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Lewis-Fei-Ranis Model (Surplus labour theory)

The theory of unlimited supplies of labour by Professor W. Arthur Lewis is a systematic classical theory of economic development which is based on the existence of two sectors in the economy of developing countries- the modern and the traditional sectors. The modern sector is small and uses considerable amounts of capital, while the traditional sector is the large labour surplus rural agricultural sector, with little amount of capital.
The argument is that poor countries have two sectors (the rural agricultural or subsistence sector and the modern industrial or capitalist sector) and that the wage level in the sector with unlimited supply of labour (rural sector) is at its subsistence. In addition to that, it is also believed that the marginal productivity of this surplus labour is zero and as such the economy is backward. Lewis argues that if this surplus labour can be transferred to the sector that has few labour supplies (the modern sector), the productivity level in the agricultural sector would not experience any noticeable reduction but rather, economic development would take place because labour would be put to good use bringing about a chain of productive reactions. Arthur in his article on “Economic Development with unlimited supplies of labour” has a model called the dual sector- model enumerated in it and the model was named in Lewis’s honor. To understand the theory better, the underlining assumptions of the model will be discussed in the next section.

The Assumptions of the Model
The following are the assumptions of the model:
(i) Existence of dual Economy: There exist a two sector economy characterised by a traditional, over-populated agricultural rural subsistence sector with zero Marginal Productivity of Labour(MPL), and the ‘capitalist’ sector which is the high productive modern industrial sector represented by the manufacturing, mining activities.
(ii) Elasticity of Labour: According to Arthur, the supply of labour is perfectly elastic. In other words, the supply of labour is greater than demand for labour in the agricultural sector and therefore the capitalist sector can have as much labour as it requires and will continue to absorb this surplus from the agricultural sector until there is no longer surplus labour left.
(iii) Reproducible Capital: The subsistence sector does not make use of ‘Reproducible Capital’, while the modern sector uses the produced means of capital. As a result of the non usage of reproducible capital in the subsistence sector, output per head is lower than in the capitalist sector.
(iv) The model also assumes that the wages in the manufacturing sector are higher than those of the subsistence sector and are also more or less fixed.
(v) Entrepreneurs in the manufacturing sector make profit because they charge a price above the fixed wage rate
(vi) There is the willingness of the capitalist to reinvest the profit in
the business and this is done in the form of fixed capital. The main people/sources from which workers would be coming for employment at the subsistence wage as economic development proceeds are “the farmers, the casual workers, small scale informal sector participants, women in the household, and population growth.

Basic Thesis of the Lewis Model
The Lewis model is a classical type model based on the assumption of a dual sector economy which are the capitalist sector and the subsistence sector. The subsistence sector is that part of economy which does not use reproducible capital and therefore, the output per head is lower than in the capitalist sector. Also there is perfectly elastic supply of labour at the subsistence sector in many underdeveloped countries but not in themodern sector. Lewis is of the opinion that the industrial and advanced modern sector can be developed and made to boost the entire economy, this according to him, can be done by transferring the surplus labour from traditional sector to the modern sector. From this surplus labour now in the modern sector, new industries will spring up and existing ones would grow. However, the capitalist sector requires skilled labour and this stands as a stumbling block to the development process as the surplus labour from the subsistence sector are mostly unskilled. This problem can be eliminated by providing training facilities to unskilled workers. So in essence, the absence of skilled labour in this sector is a temporary problem which can be solved through training.
Lewis says that the wages in industrial sector remain slightly higher than that of the agricultural sector. Consequently, labour will be attracted to the modern sector because of the higher wage incentives and as a result of this, the capitalists will earn surplus from the increase in productivity brought about by the surplus labour transferred. Such surplus will be re-invested in the modern sector leading thereby to further increase in the productivity of this sector. In this way, the surplus labour or the labour which were prey to disguised unemployment will get to be employed into productive activities. Thus both the labour transfer and modern sector employment growth are brought about by output expansion in the modern sector. The speed with which this expansion occurs is determined by the rate of industrial investment and capital accumulation in the modern sector. Here is a diagrammatical explanation of Lewis Model

