equals the the ratio of urban employment and urban Labour force multiplied by the urban wage. In this equilibrium, there will be no tendency to migrate since the expected rural income equals the expected urban income. Hence migration will be zero.

CONCLUSION
We observed that even though migrants respond sharply to differences in economic opportunities between the two sectors as postulated by Harris and Todaro, in reality, all urban migrants are not the same in terms of human capital endowments. The more educated ones tend to migrate more because they have brighter chances of securing urban job.
Migrants create positive externalities for future potential migrants by providing them with information about job availabilities. In reality, this lowers their unemployment probabilities.
The Harris-Todaro model contends that migration is determined mainly by rational economic considerations of relative benefits and costs. The actual urban-rural wage differentials and the probability of successfully obtaining employment in the urban sector are the major determinants of migration decisions. While we agree with this postulation, it is important to point out that in the real world, migration is not purely an economic phenomenon. Other factors such as psychological factors affect migration as well.
The probability of getting an urban employment is directly proportional to the urban environment rate and indirectly proportional to the urban unemployment rate.
Wide imbalances in economic opportunities between the the urban and rural sectors is the reason for urban unemployment. This economic imbalance is in form of wage differences but in the real world, it could include other economic opportunities such as the chances of accessing a better health care and education. Moreover, migration in the face of high urban unemployment is not only possible but rational due to the wide margin between the two sectors with respect to economic opportunities.
Governments should not place greater priority to the cities in terms of development strategies. This is because, developing the urban sector while neglecting the rural sector creates a huge economic imbalances, and as we pointed earlier, this scenario creates further rural-urban migration despite the rising urban unemployment rate, thereby causing a lot of socioeconomic problems like the increase in crime wave in the cities and shortage of food due to the shortage of agricultural workers. Reducing the economic imbalances between the rural sector and the urban sector is key to solving the rural-urban migration and its associated negative repercussions.
Creating more urban employment with the purpose of solving the urban unemployment problem without concurrently developing the rural sector is a mistaken policy.This could worsen the unemployment situation in the urban sector. This is because, in the face of a sharp contrast between the two sectors in terms of economic opportunities, any increase in urban employment rate will result to a triple increase in rural-urban migration rate.
Therefore, any policy that will reduce urban unemployment will aim to develope the rural sector so as to reduce or minimize the rate of rural-urban migration.

