Lewis Model

      Ranis and Fei's extension of the Lewis model of labour migration can be viewed as one theoretical interpretation of the Rostovian “take off” stage of Rostow's economic modernization model. The key element of this stage is the “transition” from a traditional to a modern economy. (Rostow 1960)

Ranis & Fei (1961) build upon the Lewis model offering a more detailed representation of the Rostow's “take off” stage and their emphasis centred on the importance of synchronised investment in both the traditional and modern sector. They argued that this was essential in ensuring a sustained industrialisation process that would later enable the economy to make the “drive to maturity.”

This essay will briefly outline the Ranis-Fei extension of the Lewis model of labour migration, and will explain how the turning points of the industrial labour supply curve effects the rate of industrialisation. I will then go on to show the importance of investment in both sectors, and this essay will conclude with an explanation of the importance of balanced sector growth.

Lewis makes a few but nevertheless critical assumptions on which his analysis relies. The first is the dualism of the economy, that is to say that the economy comprises two sectors, agriculture and industry, respectively shown in figures one and two. Lewis also assumes that labour supply is unlimited in the agricultural sector. This is a plausible assumption to make as the majority of workers in less economically developed countries are unskilled, and thus for many, the only viable employment option available is to “work” in agriculture; but the extent to which some of the labourers “work” is questionable and Lewis addresses this in his third assumption. Lewis makes the assumption that there are a number of workers employed past a certain point that contribute very little if anything to the output of the farm but whom still receive a wage equal to their average product. In short, Lewis assumes an agricultural production function subject to diminishing marginal returns to the labour input. Because agriculture is labour intensive, intuitively there will come a point when the farm's stock of fixed capital is fully utilised by a certain number of workers and additional labour will not yield an increase in output.

The notion that labourers can be employed and contribute nothing is captured what Lewis refers to as the surplus of labour, the amount of workers whose marginal productivity is zero, and thus are redundant. This is represented by the distance XC in figure 1.3

If we were to transfer XC workers from agriculture and have them work in industry, anything they produce in industry would represent sector development and represent economic growth. So workers whose contribution to agricultural output was negligible now become productive members of the industrial labour force (Ranis & Fei 1961). Critically, this could be achieved costlessly, because total agricultural production would be unaffected despite their removal (Total Output OB remains unchanged.) Given their non contribution to output, and that their wage was equal to the value of average product, a costless transfer could be achieved as they would simply “take their food parcel (from the farm) with them” into the industrial sector. (Ray 1998) Equivalently, the wage rate in industry is equal to agriculture's subsistence wage up until point T in figure 1.1 although in fact it is assumed that “factories must pay farmers a bit more than they receive in agriculture to get them to move.” (Perkins, Radelet & Lindauer 2006)

The concept of labour surplus underpins the entire model and it is its transfer from agriculture to industry that permits industrialisation and growth in the economy in phase 1, as rural to urban migration can transform a redundant labour force into a productive one.

The transfer of labour remains costless only up until point C, the first turning point, which marks the end of phase 1. The reason for this is because all unproductive labour has been exhausted. There is no longer any “marketable surplus” created by our agricultural workers, and so “unlimitedness comes to an end.” (Ranis & Fei 1961) Effectively, the farm is using as few workers as is possible to produce the same maximum level of output OB and once we pass the first turning point, we enter phase two, characterised by the fact that the marginal product of agricultural labour now becomes positive and further migration of agricultural workers will result in falling output, or equivalently food production. This is why this turning point is referred to as the shortage point. In order to attract more workers to the industrial sector, industry must offer a higher wage to compensate agricultural labourers so that migrants can still afford the same food basket that they would have received in agriculture following the decline in total production, for it is assumed that when “output falls, the price of food will rise.” (Ranis & Fei 1961). The industrial wage rise is represented by the changing slope of industrial supply in figure 1.1 at point T. In this sense, the exhaustion of labour surplus “chokes off industrial employment to some extent, because it raises the costs of hiring industrial labour.” (Ray 1998)

Let us now examine the effects of further migration. At the first turning point, the marginal product of labour became positive, but the contribution to agricultural output from the marginal worker remains small. However as we continue to transfer workers, the marginal productivity of agricultural labour rises despite total output falling. The industrial real wage is rising for every additional worker that chooses to work in industry over agriculture. This is represented by the portion of the industrial supply curve from points T to X'.

