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This article throws light upon the top three models of migration. The models are: 1. Lewis’s Model of Rural-Urban Migration 2. The Fei-Ranis Model on Rural-Urban Migration 3. Harris-Todaro Model Of Rural-Urban Migration.
1. Lewis’s Model of Rural-Urban Migration:
Prof. W. Arthur Lewis in his article, “Unlimited Supplies of Labour” has explained the process of migration from rural to urban areas in an underdeveloped economy.
An underdeveloped economy is a dual economy having two sectors:
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(i) a modern sector, and
(ii) an indigenous sector.
Out of these two, the latter is the predominant sector. The capitalist sector is defined as “that part of the economy which uses reproducible capital, pays capitalists for the use thereof and employs wage labour for profitmaking purposes.”
The distinguishing feature of a capitalist sector is that it hires labour and sells output to earn profit. The subsistence sector is that part of the economy which does not use reproducible capital. Labour is abundant and disguised unemployment is the result. The marginal productivity of labour in the agricultural sector may be zero or even negative. In order to solve the problem of disguised unemployment.
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Prof. Lewis would like the capitalist (industrial) sector to be expanded by transferring labour from the subsistence (rural) sector to the capitalist sector. He assumes that the supply of labour is perfectly elastic at the subsistence wage.
Since the supply of labour is unlimited, new industries can be established or existing industries can be expanded without limit at the current wage i.e. subsistence wage by withdrawing labour from the subsistence sector. When people migrate from the subsistence sector to the modern sector, the wages should be higher in the capitalist sector than in the subsistence sector by a small but fixed amount.
Transfer of Labour to the Capitalist Sector:
Lewis explains the process of transfer of labour with the help of figure 1.
In the figure, the quantity of labour is shown on the X-axis and Y-axis represents wage and marginal product. OA is the wage rate of the subsistence (rural) sector and OW of the capitalist (industrial) sector. WW1 shows that the supply of labour is perfectly elastic at OW wage rate. N1D1 is the curve of marginal productivity of labour, which shows the demand of labour. Since the capitalist sector maximises profits, the wage rate remains equal to the marginal productivity of labour.
At the current wage rate OW, employment is OL and the total product in the capitalist sector is N1PLO. Out of this output, wages are equal to OWPL and the capitalists profits are WPN1, which are reinvested to create new capital. The key to the process is the use which is made of the capitalist surplus.
The capitalist employment also increases with the reinvestment of profits and the expansion of the capitalist sector. The amount of fixed capital increases as a result of further investment and the marginal productivity of labour is also raised to N2D2 making the capitalist surplus and employment larger to the level of WP1N2and OL1respectively in the figure.
Further, reinvestments raise the marginal productivity of labour to N3D3 and the level of employment to OL2 and so on. This process will continue till the entire surplus rural labour is absorbed in the industrial sector. Thereafter, if additional workers are withdrawn from the rural (subsistence) sector to the industrial sector, there will be loss in food production in the rural sector because the ratio of workers to land will decline.
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This means that the marginal productivity of the remaining labour force is no longer zero. Thus the supply curve of labour WW1 will slope from left to right upwards like an ordinary supply curve (not shown in the figure) and wages and employment will continue to rise with the growth of population and labour force in the long run.
In the Lewis model, migration is the result of concerted effort on the part ofthe state to transfer surplus rural labour to the industrial sector by developing the latter for capital formation.
Its Criticisms:
The Lewis model of migration has been criticised on the following counts:
1. Wage Rate not constant in the Capitalist Sector:
The theory assumes a constant wage rate in the capitalist sector until the supply of labour is exhausted from the subsistence sector. This is unrealistic because the wage rate continues to rise over time in the industrial sector of an underdeveloped economy even when there is open unemployment in its rural sector.
2. Not Applicable if Capital Accumulation is Labour Saving:
Lewis assumes that the capitalist surplus is reinvested in productive capital. But according to Reynolds, if the productive capital happens to be labour saving, it would not absorb labour and the theory breaks-down. This is shown in Fig. 2 where the curve N2D2 has a greater negative slope than the curve N1D1thereby showing labour-saving technique.
