Lewis Ranis-Fei model | Analysis

William Arthur Lewis, with his most famous published work, “Economic Development with Unlimited Supplies of Labour” (Manchester School, May 1954) and “The Theory of Economic Growth” (Allen and Unwin, 1955), 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. I will start this paper by introducing the foundations of the model before following with the implications, basing the majority of my arguments on the analysis by Ranis and Fei in “A Theory of Economic Development” (1961).

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[1] that sets labour-supply conditions for the latter. The concept of a dual economy is heavily criticised. As Leeson (1982) pointed out, “dual economy” models are “held to imply a false picture of the nature of the historical process of change in underdeveloped countries”. In this paper, I will not assess the strengths or weaknesses of the model, but instead, for the sake of simplicity and clarity, assume that the sectors are agricultural and industrial, respectively.

Subsequently, Ranis’ and Fei’s extension to Lewis’ model can be analysed. They observed the model by reading it from left to right and assessed the changes in the output and wage as more and more people moved from agriculture to the industry. A new concept was added – namely, disguised unemployment, which appears in the traditional subsistence sector. The marginal product of labour, which is observed as the slope of the production function, in agricultural sector is lower than in industry – in fact, it is zero before point B on Figure 1.3. Under competitive assumptions, the real wage rate would fall to zero, but due to the presence of institutional or non-market forces, the institutional wage is sustained. Therefore, there are gains to be had by switching resources away to the industrial sector. Nevertheless, it is generally not likely to happen because the market, left on its own, does not change. If the industrial sector does pay according to marginal product, then, as noted by Ray (1998), there would be efficiency gains available as long as the marginal product of the agricultural labour is less than the wage, whether it is zero or not. By decreasing the labour force in agriculture by a small amount (whilst still remaining in the surplus labour area), the total wage bill in agriculture falls along the diagonal straight line in Figure 1.3 , provided that the wage in agriculture does not rise. Since output does not fall, the reduction in the total wage bill gives an economy an agricultural surplus. Only at point C will this process come to an end because there is no more disguised unemployment – it only appears at points at which the marginal product of labour is less than the institutional wage. Hence, condition for the existence of disguised unemployment is:

W > MPL

Ranis and Fei subsequently claimed that the average wage bill in agricultural sector is no longer measured as a straight line. At point C, the slope of the production function is parallel to the wage bill line, yielding that the disguised unemployment is no longer observed. Furthermore, beyond point C (when the disguisedly unemployed have been absorbed) the marginal product of labour exceeds the traditionally given wage rate (Ranis and Fei, 1961). The wage in agriculture begins to rise, because it becomes profitable to bid for labour[2] . As a result, wage bill falls more slowly.

This brings me to the central point of the paper – capturing the “turning points” in the Lewis-Ranis-Fei model. Ranis and Fei divided the model into three phases[3]. I have used Figure 1.1. to illustrate this issue. This figure contains the demand curves for labour by industry (downward sloping). The supply curve is initially a vertical line, because of surplus labour. Hence, the intersection of the labour and demand curves gives the equivalent quantity of labour and wage rate – x and w*, respectively. Since the economy is in the surplus phase, there will be a certain quantity of labour transferring from agricultural to industrial sector, which explains the increase of the labour in industry from x to y whilst keeping the wage rate constant. The wage rate remains constant as long as there is surplus labour in the agriculture that can be employed more productively in the industry at a constant subsistence wage rate (Berry, 1970). It must be noted though that for any further investment, the demand curve for labour is going to shift to a point where the compensatory wage must rise. The phase where the supply wage of labour tilts upwards is referred to as the “first turning point”. At this point, redundant labour disappears altogether (Jorgenson, 1967). Employment in the industry would have risen as far as point z’ had the turning point not occurred. However, since it did and since the wage rate began to rise as demand was pushed upwards, employment can only rise up to z where demand meets supply.