QUANTITY OF LABOUR
Diagramatic Representation of Lewis Model
In this diagram, the horizontal axis (x) represents the quantity of labour employed, while the vertical axis (y) represents the wage rate/Marginal Productivity of Labour. Also in the diagram, OS represent average subsistence wage in the agricultural sector, and OA the capitalist wage, the supply of labour is unlimited and this is shown by the horizontal supply curves of labour AW and Sw. The analysis goes thus: The marginal productivity of labour in the industry is M1P1, with OL1 labour employed , OAKL1 wage rate is paid from the total product of OM1KL1, giving the capitalist a profit of AM1K. With the reinvestment of this profit, the marginal productivity of labour of labour increases from M2P2 and then further reinvestment brings it to M3P3 and so on. As the capitalist continues to reinvestment his profit, his surplus continues to grow. Overtime, as the transition continues and the capitalist continues to reinvest surplus derived from the use of surplus labour from the subsistence sector, the capital stock increases, the marginal productivity of workers in the manufacturing sectors will be driven up by capital formation. Capital formation resulting from this increase in investment leads to quicker utilisation of surplus labour. As more labour is supplied, the marginal productivity falls, and in the long run, the wage rates of the agricultural and manufacturing sectors will equalise because as workers leave the agricultural sector for the manufacturing sector, they increase marginal productivity and wages in agricultural sector while reducing them in manufacturing. The process of modern self sustaining growth and employment expansion will continue till all the surplus rural labour is absorbed in the new industrial sector. Thereafter, additional workers can be withdrawn from agricultural sector only at a higher cost of lost of food production because this will decrease the labour to land ratios. In this way, the MPL will no more be zero and the labour supply curve will become positively sloped along with the growth of modern sector.

CRITICISMS OF THE THEORY
Despite the theory’s huge success in identifying the two key sectors in the developing countries and stating how growth can be achieved in these usually over populated countries, most of the theory’s assumptions do not fit into the institutional and economic realities of the Developing countries and as such can be said to be irrelevant to these countries.
Below are some of the flaws of the theory.
(i) The industrial real wage continues to rise and is not constant as Lewis assumes
(ii) There is the likelihood of the capitalist reinvesting in labour saving techniques like investments in machineries and this would reduce the amount of labour needed causing urban unemployment.
(iii) Lewis ignored the balanced growth between agricultural sector and industrial sector. But we know that there, exists a linkage between agricultural growth and industrial expansion in poor countries. If a part of profits made by capitalists is not devoted to agricultural sector, the process of industrialisation would be jeopardised (perhaps, due to reduced supply of raw material).
(iv) Lewis model underestimates the full impact on the poor economy of a rapidly growing population, i.e., its effects on the capitalist profit share, wage rates and overall employment opportunities.
(vi) Lewis has ignored the role which the leakages can play in the economy. As Lewis assumed that all increases in profits are
diverted into savings. It means that the savings of producers is equal to 1. But, this is unrealistic as the increase in profits may accompany an increase in consumption.
(vii) Lewis assumed that the transfer of unskilled labour from the subsistence agricultural sector to the industrial sector is regarded as almost smooth and costless. The model however fails to take account of the cost of educating and training rural workers for urban employment and also, there is also other indirect cost associated with rural-urban migration. Amongst these are: a lack of sufficient housing, leading to the development of squatter townships or shanty towns, pressure on social infrastructure such as schools and hospitals, increases in disease due to a lack of clean water and sanitation.

CONCLUSION
Arthur Lewis theory of economic development is a structural change theory which explains the mechanism of changing structure of underdeveloped economies from the subsistence rural sector to a modern urbanised one. According to the theory, the economies of most developing countries are made up of two key sectors, the subsistence agricultural sector and the modern capitalist sector. Lewis is of the opinion that economic development occurs when the capitalist gets labour from the unlimited supply of labour in the subsistence sector, which it uses to set up new industries and also grow existing ones. The capitalist gets profit from the activities of the surplus labour and according to Lewis, the capitalist reinvests this profits and this sets off a growth process that continues until there is no longer surplus labour to be absorbed. The theory was criticised by some scholars and one major criticism raised is that the transition from rural sector to urban sector does not come without cost like the theory would like us to.
However, despite the criticisms, the theory still helps to point us to the reality of the existence of the overpopulated subsistence agricultural sector and a modern capitalist sector in most underdeveloped countries. The way we go about developing these sectors to achieve a balanced growth in the economy (which the theory was criticised for not doing) was latter addressed by Fei-Ranis.

