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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 outcomes of the Lewis model?
The Lewis model is an early traditional model which seeks to explain how labour movement from one sector to another leads to economic development in a country, particularly developing countries. Whereas the Harris-Todaro model is a model used to address issues concerning rural-urban migration by analysing income differentials. These models are similar but are based on different assumptions which shape their outcomes. I will be analysing these assumptions & outcomes and making comparisons between the two models.
The Lewis model seeks to explain the growth of a developing country in terms of labour transition from a traditional agricultural sector to a modern industrial sector. This model (sometimes known as the Dual Sector Model) was initially developed by Sir Arthur Lewis in his article, ‘Economic Development with Unlimited Supplies of Labour’. This article was published in 1954. This article and model are instrumental in laying the foundation in this area of Economics.
The Lewis Model is about how surplus labour  from the traditional agricultural sector is transferred to the modern industrial sector, whose growth over time absorbs the surplus labour. This is promotes industrialisation as well as encourage sustainable development  .
In this model, the traditional agricultural sector is usually characterised by low wages, an abundance of labour and low productivity through a labour intensive production process. Whereas, the modern industrial sector or manufacturing sector is defined by higher wages, higher marginal productivity  , and initially a demand for more workers, compared to the agricultural sector. The manufacturing sector is also assumed to use a production process which is capital intensive, therefore, investment and capital restructuring in the manufacturing sector is possible over time as capitalists’ profits are reinvested in the capital stock  . The assumption is that there is low marginal productivity in the agricultural sector because it is believed to be low priority as the hypothetical developing nation’s investment is going towards the physical capital stock in the manufacturing sector.
The agricultural sector has a limited amount of land to cultivate, so this means that the marginal product of an additional farmer is assumed to be zero as the law of diminishing marginal returns  takes place as a result of the fixed input, land. This means that the agricultural sector has a quantity of farm workers that are not contributing to output in agriculture because their marginal productivities are zero. These farmers that are not producing any output are termed as surplus labour as they can move to another with no impact on the agricultural sector. Due to the wage differential between the agricultural sector and the manufacturing sector, workers tend to leave agriculture to work in manufacturing sector over time to reap the reward of higher wages.
The idea is that if the quantity of workers moves from the agricultural sector to the manufacturing sector equal to the surplus labour from the agricultural sector, regardless of who actually transfers, general welfare and productivity will improve. Total agricultural product will remain unchanged while total industrial product increases because of the additional labour; however, this additional labour drives down marginal productivity and wages in the manufacturing sector. Over time, as this transition continues and investment results increase in the capital stock, the marginal productivity of workers in manufacturing will be driven down by additional workers entering this sector. Eventually, the wage rates of the agricultural and manufacturing sectors will equalise as workers leave the agricultural sector for the manufacturing sector, which increases marginal productivity and wages in the agricultural sector whilst driving down productivity and wages in manufacturing.
The end result of this transition process is that the agricultural wage equals the manufacturing wage; the agricultural marginal product of labour equals the manufacturing marginal product of labour, and no further enlargements in the manufacturing sector takes place as workers no longer have a monetary incentive to move.
The Lewis Model of Modern-Sector Growth in a Two-Sector Surplus Labour Economy
The Harris-Todaro Model is an economic model used in developmental economics and welfare economics. This model is used to explain some issues surrounding rural-urban migration. The main result of the model is that the migration decision is based on the income differentials between rural and urban areas, not wage differentials. Therefore, this implies that rural-urban migration, in the context of high urban unemployment, can be economically rational if it is expected that urban income exceeds rural income.
The Harris-Todaro Model
The model asserts that equilibrium will be reached when the expected wage in urban areas, adjusted for the unemployment rate  , is equal to the marginal product of an agricultural worker. The model assumes that unemployment is non-existent in the rural agricultural sector and that rural agricultural production and the subsequent labour market is perfectly competitive  . This means that the agricultural rural wage is equal to agricultural marginal productivity. In equilibrium, the rural-urban migration will be zero because the expected rural income equals the expected urban income.
The formal statement of the equilibrium condition of the Harris-Todaro model is as follows:
Wa = Lm (Wm)
In this formula, Wa stands for agricultural income, Lm stands for employment in the manufacturing sector, Lus stands for the total urban labour pool and Wm stands for the urban minimum wage.
The equations illustrates that the expected agricultural wage rate equals the expected urban wage rate, which is the urban wage rate multiplied by the total number of jobs available in manufacturing divided by the total number of the urban labour pool.
Rural-urban migration will take place if:
Wa < Lm (Wm)
On the other hand, urban-rural migration will take place if:
Wa > Lm (Wm)
This suggests that migration from rural areas to urban areas will increase if urban wages (Wm) increase in the manufacturing sector (Lm), increasing the expected urban income. If agricultural productivity decreases, which lowers marginal productivity and wages in the agricultural sector (Wa), there will be a decrease in the expected rural income. This also leads to a rise in migration from rural to urban areas.