With the shifting of the marginal productivity curve upwards from N1D1 to N2D2 the total output has risen substantially from ON1Q1L1to ON2Q1L1. But the total wage bill OWQ1L1 and the labour employed OL1 remain unchanged.
3. Skilled Labour not a Temporary Bottleneck:
Given an unlimited supply of labour, Lewis assumes the existence of unskilled labour for his theory. Skilled labour is regarded as a temporary bottleneck which can be removed by providing training facilities to unskilled labour. No doubt skilled labour is in short supply in underdeveloped countries but skill formation poses a serious problem, as it takes a very long time to educate and train the multitudes in such countries.
4. One-sided Theory:
This is a one-sided theory because Lewis does not consider the possibility of progress in the agricultural sector. As the industrial sector develops with the transfer of surplus labour, the demand for food and raw materials will rise which will, in turn, lead to the growth of the agricultural sector.
5. Mobility of Labour not so Easy:
Higher capitalist wage will not lead to the movement of surplus labour from the subsistence sector to the capitalist sector. People are so intensely attached to their family and land that they do not like to leave their kith and kin. Moreover, differences in language and custom, the problems of congestion, housing and high cost of living in the capitalist sector stand in the way of mobility of labour of this sector. This is the weakness of the theory.
6. Marginal Productivity of Labour not Zero:
Schultz does not agree that the marginal productivity of labour in overpopulated underdeveloped countries is zero or negligible in the rural sector. If it were so, the subsistence wage would also be zero. The fact is that every worker receives the subsistence wage, may be in kind, if not in cash.
It is, therefore, difficult to find out the exact number of surplus labourers who are to move to the capitalist sector, their number hardly exceeding 5 per cent, as is now generally accepted.
7. Productivity falls with Migration of Labour from the Subsistence Sector:
Lewis assumes that when the surplus labour is withdrawn from the subsistence sector to the capitalist sector, the agricultural production remains unaffected in the subsistence sector. But, according to Schultz, the transfer of even, say, 5 per cent of the existing labour force out of agricultural will reduce output.
2. The Fei-Ranis Model on Rural-Urban Migration:
John Fei and Gustav Ranis have presented in an article entitled, “A Theory of Economic Development”, the process of rural-urban migration in underdeveloped countries.
The model is related to an underdeveloped economy having surplus labour but scarcity of capital. The major part of the population is engaged in agriculture which is stagnant. Non-agricultural occupations use small capital. There also exists an industrial sector.
The process of development involves transfer of surplus labour from the agricultural sector to the industrial sector, so as to increase its productivity from zero to a wage level equal to the institutional wage in agriculture.
Its Assumptions:
The assumptions of the theory are:
1. Land is fixed in supply.
2. Population growth is taken as an exogenous phenomenon.
3. There is a dual economy consisting of a stagnant agricultural sector and an active industrial sector.
4. Agricultural activity is characterised by constant returns to scale with labour as a variable factor.
5. The output of the agricultural sector is a function of land and labour alone.
6. The output of the industrial sector is a function of capital and labour alone.
7. Workers in both the sectors consume only agricultural products.
8. If population increases above the point where marginal productivity of labour becomes zero, labour can be shifted to the industrial sector without loss in agricultural output.
9. The real wage in the industrial sector remains fixed and is equal to the initial level of real income in the agrarian economy, which they call the institutional wage.
The Model:
Based on these assumptions the model analysis the development process in three phases.
In the first phase, disguised unemployed workers, who are not adding to agricultural output are shifted to the industrial sector at the constant institutional wages.
In the second phase, agricultural workers add to the agricultural output but produce less than the institutional wage they get. These workers are also shifted to the industrial sector. If the migration of workers to the industrial sector continues, a point is ultimately reached when farm workers produce output equal to the institutional wage.
In the third phase, farm workers produce more than the institutional wage they get. Thus the surplus labour is exhausted and the agricultural sector becomes commercialised.
These three phases are explained in Fig. 3. In Panel (C) the labour force in the agricultural sector is measured from right to left on the horizontal axis ON and agricultural output downwards from O on the vertical axis OY. The curve OCX is the total physical productivity curve (TPP) of the agricultural sector.