UGWOKE FAITH CHINAZAEKPERE
2017/249582
ECO.361-DEVELOPMENT ECONOMICS
HARRIS- TODARO MODEL OF MIGRATION
INTRODUCTION
The Harris –Todaro model was named after after John R.Harris and Micheal Todaro,it is an economic model developed in 1970 and used in development economics and welfare economics to explain some issues concerning rural urban migration .The main assumption of the model is that the migration decision is based on expected income differentials between rural and urban areas rather than just wage differentials. It is equally the rural- urban migration process is revisited under an agent- based approach, such an equilibrium is characterized by stabilization of rural –urban expected wage differential.
The policy implication of the HT model is understanding different from the orthodox models. When there is a wage differential with no urban unemployment ,a wage subsidy in the manufacturing sector is clearly in the first best policy, which restores the output of the modern sector to its level under no market distortion. With urban employment, a wage subsidy to the manufacturing sector is clearly the first best policy, which restores the output of a modern sector. In the traditional sector however, labor surplus is no longer a prominent phenomenon and labor surplus is no longer and labor productivity have improved, partly due to technological investment taken place in the sector. We are aware of the fact that the first best policies to correct the labor market distortion caused by minimum wages are wage subsidies or package that include wage subsidy. In practice however, wage subsidies are often politically and financially infeasible.
ASSUMPTION OF HARRIS-TODARO MODEL OF MIGRATION
The key assumption of the model of Harris –Todaro is that there will be a migratory flow from rural to urban sector while the expected urban wage will be higher than the rural wage. The model assumes that employment is non-existent in the rural agricultural sector. It is also assumed that rural agricultural production and the subsequent labor market is perfectly competitive. As a result, the agricultural rural wage is equal to agricultural marginal productivity. The structure of HT model is based on the premises that a fixed wage leads to an outbreak of distortation and urban unemployment. By introducing the concept of expected wage in one sector is added to the assumptions of the model. The rural sector is specialized in production of agricultural goods. The productive process of this sector can be described by a cob-douglas production function.
Ym=AmNma
Where ya is the production level of the agricultural good, Na is the amount of workers used in the agricultural production, Aa>0and 0<f<1 are parametric constants.
Similarly, the urban sector also has a productive process described as cobb-Douglas production function:
Ym=AmNma
CRITISIM OF HARRIS- TODARO MODEL
Cole and Sander(1985) has critized the harris- Todaro model for not explicitly modeling the subsistence sector employing uneducated migrants, arguing that it flawed the selection process and expected income calculations if, by lack of qualification, uneducated migrants could not find a job in the modern urban sector.
The model assumes that unemployment is non-existent in the rural agricultural sector. it is also assumed that rural wage is equal to agricultural marginal productivity .In equilibrium, the rural to urban migration rate will be zero since the expected rural income equals the expected urban income. However, in this equilibrium there will be positive unemployment in the urban sector. The model explains internal migration in china as a regional income gap has been proved to be a primary drive of rural-urban migration, while urban unemployment is local government’s main concern in many cities.
Migration from rural to urban areas will increase if:
1) Urban wages increase in the urban sector, increasing the expected urban income
2) Agricultural productivity decreases, lowering marginal productivity and wages in the agricultural sector, decreasing the expected rural income.
However, even though migration creates unemployment and induces informal sector growth, this behavior is economically rational and utility maximizing in the context of the Harris –Todaro model. As long as the migrating economic agents have complete and accurate information concerning rural and urban wage rates and probabilities of obtaining employment, they will make an expected income- maximizing decision.
CONCLUSION
There is a large portion of migrants do follow Harris-Todaro model who search for better job in terms of greater income, it is not 100% concrete for making migration decision. This model is applicable in under developing and developing countries. Therefore in order to solve the problem of urban–rural migration, Government has to develop and establish the rural sector in order for people to be comfortable and not see any reason to leave the rural sector such as creating employment opportunity ,provision of social amenities etc.
LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)
INTRODUCTION
Fei-ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C.H.Fei and Gustavo Rican is understood as an extension of Lewis model. It can equally be known as the surplus labor model. It recognizes the presence of dual Economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector is the rapidly emerging but small industrial sector. Both sectors co-exist in the economy, wherein lies the crux of the development problem .
article entitled “Economic Development with unlimited Supplies of labor” written in 1954, the model itself was named in Lewis’s honor. First published in Manchester School in May 1954, the article and the subsequent model were instrumental in laying the foundation for the field of development economics. The article itself has been characterized by some as the influential contribution to the establishment of the discipline.
ASSUMPTIONS OF LEWIS-FEI RANIS MODEL
1) The model assumes that a developing economy has a surplus of unproductive labor in the agricultural sector
2) These workers are attracted to the growing manufacturing sector where higher wage.
3) It also assume that the wages in the manufacturing sector are more or less fixed
4) Entrepreneurs in the manufacturing sector make profit because they charge a price above the fixed wage rate
5) The model assumes that these profit will be reinvested in the business in form of fixed capital

CRITISM OF LEWIS-FEI RANIS MODEL
One of the biggest drawbacks of Lewis- rains model was undermining of the role of agriculture in boosting the growth of the industrial sector. Others include the following:
1) MARGINAL PRODUCTIVITY OF LABOUR IN PHASE 1: The FR model is of the view that MFL=0 in the first phase of growth, and the transfer of labor from agricultural sector to phase 1.
2) PRODUCTIVITY OF LABOUR IS NOT ZERO: Prof.jorgenson who has also presented a model of dual economy has object FR model’s contention of zero MP in phase 1.He says whether MPL will be zero is an empirical issue.
3) IGNORING THE ROLE IF CAPITAL: The FR labor concentrated upon land and labor as determinants of output ignoring the role of capital.
4) SUPPLY OF LAND IN THE LONG RUN: FR model assumed that in the process of economic development the supply of land remained fixed. But is not true. The supply of land can be increased in case of long run fellowship.
5) COMMERCIALIZATION OF AGRI. AND INFLATION: According to the FR model, when third phase start the agri. Sector becomes commercialized. LOW PRODUCTIVITY OF AGRICLUTURAL SECTOR: According to Jorgensen, it has been observed that there has been a very slow rise in productivity of agricultural sector.
CONCLUSION
In my own opinion, Lewis fei -Ranis model is mostly applicable in an underdeveloped country because our present world, mostly underdeveloped country which comprises both the primitive and modern sector. There is a gradual shift agricultural sector to industrial sector .the primitive sector is rapidly emerging to small industrial sector which help to complete the focal point of progress and develop

Udeh Amarachi M.
2017/249576
maryamarachi2010@gmail.com
Maryudeh.blogspot.com

LEWIS-FEI-RANIS MODEL (SURPLUS LABOUR THEORY)