Harris-Todaro Model of migration.

The Harrod-Domar Models
The Harrod- Domar models attempt to analyse the requirement of a steady growth in the advanced economies. They are interested in discovering the rate of income growth necessary for a smooth working of an economy and as such, believed that investment plays a key role in the process of economic growth. Investment according to the models is divided into two, based on its ability to:
(a) create income, which is the demand effect of investment and
(b) augmenting the productive capacity of the economy by increasing capital stock, this is the supply effect of investment. Expansion of net investment would result in increase in real income and output in the economy and if this expansion is stopped, income and employment will fall, thereby moving the economy off the equilibrium path of steady growth. For net investment to grow however, the real income is required to also grow continuously at a rate sufficient enough to ensure capacity use of growing stock of capital. The real income growth rate required here is called the full capacity growth rate or the warranted rate of growth.

Assumptions of the Model
The following are the assumptions of the models:
1. There is an initial full employment equilibrium level of income
2. There is an absence of government interference and the models operate in a closed economy which has no foreign trade
3. The average propensity to save is equal to the marginal propensity to save and marginal propensity to save remains constant for the period
4. There are no changes in interest rates
5. There is a fixed proportion of capital and labour in the productive
process
6. The general price level is constant i.e. nominal and real incomes are the same
7. There is no separation between fixed and circulating capital. They are both lumped together under capital
8. There is no depreciation of capital goods, which are assumed to possess infinite life
9. The above are the assumptions of the Model. Let us now examine each of the models independently.

The Domar Model
Domar builds his model based on a self asked question which goes thus “since investment generates income on the one hand and increases productive capacity on the other, at what rate should investment increase in order to make the increase in income equal to the increase in productive capacity, so that full employment is maintained?” In answering the question, Domar forged a link between aggregate supply and aggregate demand through investment. On the supply side, starting from the increase in productive capacity, annual investment rate is taken to be (I), and the annual productive capacity per dollar of newly created capital on the average equals to (s) and this represents the ratio of increase in real income or output to an increase in capital or is the reciprocal of the accelerator or the marginal capital-output ratio. So the productive capacity of I dollar invested will be I.s dollars per day. However, some new investment will be at the expense of the old because the new investment will bring about a competition, for available factors of production and competition in the labour market which brings about a reduction in the old plants output and the annual increase in the economy i.e. the productive capacity of the economy will be less than I.s. This can be represented as Iσ, where σ (sigma) stands for the net potential social average productivity of investment (=∆Y/I). Note that Iσ is less than I.s, and it is the total net potential increase in output of the economy known as the sigma effect of the supply side of the economic system. To explain the demand side, the Keynesian multiplier was used. Here, the annual increase in income is denoted by ∆Y, increase in investment as ∆I and the propensity to save α (alpha) is (∆S/∆Y). Increase in income will therefore be 1 which is also the multiplier effect 1/α. 1-MPC
Note that 1-MPC = MPS. Where MPC and MPS (α) are marginal propensity to consume and marginal propensity to save respectively. Increase in income would be equals to the multiplier (1/ α) multiplied by the increase in investment, which is ∆Y =∆I. I/α. …………………………………. (1)
For full employment equilibrium level of income to be maintained aggregate demand should be equal to aggregate supply which will bring the equation to, ∆I.1/α = σ…………………………………………………………… (2)
Equation (2) is the fundamental equation of the model.
To solve the equation, divide the two sides by I and multiply by σ, we would have, ∆I/I= α σ……………………………………………………………..… (3)
Equation (3) shows that to maintain full employment, the growth rate of net autonomous investment (∆I/I) must be equal to the product of MPS and capital productivity (α σ).This is the rate at which investment must grow to ensure the usage of potential capacity in order to maintain a steady growth rate of the economy at full employment.