The horizontal portion CX of the curve shows that the total productivity is constant in this region so that the marginal productivity of MN labour is zero. Thus MN labour is surplus and its withdrawal to the industrial sector will not affect agricultural output.
The allocation process in three phases is depicted in Panel (B) of Fig. 2 where the total labour force is measured from right to left on the horizontal axis ON and the
average output on the vertical axis NY. The curve NMRU represents the marginal physical productivity of labour (MPPL) in the agricultural sector. NW is the institutional wage at which the workers are employed in this sector.
In Phase I, NM workers are disguised unemployed. Their marginal physical productivity is zero, as shown by NM portion of the MPP curve in Panel (B) [or CX portion of the TPP curve of Panel (C)]. This surplus labour force NM is transferred to the industrial sector shown as OM in Panel (A) at the institutional wage OW (= NW).
In Phase II, after NM, the MPP of agricultural workers begins to rise in Panel (B), as shown by the rising portion of the MPPL curve from M upwards. As a result, the labour force in the industrial sector increases from OM to OL in Panel (A). When workers migrate from the agricultural to the industrial sector, agricultural output declines. As a result, there is shortage of agricultural goods leading to rise in their prices relative to industrial goods.
This leads to the worsening of the terms for the industrial sector, thereby requiring a rise in the nominal wage in the industrial sector. This is met by making investment in the industrial sector which shifts the MPP curve PT outwards to P1H to P2Q in Panel (A).
The nominal wage rises above the institutional wage OW to LH and KQ. This is shown by the upward movement of the supply curve of labour from WT to H and Q, as ML and LK workers gradually shift to the industrial sector in Panel (A). The movement on the supply curve of labour WTW1from Tupwards is “the Lewis turning point.”
When Phase III begins, agricultural workers start producing agricultural output equal to the institutional wage and ultimately more than the institutional wage they get. This is shown by the rising portion RU of the MPPL curve in Panel (B) which is higher than the institutional wage KR (=NW).
Consequently, KO of labour will be transferred from the agricultural sector to the industrial sector at a rising nominal wage above KQ in Panel (A) of the figure. This leads to the exhaustion of the surplus labour in the agricultural sector which becomes fully commercialised.
Fei and Ranis point out that as agricultural workers are shifted to the industrial sector, there begins a surplus of agricultural commodities. This leads to the total agricultural surplus (or TAS) in the agricultural sector. The excess portion of total agricultural output over the consumption requirement of the agricultural labour force at the institutional wage is the TAS.
The amount of TAS is a function of the number of workers shifted to the industrial sector in each phase of the development process. The TAS is measured in Panel (C) of the figure by the vertical distance between the line OX and the TPP curve OCX. In Phase I when NM labour is transferred (Panel B), the TAS is BC. In phase II, as ML and LK workers (Panel B) are shifted to the industrial sector, DE and FG amounts of TAS arise (Panel C).
Criticisms:
This model is not free from criticisms which are discussed below:
1. Supply of Land not Fixed:
Fei and Ranis begin with the assumption that the supply of land is fixed. In the long run, the amount of land is not fixed, as the statistics of crop acreage in many Asian countries reveal.
2. Institutional Wage not above the MPP:
The model is based on the assumption of a constant institutional wage which is above MPPL during Phases I and II. But there is no empirical evidence to support this assumption. In fact, in labour surplus underdeveloped countries, wages paid to the agricultural workers are much below their MPP.
3. Institutional Wage not constant in the Agricultural Sector:
The theory assumes that the institutional wage remains constant in the first two phases even when agricultural productivity increases. This is highly unrealistic because with a general rise in agricultural productivity, farm wages also tend to rise.
4. Closed Model:
According to Fei and Ranis, the terms of trade move against the industrial sector in the second phase when agricultural output declines and prices of agricultural commodities rise. This analysis is based on the assumption of a closed economy where foreign trade does not exist. But this is unrealistic because underdeveloped countries are not close but open economies which import agricultural commodities when shortages arise.
5. Commercialisation of Agriculture Leads to Inflation:
According to this model, when the agricultural sector enters the third phase, it becomes commercialised. But when many workers shift to the industrial sector, the agricultural sector will experience shortage of labour. In the meantime, the institutional wage also equals the MPP of workers and the shortage of agricultural products arises. All these factors create inflationary pressures within the economy.