In this model lewis divided the economy in an underdeveloped country into two parts namely; the subsistence sector and the capitalist sector the subsistence sector is characterized by agricultural sector while the capitalist sector is characterized by manufacturing of goods and services whereby labor is employed for the sole purpose of production. The subsistence sector, that is the agricultural sector is considered to be labor intensive, meanwhile, the capitalist sector can be either private or public. The basic assumption of the model is that there exists surplus labor in the subsistence sectors. It includes labor whose marginal productivity is zero as well as that whose marginal productivity is positive but is less than the institutional wage. This labor comprises farmers, agricultural laborers, petty traders, domestic servants and women. The surplus labor in the agriculture sector acts as a source of unlimited supply of labor for the manufacturing sector. By unlimited supply of labor, Lewis means that the supply of labor is perfectly elastic at a particular wages. This particular wage is somewhat higher than the institutional wage which each worker in the agricultural sector gets.
John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes into account the economic situation of unemployment and underemployment of resources, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries. One of the biggest challenges which Lewis model encountered was the unrecognition of the role of agriculture in boosting the growth of the industrial sector. In addition to that, he did not acknowledge that the increase in productivity of labor should take place prior to the labor shift between the two sectors. However, these two ideas were taken into account in the Fei–Ranis dual economy model of three growth stages. They further argue that the model lacks in the proper application of concentrated analysis to the change that takes place with agricultural development.
The three fundamental ideas used in this model are:
1. Agricultural growth and industrial growth are both equally important;
2. Agricultural growth and industrial growth are balanced;
3. Only if the rate at which labor is shifted from the agricultural to the industrial sector is greater than the rate of growth of population will the economy be able to lift itself up from the Malthusian population trap.
This shifting of labor can take place by the landlords’ investment activities and by the government’s fiscal measures. However, the cost of shifting labor in terms of both private and social cost may be high, for example transportation cost or the cost of carrying out construction of buildings. In addition to that, per capita agricultural consumption can increase, or there can be a wide gap between the wages of the urban and the rural people. These three occurrences- high cost, high consumption and high gap in wages are called leakages, and leakages prevent the creation of agricultural surplus. In fact, surplus generation might be prevented due to a backward-sloping supply curve of labor as well, which happens when high income-levels are not consumed. This would mean that the productivity of laborers with rise in income will not rise. However, the case of backward-sloping curves is mostly unpractical.

THE HARRIS TODARO MODEL OF MIGRATION
The Harris-Todaro model named after John R. Harris and Michael Todaro was developed in 1970 and used in development economics and welfare economics to explain some of the issues that concerns rural-urban migration. The model assumes that migration decision (i.e. the decision to move from one place to another) is based on expected income differentials between rural and urban areas rather than just wage differentials. This by implication shows that in a context of high urban unemployment, rural-urban migration will be economically rational if expected urban income is greater than expected rural income. In the model, when the expected wage in urban areas equals the marginal product of an agricultural worker, we say that an equilibrium level has been reached. The massive influx of rural migrant in the cities has been instrumental in breeding an overwhelmingly faster population growth in urban areas than in rural areas. Rural workers are lured to migrate by economic incentives as well as by other attractions of an urban life. While some migrants do manage to secure jobs in industries, the less fortunate ones get absorbed only in the urban informal sector and the rest wait for their own opportunity to get employed and thus increase the number of open urban unemployment. The most relevant idea of the Harris-Todaro model is that labor migration in underdeveloped countries is due to rural-urban differences in average expected wages rather than actual wages. The migrants consider the various opportunities of employment available to them in rural and urban sector and choose the one that maximize their expected wages from migration. The Harris-Todaro model can be compared with other models such as; Lewis’s model of rural-urban migration and the Fei-Ranis model on rural-urban migration. The Lewis model elaborated the unlimited supply of labor which explains the migration process from rural to urban areas in an underdeveloped economy. Unlimited supply of labor causes establishment of new industries and expansion of already existing industries without limit at current wage. In other words, these authors posit that rural-urban migration will occur while the urban expected wage, exceed the rural wage. From this crucial assumption, as denominated by Harris-Todaro, is deduced that the migratory dynamics leads the economic system towards equilibrium with urban concentration and high urban unemployment. There was an analysis that the rural-urban migration by means of an agent-based computational model, takes into account the influence of the neighborhood in the migration decision. The inclusion of the influence of neighbors was done via an Ising like model. The economic analogous to the external field in the Ising Hamiltonian was the differential of expected wages between urban and rural sectors. Therefore, the crucial assumption of Harris and Todaro were taken for granted. Now, we are motivated by the following question: can the crucial assumption and equilibrium with urban concentration and urban unemployment obtained from the original Harris-Todaro model be generated as emergent properties from the interaction among adaptative agents? In order to answer this question we implemented an agent-based computational model in which workers grope for best sectorial location over time in terms of earnings. The economic system simulated is characterized by the assumption originally made by Harris and Todaro. The paper is arranged as follows. Section describes the analytical Harris-Todaro model showing its basic equilibrium properties. In Section we present the implementation of the computational model via an agent-based simulation and compare its aggregate regularities with the analytical equilibrium properties. Harris and Todaro studied the migration of workers in a two-sector economic system, namely, rural sector and urban sector. The differences between these sectors are the type of goods produced, the technology of production and the process of wage determination.