Figure 1 Production Possibility Frontier for the Urban sector
Assuming capitalists do not consume their profit but rather want to reinvest in order to gain more we can see that from the PPF above, reinvesting shifts the PPF from N1, to N2.
Employment in this case raises from M1 to M2 as well. In fact, this will keep on until there is no surplus labour in the economy and eventually the capitalists will have to start paying higher wages in order to get more labour.
Now the majority of the people work in the industrial sector and the agricultural sector has now been modernised with wage equal to the marginal product of labour.
Now suppose as workers go to the industrial sector the wages rise. The profits of the capitalist will decrease. Therefore, for this theory to work the wage must be constant. With little profits the capitalist sector will be small with not much to invest.
The wage may rise due to trade unions demanding higher wages and government intervention may also cause wages to rise, which would again reduce capitalists’ profits.
One reason endogenous to the model for rising wages would be the following. Clearly, the agricultural level will be getting smaller. However, the demand for food will still be there and this can only be met by the agricultural sector. Therefore the demand for food will increase but the supply will decline causing food prices to go up. So in order to buy food you will need bigger wages.
Therefore, as we have already established the wage must remain constant in order for the economy to grow so how can this be achieved? Only by increasing supply in the agricultural sector at the same time. Agricultural reinvestment is a pre-requisite for the industrial revolution. If it doesn’t happen then the price of food will not remain constant.
A further way to look at the model is to use the above diagram. Here point a is considered to be the equilibrium. P.dxa/dna is the productivity or marginal product of the agricultural sector and dXm/dNm is the productivity of the manufacturing sector. Remember, migration occurs when there is a wage differential. So at point b we can see P.dxa/dna > dXm/dNm which implies the wage is greater in the agricultural sector than in the manufacturing sector, so people will migrate there until we reach point a. The reverse is also true. When dXm/dNm > P.dxa/dna then the wage is greater in the manufacturing sector and so the rural sector inhabitants will migrate to the urban sector from point c up until they reach point a.
Implications of the Lewis Model
- Saving and investment are vital for growth. You need capitalists in order to grow!
- Structural transformation of the economy is crucial if you want to grow.
- Income distribution will be uneven to start with. The share of wages will increase in the early stages causing the share of profits to fall. In the long run however, this should even out.
- Agricultural development is a pre-requisite to industrial development. Without agricultural surplus, the urban economy cannot grow.
- Rural to Urban migration is desirable and conclusive to development. Or in other words, urbanisation is a good thing.
The Todaro Model
Michael P Todaro studied Lewis model and then decided to create his own model by changing one assumption. Todaro decides that rural sector wages should be assumed to be determined competitively and that it is urban sector wages that are institutionally set.
What this implies to the Lewis model is that the urban wage is no longer roughly equal to the rural wage, but rather due to trade union pressure etc… it is a reasonable amount higher. This rigid minimum wage in the urban sector lies above the competitive rural sector wage causing a high rate of rural to urban migration. However, Todaro argues that this over urbanisation is bad as the probability of getting a job for these migrant workers is low.
To give a simple example, assume the probability of getting a job in the urban area equal the number of vacancies in the urban sector divided by the number of job seekers in the urban area. Therefore, the expected wage of a migrant worker is determined by the urban wage multiplied by the probability of getting a job. Say the urban wage is set at £400 and let’s say there are ten jobs made available, with 40 people migrating to apply for the job. Then the expected wage of each migrant is only £100. If this wage is higher than the rural wage then people will migrate to apply for jobs. And if they don’t get any of these jobs they will wait about, unemployed, until they can apply for another opening. This leaves 30 people being unemployed and being a drain on the economy. The situation actually gets worse if there is more jobs made available. If there is now 11 jobs made available 44 people will apply for the job. This happens as the expected wage has become even higher [£400 * 11/44 = 106] rising to £106. However this leaves a new total of 33 people being made unemployed causing a bigger drain on the economy. Therefore Todaro states that over urbanisation is actually a problem to the economy, rather than the benefit that Lewis says that it is.
I will now present the above simple example in the more mathematical form presented in Todaro’s 1959 Paper in the American Economic review. First, here is the supply function and it’s mathematical definition.
.
S/S(t) = F[Vu(t) – Vr(t) / Vr(t)], F’ > 0
Where,
S’ represents net rural migration
S is the existing size of the labour force
Vu(t) is the discounted present value of the expected urban real income stream over an unskilled workers planning horizon.
Vr(t) is the discounted present value of the expected rural real income stream over the same planning horizon
Assuming the planning horizon is the same for each worker, as are fixed costs of migration and finally that the discount factor is constant over the same planning horizon then we can begin to formulate the following labour supply model.
Vr(0) = ∫ Yr(t)e^-rt dt
Here,
Yr(t) represents net expected rural real income in period t based on the average real income of x previous periods, and
R is the discount factor reflecting the degree of consumption time preference of the typical rural unskilled worker.
The following equation represents the sum of future income between period t and period m.
Vu(0) = ∫ p(t).Yu(t)e^-rt dt – C(0)
Where,
Yu(t) represents net urban real income in period t.
C(0) is the initial fixed cost of migration and relocation in the urban area and,
P(t) is the probability of having a modern sector job in period t.
Finally to complete the model we need to define profit π in some meaningful economic sense.
N(t) = Noe^(λ-p)t
Where
N(t) is the total modern sector employment in period t,
λ is the rate of industrial output growth, and
p is the rate of labour productivity growth in the modern sector
Thus, if we let the rate of job creation γ = λ-p, we have
π(t) = γN(t)/S(t) – N(t)
here, S(t) – N(t) measures the size of the urban traditional sector
Using this framework we can now begin to see the implications of the model.