As I briefly mentioned earlier, it is evident that as more and more agricultural workers are withdrawn and no longer demand a portion of the agricultural goods, the surplus of agricultural goods begins to appear. It must be noted that each individual that moves from agricultural sector to the industry carries their own subsistence bundle together with them, meaning that they must be compensated for the transfer. Ranis and Fei named the portion of total agricultural output in excess of the consumption requirements of the agricultural labour force at the institutional wage as the total agricultural surplus – TAS (Ranis and Fei, 1961). They described the TAS (captured in Figure 1.3) as the vertical distance between the straight line OX and the total physical productivity curve (with the exception of phase 3 where the distance will be reduced).

In order to find out the required minimum industrial wage, the average wage must be multiplied by the relative price between agriculture and industry. In the surplus phase, it remains constant, because the average agricultural surplus is not changing (captured in Figure 1.2.). At this point, an expansion in the industrial sector would not drive up the wage rate. If an individual that moves from agriculture to the industry when labour in agriculture is at the surplus phase, there will be no compensation needed for that particular individual, as he carries his own food basket to the industry. In fact, industrial wage is constant and this individual is not worse off as a result. At the second phase, however, the average agricultural surplus begins to decline, because there will not be sufficient agricultural output to feed all the new industrial arrivals at the institutional wage level (Ranis and Fei, 1961). In other words, the same wage would not compensate them for the move anymore, because the agricultural surplus has fallen below the average wage (A.W.) and it is not possible for them to buy A.W. units of food. As a result, the supply curve tilts up. There appears to be a worsening of the terms of trade. The relative prices begin to increase and in order to compensate for this price effect and facilitate the move, the industrial wage must rise. The wage must also compensate for the declining agricultural surplus and a movement of the terms of trade against industry. Put differently, the shortage of agricultural goods measured in agricultural surplus lead to a rise in the industrial wage measured in terms of industrial goods.

Simultaneously, the agriculture gains some extra resources, because the agricultural output is divided between less people as more and more people move away from agriculture. If it happened that the individuals at the surplus zone wanted to consume more than the average, the government could step in and tax them to restrict their consumption. That surplus could then be used up in the investment to feed those individuals that move to the industry. In addition, it could also be used to support the new industrial arrivals as the wage rate in industry is set to increase. During phase three, this process becomes even more apparent as the now commercialized wage in agriculture becomes operative. Hence, there is an even sharper decrease in the agricultural surplus. What is more, beyond the “commercialization” point, the contribution from a worker is greater than the wage (as MPL > W). This, on the other hand, increases agricultural wage rate as was seen in Figure 1.3. From the previous results, it is clear that after a second turning point the industry would have to compensate even more to get the workers. As a result, it gives an incentive to bargain for a worker. According to Chen (2005), Lewis-Ranis-Fei model should be considered a classical model because of the usage of industrial wage. However, Jorgenson claims that once the commercialization point is reached, instead of the classical approach, the neo-classical theory of growth for an advanced economy is to be observed (Jorgenson, 1967).

Berry came to a significant conclusion of the Lewis-Ranis-Fei model. In effect, a shift in the terms of trade has a negative effect on the industry, forcing capitalist employers to pay a higher wage and thus generating less profits and less investment (Berry, 1970). However, there is a role of interdependence between the two sectors (Ranis and Fei). In fact, raising the price of goods in agriculture would give an agricultural sector an incentive to raise the output, thus encouraging investments in agriculture, leading to a decline in the terms of trade, which in turn lowers wages, increases profits and generates more investment in the industry. Consequently, there will be a balanced expansion in both, agriculture and industry. In other words, what Ranis and Fei observed was that the allocation of investment funds must be such that as to “continuously sustain investment incentives in both sectors of the economy”. The terms of trade should not deteriorate substantially against either sector. I have illustrated this in Figure 2. The lower diagram in Figure 2 contains a supply curve S and a demand curve D1. Initially, the size of industrial labour force is OB and the industrial sector is making a profit equal to the area B0. This profit can be considered as an investment fund and could be allocated in part to both sectors. Consequently, the demand curve shifts up and there will be a new intersection point which lies on the balanced-growth path and this new equilibrium allows the economy to enjoy even further profits. After the first turning point, there will be a small proportion of profit that will be forgone because the first turning point occurs, yet the overall amount of profit increases. Nevertheless, it becomes clear that it is reasonable to have a policy to invest in both sectors as the economy will then maintain the balanced growth path.

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.