However, there comes a point R (equivalently U) when the remaining agricultural workers are becoming increasingly productive until they become so productive that the agricultural sector is now prepared to increase the wage rate for the remaining workers so as discourage them from leaving the sector to the extent where the agricultural sector is willing to pay a wage equal to if not greater than the marginal productivity of labour. This is represented by the new agricultural wage rate in phase 3, represented by the line going from Q to 0 in figure 1.3. The continuation of industrialisation process thus necessitates a “further accentuation of the industrial wage rate” to induce more agricultural workers to migrate. (Ranis & Fei 1961) This is graphically illustrated by the second kink in the industrial supply curve at point X'. This point is thus referred to as the commercialisation point, where there is no longer any disguised unemployment and for the first time, the two sectors are in competition with each other for labour.

It is worth mentioning what ‘a point of commercialisation' signifies. Up until now, there was a certain wage level in agriculture below which the agricultural wage rate could not fall. Referred to as the subsistence wage W*, it was assumed to be fixed, regardless of the number of workers on the farm. Ranis and Fei (1961) argue that the second turning point thus marks the transition of the traditional sector into a ‘modern' agricultural sector where the wage is solely determined by market forces.

Having now described the forces at work behind the two turning points, I will now show their effects on the rate of industrialisation using figure 2. S' is the industrial labour supply curve and the three remaining curves are marginal physical productivity (MPP) curves, all of which represent increasing industrial labour demand. The intersection of supply and demand yields level of industrial employment.

Industry profits are equivalent to the area under the demand curves but above the industrial supply curve. Increases in the demand for labour yield increases in industrial profits. However, because of the turning points of the industrial labour supply curve, the rate at which industry profits grow (for labour demand increases) begins to slow.

Alternatively expressed, industrialisation is increasing at an increasing rate up to the shortage point T, where the “terms of trade gradually turn against industry” (Ray 1998) as the marginal productivity of agricultural labour becomes positive. This necessitates an industrial real wage rise which slows down the rate of industrialisation. The turning up of the industrial supply curve means that industry profits are lower than they would have been had agriculture had a larger surplus of labour, because industry now has to offer an increasingly higher wage for the marginal worker who leaves agriculture. The red area represents foregone profit due to industrial wage increases. In short, the first turning point constrains the rate of industrialisation. Nevertheless, it is important to note that growth in industry is still positive for increases in labour demand, despite the wage increases, but the process of development is slower than before. This becomes even more acute when the commercialisation point, X' is passed.

Now that we have looked at the effect of the turning points on the rate of industrialisation, I will now turn to the role of investment, and its importance in both sectors in continuing the development process.

The position of the industrial labour demand curve, or MPP “depends on the size of the capital stock cooperating with the labour force.” (Ranis & Fei 1961) Higher levels of industrial output can be achieved when the labour input is increased (achieved by migration) but only if the industrial capital stock is sufficiently large. In essence, “capital accumulation is the engine of growth.” (Ray 1998). Another way to think about this is how industry uses its profits. Only if industry consents to reinvest a portion of its profits for capital accumulation can it increase its demand for labour, and crucially its profits in the next period, so for the industrialisation process to continue, there must be investment in industry, but the story does not end here.

