The Lewis Model

Describe the Lewis model as a model for structural change. How does the Harris-Todaro model of rural-urban migration differ from the assumptions and the outcomes of the Lewis model?

Economic growth refers to the increasing productive capacity of the country, which results in an increase in productive output and national income. There are numerous theories relating to economic growth and impacts as a result growth. Rural to urban migration has played an important role in growth and has resulted in structural change of an economy. Structural change can be defined as change in the sectors of an economy over a time series. Specific to this The Lewis model demonstrates when underdeveloped economies convert their traditional economic sectors in rural areas into a modern, industrialised urban areas (Todaro, Smith; 2009). The Lewis model is one of two approaches that are based on the structural transformation. The model is based on two sectors and the relationship between the supply and transition of labour and its resulting impact upon development. The Harris-Todaro model focuses upon incomes between rural and urban areas and how they vary, it states that income levels are seen as higher in urban areas which influence migration to the area. Principally, the essence of both models link back to the development of urban areas, and the migration process, however, the assumptions of each model varies which impacts upon the results.

The Lewis model, also known as the two or dual sector model, was developed by Nobel Laureate W. Arthur Lewis in the 1950’s, nevertheless it is still used 60 years on. There are two main aims of the model firstly the transfer of labour, and secondly the impact upon the modern sector through growth of output and employment. One of the two sectors discussed in this model is the traditional agricultural sector in rural areas. The second sector is the industrialised urban area. Labour supply extracted from the traditional agricultural rural area does not affect its output as it is transferred to the modern industrial urban sector. The marginal product of labour is defined as the change in productivity that occurs from a one unit change in labour. The reason as to why output is not affected is due to the marginal productivity of labour being zero due to the overpopulation, which is a key characteristic in the rural area, and thus leading to a surplus of labour. Urban industrialised sector is characterised by high productivity.

The diagram below of the Lewis model illustrates the impact of the transfer of labour on both the traditional and modern sector. I will first discuss the traditional sector diagram (1a and 1b). Diagram 1a demonstrates that as quantity of labour increases total food production increases. This is until a certain point, where it then stabilises and levels off, due to restrictions at this level by labour. Using the total product curve we can then derive the marginal product of labour and the average product of labour. The dashed line passing through both diagrams illustrate the level of labour accessible in the rural economy. Firstly, as discussed previously due to surplus of labour, the diminishing marginal product of labour is zero which is reflected in the diagram. The average product (APLA) of labour is calculated by using the total product of food and dividing it by the labour available, thus giving us the a level of WA food per person. WA represents the real wage income earned in the agricultural sector. The surplus labour which is transferred to the modern sector can be illustrated by the red arrows in diagram 1b.

The next set of diagrams (2a and 2b) focuses on the modern industrial sector. Diagram 2a illustrates the total product of manufacturing curves for three different levels of labour. The total product of manufacturing is a function of capital (KM) and labour (L). The marginal product of labour can be interpreted as demand curves for labour. WA represents average real income in the traditional sector in 1b, whereas WM is the real income in the modern sector. The supply curve in the diagram is completely horizontal, this suggests a perfectly elastic supply, and this would link well with the surplus labour (shown in figure 1b). The demand curve for labour is negatively sloping this is due to declining marginal product influencing. This is highly likely due to the assumption of the modern sector to employ until marginal physical product is equal to real wage (L1 on diagram). The KM curves also represents demand, it rises from KM1 to KM2 and KM3. This is due to the reinvestment assumption that the Lewis model makes, increasing capital stock and in the long run economic growth. The process then continues up until a point where the surplus labour is transferred to modern industrialised sector.

After the self sustaining growth process has stopped, labour from the rural sector will only be transferred at a higher cost of lost food production. One of the key changes is that the marginal product of labour is no longer zero in the rural sector. The structural shift of the rural economic reliance to the urban industrial sector is complete.

An essential idea to consider before discuss the next model is that rural to urban migration has become extremely high, this could affect the probability of employment opportunities and also the impact upon social services of the developing urban area. A model which can explain this relationship between rural urban migration and rising unemployment is the Harris Todaro model. The model states that income is the primary influence the decision making process of migrants, and that they do not consider the difference between expected and actual income they might receive. If the potential income earned in the urban sector is more than expected income in the rural agricultural sector, the higher income would draw the workers to migrate from rural to urban. This would suggest that the only reason for migration is to get higher paid jobs. This process should indeed result in the income difference narrowing due to the interactions of supply and demand. However, the likelihood of this occurring is small, due to high unemployment in urban areas many people have to settle for jobs in the low paid informal sector. Skilled labour and labour with a greater level of education are likely to get better jobs for a good pay in the formal sector. However, it is never guaranteed and many could be over skilled for the job they are doing. Time horizons can be an important factor to consider when making rational decisions. If a worker only considers the current time frame it is highly unlikely that he or she would enter employment at a higher wage than in rural areas. However, the probability would increase if the future likelihood of getting a job is considered. The worker may plan that initially pay is low and the job is fairly low skilled, nevertheless, in time skills improve, connections develop and the job is likely to improve and the probability of a higher income also increases. In this model urban incomes would have to be equated in order for migration from rural to urban to be seen as unbeneficial. Expected income considers two factors; wages and unemployment. If wages in urban areas are higher than rural, the unemployment rate would have to be in accordance to the percentage difference in income. However, there are seen to be more benefits than income in the urban areas, therefore even though unemployment rate may be chronically high people still do attempt to migrate for better quality of life.

The diagram above includes two main sectors; agriculture in the rural area and manufacturing in the urban area. The line AA’ represents labour demand for the agricultural sector and MM’ for the manufacturing sector. Total labour force is on the horizontal axis from OA to OM. The equilibrium wage is thus at the point where the AA’ and MM’ curves cross, E on the diagram. However, if wages in the manufacturing industry is set higher than agriculture at a level WM, the difference from the equilibrium (E) wage rate for agriculture (WA*) is high. When considering the impact of this upon labour it would mean less labour would be able to find jobs in the urban area. From LM to OM to be exact, on the diagram highlights urban area employment, thus leaving OA to LM as rural labour or even unemployment at wage WA**. Nevertheless, many people still chance for employment at a higher wage and migrate to urban areas. The line qq’ shows the line of indifference between rural and urban sectors for jobs. This is calculated by using a formula which shows probability of the likelihood of finding a job in the urban area and the rate at which it is able to equate agricultural income with potential income earned in urban areas (Todaro, Smith; 2009). This results in the equilibrium shifting to point F on the diagram, this lowers the wage from WM bar to WA. However, the labour gap is not reduced, OA to LM is still employment in rural areas or unemployment; as urban labour is LM OM. Thus illustrating the reason as to why unemployment in urban area occurs, people risk migrating in order to achieve a higher wage. However, the probability of finding a well paid job in the formal sector is very low.

Describe both models in detail, with graphs

Compare and contrast the assumptions and how they shape the outcomes.