The Harrod Model
The Harrod model like that of Domar, examines the possibility of steady growth. Harrod made efforts to show how economy can havegrowth path and if by any chance this steady growth is interrupted, the economy falls into disequilibrium and cumulative forces prolong the divergence from the ‘golden path’ which eventually leads to either secular deflation or secular inflation, showing that the process of steady growth is never smooth. Harrod developed his model on three basic concepts of rates of growth, and they are
(1) actual growth, (2) warranted growth and (3) natural growth.
(1) The actual rate of growth which is given as G, is determined by the saving ratio indicated by s and the incremental capital-output ratio indicated by C. It shows a short run cyclical variations in the rate of growth;
(2) Warranted rate of growth represented by Gw is taken to be the full capacity growth rate of income in an economy. It is the rate of growth required for the full utilisation of a growing stock of capital. The warranted growth rate can therefore be said to be the growth rate at which all saving is absorbed into investment. The demand at this growth rate is high enough for businessmen to sell what they have produced. And
(3) the natural growth rate represented by (Gn), is the rate of advancement which the increase in population and technological improvements allow. This growth rate depends on variables like technology, population and natural resources. The natural growth rate is therefore the rate required to maintain full employment. If the labour force grows at 3 percent per year, then to maintain full employment, the economy’s annual growth rate must be 3 percent (assuming no growth in productivity). According to Harrod, Warranted growth rate Gw is a self-sustaining rate of growth and if the economy continues to grow at this rate, it will follow the equilibrium path. He asserted that on a long run basis, the actual growth rate (G) should be equal to warranted growth rate (Gw). For full employment growth realisation, actual capital goods (C) must equal required capital goods C(r) if not, the economy would be in disequilibrium. Equation for full employment growth Gn =Gw= G. The full employment equilibrium is difficult to achieve and any divergent would lead to disequilibrium either in form of secular stagnation or inflationary conditions in an economy. Harrod model presents a situation where savings is a virtue when there is inflationary gap and a vice when there is deflationary gap in the economy. This model therefore would enable policy makers in an advanced country to use savings adjustments to correct inflation or deflation in the economy

Criticisms of the Models
Some of the criticisms of the models are as follows:
Harrod -Domar model was formulated primarily to protect the developed countries from chronic unemployment, and was not meant for developing countries.
Most less developed countries lack sound financial system and therefore, increased saving by households does not necessarily mean there will be greater funds available for firms to borrow for invest.
Improving capital/output ratio is difficult to achieve in developing countries this is often due to a poorl educated work force. New capital is often inefficiently used by labour.
Increasing the savings ratio in developing countries is not always easy.
Majority of these developing countries have low marginal propensities to save and low income.
Research and Development needed to improve the capital/output ratio is often underfunded in developing countries.The model fails to address the nature of unemployment which exists in
different countries.
In developed countries, the unemployment is ‘cyclical unemployment’, which is due to insufficient effective demand; whereas in developing countries, there is high level of ‘disguised unemployment’ in the urban informal sector and rural agricultural sector.
Finally, the model failed to recognise the effect of government programs on economic growth.

CONCLUSION
Harrod-Domar models are models developed independently by Sir Roy Harrod and Evsey Domar. The models explain economy growth rate in terms of level of saving and productivity of capital. The Harrod -Domar growth model is based on the experiences of advanced capitalist countries and is interested in knowing the rate of income growth that would bring about smooth and sustained growth of the economy. The model has it that growth depends on the quantity of labour and capital, noting that more investment leads to capital accumulation which brings about the growth in an economy. The model’s implication for the less developed country is that because labour is in excess supply and physical capital is not, the LDC’s do not have sufficient average incomes to enable high rates of saving which the model believes is necessary for the accumulation of capital stock. Therefore these countries have low rate of investment caused by low savings rate. For economic growth to be achieved in these countries policies geared towards increasing investment through increased savings should be pursued and also the savings can be used by policy makers to correct inflation or deflation as the case may be.