The sustainability of industrialisation also necessitates investment in the agricultural sector. The emphasis on the need for agricultural investment was one of Ranis & Fei's most fundamental extensions to the Lewis model. They insisted that the agricultural sector must receive investment “if the mechanism that Lewis described was not to grind to a halt,” at the shortage point (Ghatak, 1995). This point “represents another formulation of the Ricardo-Schultz food trap in which developing economies may be caught when they try to achieve economic modernisation by forcing resource allocation from agriculture to industry, as a result of neglecting efforts to increase agricultural productivity.” (Hayami, 1997)

Let us now take a more detailed look at the effects of an increase in the agricultural productivity of labour, (achievable following a technological advancement.) This is represented by an upward shift of the production function TPP1 to TPP2 shown in figure 3.3 and of the MPP curve, MPP 1 to MPP2 shown in figure 3.2

For any amount of labour employed in the agricultural sector, the workers are more productive. This will be reflected in a bigger labour surplus, shown in 3.3. Consequently, more workers could be removed without cost before total production begins to fall.

Ranis and Fei argue that an increase in agricultural productivity also has an impact of the industrial supply curve. Before the first turning point, increased agricultural productivity will shift the industrial supply curve downwards, which results in a decrease in the industrial wage rate thus “depressing the terms of trade for the agricultural sector.” (Ranis-Fei 1961) “After the crossing of the second turning point, the higher marginal productivity of labour and an agricultural wage rise results in an upward shift of the supply curve.” (Ranis-Fei 1961) This is shown in figure 3.1

Investment in agriculture also affects the turning points. Firstly, it delays the shortage point, as the decline in food production occurs later due to the increased productivity of labour. More workers can migrate for a higher level of productivity before total output begins to fall. This is represented by point S2 which is to the right of S1 as the Average Agricultural surplus curve in figure 3.2 cuts the unchanged wage rate further along. However, the point of commercialisation arrives sooner for increases in agricultural labour productivity. This is represented by R2 which is to the left of R1 as the MPP curve cuts the unchanged wage rate before R1. If labour productivity increases, the difference in the reduction of output when marginal product is positive (in phase 2) from the migration of an extra worker is greater than if workers were not so productive. As a result, the point at which workers become so productive that the sector has to offer a higher wage to induce them to stay arrives sooner. Hence what occurs is the convergence of the two turning points occurs for continued increases in labour productivity in agriculture. Oshima (1963) emphasises that if the increase in agricultural labour productivity is substantial enough, phase two will be eradicated.

Ranis and Fei (1961) attach another condition to the sustainability of the rate of industrialisation. It is not only that investment required in both sectors for the development process to continue, but of vital importance is the simultaneous synchronisation of these shifts to ensure that the development process is “as harmonious as possible.” I will now show why this is important.

Ranis and Fei (1961) define the balanced growth approach as “consistent with both the input and output criterion” where labour is free to migrate according to shifts in industrial demand and there exists enough incentives in both sectors of the economy for the provision of “mutual market outlets” for both goods. If investment was continually biased towards industry, successive demand for labour increases would for high levels of industrial employment result in industry having to pay a higher wage to migrating workers than would have been the case if part of the investment was dedicated to improving agricultural labour productivity. This would imply a substantial deterioration in industry's terms of trade, “ not consistent with the output criterion.” (Ranis-Fei 1961) Effectively, the industrial supply curve would still have '2 kinks' in it. Conversely, if investment was biased towards agriculture, there would be a limit to the amount of labour that could migrate to industry constrained by stagnant industrial demand for labour. Such a situation is not consistent with the input criterion. If both of the balanced growth criterion are satisfied, a balanced growth path emerges, represented by the horizontal line between points L1 and P3 in figure 3.1

In conclusion, this essay has illustrated Lewis' model of rural urban migration, outlining a principal economic development theory that explains how the foundations of an industrial sector may be rooted in the agriculture. I have shown how the rate of industrialisation may be constrained at points throughout the development process due to interplay between the two sectors. I have also illustrated the key difference between the Lewis model, and the Ranis-Fei extension which is the need for investment, in agriculture as well as industry to deliver efficient growth. Finally, as well as the value of investment, I have highlighted the importance of its synchronisation and timing in achieving harmonious and sustainable growth.

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