First of all we have our demand equation, N(t) = Noe^λt or N’/N(t) = λ.
Next we can specify an aggregate labour supply equation, which is a simplified version of the earlier equation as we are only assuming a one-period model.
S’/S(t) = β + π(t)F(α(t))
Where,
β is the natural rate of increase of the urban labour force
α(t) is the percentage urban-rural real income differential and,
F(α(t)), is a function that such dF/dα > 0.
Thus π(t)F(α(t)) is the rate of the urban labour force increase as a result of migration i.e. we are assuming that migration varies directly with the probability of finding a job. Furthermore, from the earlier profit equation we can re-substitute this to give us
S’/S(t) = β + γN(t)/S(t) – N(t) (F(α(t))
Let me just say a few things about the mechanics of Todaro’s equations. Considering an economy in its early stages, where the majority of the population lives in the rural areas we can see that the urbanisation process is just beginning and so to this point the number of urban unemployed is relatively small so the probability of obtaining a job is high. If there is a reasonable urban real wage at this point (α>0) and a positive job creation exceeding the natural rate of urban population growth (γ > 0) then the expected real income induces a migration where the urban labour force grows at a faster rate than job creation (β + π(t)F(α) > γ). This growth in the labour supply results in the probability of the rural sector finding employment in the next sector much lower. This lower probability causes the migration to the urban sector to slow down although the supply will still exceed demand causing an excessive strain on the economy. Therefore this is why Todaro thinks that over urbanisation is a problem. More conclusions are drawn in Todaro’s paper on labour migration and unemployment but this is all I want to mention at this time other than equilibrium is found when supply is equal to demand and this can be done by equating the above equations and setting them equal to zero.
Empirical Evidence
Now that we have explained both the models and the differences between the two I will now go on to discuss what actual evidence there is to support or reject these theories amongst developing countries. In particularly I looked at 3 papers and their findings. These papers were Collier and Lal, Labour and Poverty in Kenya; G.A. Calvo, Urban Development and Wage Determination in LDC’s and J.E. Stiglitz, unemployment in LDC’s. The general findings of these papers are given below.
Studies lend little support to the “over urbanisation” thesis suggested by Michael Todaro.
In reality studies have shown that migrants significantly improve income by moving from the rural sector to the urban sector. The evidence does not support the view that migrants earn less than non-migrants, especially when age and human capital is taken into account. Also in these studies it does not appear as though migrants dominate the urban informal sector nor does it appear as though the informal sector is the point of greatest entry to migrants as suggested in the Harris-Todaro model. The major argument against the Todaro model is that unemployment is actually low amongst migrants according to findings. In fact their labour participation is high compared to that of non-migrants. So rather than being slow to assimilating into urban life the migrants tend to find jobs quickly and hence improve their economic status.
The Todaro model also fails in it’s prediction that there is a large and growing gap between the urban and rural wages. Empirical evidence suggests that gap os about 41 percent, which is large, but there is no evidence to support the claim that this gap is growing. And the size of the actual gap can be explained if you think about the fact that there is differences in education and experience amongst these sets of workers.
Post World-War II studies yield the reality of employment and migration in the most informative way. Industrialisation proved to be neither a solution for employment nor for economic development. Only in Asian developing countries did growth seem to rise with industrialisation. [This is perhaps down to the fact that labour was at a great surplus in these countries and these employees were well educated and skilled. Therefore the human capital and labour could be fully exploited.]
Outside of Asian, however, the expansion of industrial employment was disappointing at best. In developing countries experiencing rapid industrialisation the growth of the industrial employment was generally about half the rate of growth of industrial output causing economists to take a more critical look at the role of industrialisation and the problems of employment and migration. Often this is because many developing countries have an abundance of natural resources but lack the human capital. And so industrialisation is capital and resource intensive rather than labour intensive.
To test this theory I thought I would look at the role of industrialisation and economic growth in a developing country to see how it compares.
You can see even from this rough data that I have collected from the World Banks’ website that as Zimbabwe’s industrial sector has grown it’s economy has not although I could not find any specific data relating to there unemployment levels over this period.
Finally, empirical surveys of rural labour markets in developing countries generally do not support the assumption of surplus labour. Therefore, empirically neither model seems to be correct if you apply it to the real world although both provide a good base from which to start further theories. What has been specifically found in developing countries is that small peasant farmers tend to participate in rural labour markets both by supplying and demanding labour. And that this supply and demand of labour varies considerably over the different crop seasons. Therefore there are labour shortages as well as labour surpluses depending upon the season.
Macroeconomic Analysis Essay : Week 7
Essay 7: Examine the difference between the Lewis and Todaro models of economic development. Discuss the view that neither model adequately explains the process of development in contemporary less developed countries.
Mark Macrae 015157753
Dr. P.C. Bhattacharya / Mr. Nikita Kuksin
Bibliography/References
Todaro, M.P. “A model of Labour Migration and Urban Unemployment in Less Developed Countries”, The American Economic Review, Vol. 59
Harris, J.R and Todaro, M.P. “Migration, Unemployment, and development: a Two Sector Analasis”, The American Economic Review, Vol 60
Collier and Lal, Labour and Poverty in Kenya
G.A. Calvo, Urban Development and Wage Determination in LDC’s
J.E. Stiglitz, unemployment in LDC’s