6. MPP not Zero:
According to Fei and Ranis, MPPL is zero in the agricultural sector. But Schultz does not agree that in labour-surplus economies MPPL is zero. According to him, if it were so, the institutional wage would also be zero. The fact is that every worker receives a minimum wage, may be in kind, if not in cash. Thus it is wrong to say that MPPL is zero in the agricultural sector.
3. Harris-Todaro Model Of Rural-Urban Migration:
Prof. J.R. Harris and P. M. Todaro in an article “Migration, Unemployment and Development: A Two-Sector Analysis” in 1970 presented a model on rural-urban migration in underdeveloped countries.
The main idea of the Harris-Todaro model is that labour 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 sectors and choose the one that maximises their expected wages from migration.
The minimum urban wage is substantially higher than the rural wage. If more employment opportunities are created in the urban sector at the minimum wage, the expected will rise and rural-urban migration will increase. Expected wages are measured by the difference in real urban income and rural agricultural income and the probability of a migrant’s getting an urban job.
In fact, a migrant compares his expected income for a given time horizon in the urban sector with his prevailing average rural income and migrates if the former is more than the latter.
Thus migration in the Harris-Todaro modal is viewed as the wage or income gap between the urban and the rural sectors. But all migrants cannot be absorbed in the urban sector at high wages. Many fail to find a job and get employment in the informal urban sector at wages which are even lower than in the rural sector. Thus they join the queue of the underemployed or disguised unemployed in the urban sector.
Assumptions of the Model:
The Harris-Todaro model is 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 model operates in the short run.
3. The marginal production of labour in agriculture (MPLA) and of industry (MPLM) are determined by their respective technologies.
4. Capital is available in fixed quantities in the two sectors.
5. There are L workers in economy with LA and LM numbers employed in the rural and urban sectors respectively.
6. The number of urban jobs available (LM) is exogenously fixed. In the rural sector some work is always available. Therefore, the total urban labour force LM comprises L-LAalong with an available supply of rural migrants.
7. The urban wage is fixed at WM and the rural wage at WA, WM> WA.
8. The rural wage equals the rural marginal product of labour and the urban wage is exogenously determined.
9. Rural-urban migration continues so long as the expected urban real income is more that the real agricultural income.
The Model:
The Harris-Todaro model is explained in Fig. 4. where total labour force in the two sectors is measured along the horizontal axis. Employment in the agricultural sector (A) to the right starting from OA and in the industrial sector (M) to the left starting from
The left vertical axis from OA upwards measures the MP and wages of labour in agriculture (MPLA and WA). The right vertical axis measures the MP and wages of labour in industry (MPLM and WM). AA1 is the MP of labour curve in agriculture. It slopes downwards to the right as employment in agriculture (LA) increases. Similarly, MM1 is the MP of labour curve in industry which slopes downward to the left as LM increases.
WM is the wage level at which OMLM workers are employed in the urban sector. The remaining OALM workers are employed in the rural sector at OAWA, wage level. So the rural-urban wage gap is WM – WA, with WM wage fixed.
This wage gap attracts rural workers to the urban sector even in the face of urban unemployment and under-employment. Despite this, the rural jobseekers are willing to take their chance in the “urban job lottery” to find their favoured jobs. If the probability (chances) of getting the favoured jobs is the ratio of employment in manufacturing, LM, to the total urban labour pool Lu, then the expression
WA = 
shows the agricultural wage at which the potential migrant equates the urban expected wage and is indifferent about job location. The locus of such points of indifference is given by the I1I1 curve. The unemployment equilibrium point is given by point Z.
The equilibrium agricultural wage is WAthe new urban-rural wage gap is WM-WA. OA LAworkers are working in the agricultural sector instead of OMLM before migration. OMLM workers in the manufacturing urban sector are still employed at the institutional fixed wage WM. But Lu= OALA-OMLM migrants to the urban sector are engaged in low-wage jobs in the informal sector getting less than OAWA wage rate which they would have received in the rural sector.
Conclusion:
The main drawback of this model is that it does not incorporate the costs of rural-urban migration or the relatively higher costs of urban living which the migrants have to incur in the urban sector.