Mega-cities: Cities with Ten Million or more inhabitants
Source: Data from United Nations Population Division, March 2002
Migration rates exceed urban job creation rates, this is because rural-urban migration causes overcrowding and unemployment in cities. This leads to many people ending up in unproductive or underproductive employment in the informal sector  . However, even though this migration causes such problems as in inducing informal sector growth and unemployment, this behaviour is economically rational and utility maximising in the context of this model. As long as the migrating economic agents have complete and accurate information concerning rural & urban wage rates and the probability of obtaining employment, they will make an expected income-maximising decision.
Estimated and Projected Urban and Rural Population of the More and Less Developed Regions, 1950-2030
To summarise, the assumptions of the Lewis Model include the idea capitalists reinvest profits which leads to fast growth expansion in the modern sector. The level of wages in the modern industrial sector is assumed to be constant and determined as a given premium over a fixed average continuation level of wages in the traditional agricultural sector. The assumption that there is surplus labour in the sense that marginal product of labour is very important. It is partially because of this that workers will move as they are believed have no impact on the agricultural sector. Another assumption is all rural workers share equally in the output so that the rural real wage is determined by the average and not the marginal product of labour. Moreover, under the assumption of perfectly competitive labour markets in the modern sector, the marginal labour curves (Diagram 1) are actually demand curves for labour. Lewis also assumes that modern sector employers can hire as many surplus rural workers as they like with out the fear of rising wages because urban wage is above rural income. Finally, it is assumed to employment expansion continue until all surplus labour is absorbed by the industrial sector.
These assumptions shape the conclusion that labour transitions take place for workers who leave the traditional agricultural sector for the modern sector in search for a better wage. However, some of these assumptions do not hold in reality and changes the shape of the model.
This model is complicated because of the fact that surplus labour is both generated by the introduction of new productivity enhancing technologies in the agricultural sector and intensification of work. Also, the migration of workers from the countryside to the cities is an incentive towards those two phenomena as the relative bargaining power of workers and employers varies and with this so does the cost of labour.
The wage differential needs to be sufficient between industry and agriculture to incentivise movement between the sectors but the model assumes that any differential will result in a transfer.
The assumption that surplus labour in rural areas and there is full employment in urban areas has been proved wrong by contemporary research indicators. These show that there is little general surplus labour in rural locations. The model also assumes diminishing returns in the modern sector, but there is much evidence that increasing returns exist in this sector.
The Harris Todaro model is based on different assumptions compared to the Lewis model even though their models lead to similar conclusions. The Harris-Todaro model assumes that it is the difference in expected income earnings rather than actual wage differentials that causes workers to switch from rural areas to urban areas if expected income is higher. The model assumes potential migrants are risk neutral. This means they are indifferent between a certain expected rural income and an uncertain expected urban income of the same magnitude. This assumption’s indication of economic realities is debatable. This is because poor migrants will more likely to be risk adverse and require a significantly larger expected urban income to migrate. However, the Harris-Todaro model can be adjusted to reflect risk aversion through alteration of the expected urban income calculation. Although, when the model assumes risk aversion instead of risk neutrality, the results are practically indistinguishable. The Lewis model uses a competitive model whereas the Harris-Model does not do this. This is seen because rural-urban migration acts as an equilibrating force that equates rural and urban expected incomes.
To conclude, the Lewis model and Harris-Todaro model have similar outcomes in the sense of labour moving from rural agricultural areas into urban areas in search of modern industrial work as an approach to earn more money and leave poverty. However, the assumptions of the two models are very different and maybe this is why each model has had different impacts in terms of economic development history. The Lewis model is an early traditional model. which in practical situations does not work properly because of the assumptions. Therefore, the extent of the model is rarely realised. Although, this model does provide a good general theory on labour transiting in developing economies. The Harris-Todaro model, on the other hand, even with its problems with the assumptions, has lead to policy implications such as ways to reduce inequalities and bias between rural areas and urban cities as an attempt to reduce this migration problem.
Overall, both models have increased awareness of the growing issues surrounding rural-urban migration. As many countries like India, Singapore and China act as success stories of this type of migration and economic transition as a catalyst towards leaving poverty, there are many developing nations who have not had the same success, but have suffered from a rise in urban poverty, unemployment and fall in living standards (figure 3) and (figure 4).
Harris J. and M. Todaro, Migration, Unemployment & Development: A Two-Sector Analysis (American Economic Review, March 1970); 60(1):126-42
Todaro and Smith, Economic Development (Addison Wesley; 9th edition, July 2005) pg. 108-113, 339-343
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