The Todaro model Hypotheses: 1-Migration is an individual rational decision 2-Migration proceeds in response to urban-rural differences in expected income rather than actual earnings 3. Compare of expected incomes for a given time horizon in the urban sector (returns minus costs of migration) with prevailing average rural incomes in a context of a urban job lottery The Harris -Todaro Model If wages were perfectly flexible, equal wages would be paid in industry and agriculture and there would be no involuntary unemployment 1

In a perfectly competitive labor market 2

For a variety of reasons however workers in the urban formal sector are paid higher than equilibrium wages 1. Unions 2. government policy 3. incentives to workers to expend effort when labor cannot be directly supervised without tremendous costs. 4. The threat being fired. Then one would have to return to the country or find work in the urban informal sector. 3

Here L F workers find employment in good jobs in the cities, L A remain behind in the countryside working at a lower wage of w A. Those who migrated from the countryside to the city find themselves employed in the urban informal sector, L I How does the urban labor work? The Harris-Todaro Migration model LILI 4

As a result, many people end up in relatively unproductive dead-end service sector jobs in the cities. Urban overcrowding due to high rates of migration from rural areas to cities and high informal sector employment is a fact of life in many low and middle income countries. The Harris-Todaro model helps to explain this seemingly irrational phenomenon First, let’s define real per capita income in the rural sector= P A =agricultural prices P=general price level Q T A =total agricultural production. Next we define urban formal sector income= W F =the wage paid for good jobs in the city. N=the number of hours worked per period per worker u=the formal sector unemployment rate Finally let’s define urban informal sector income= where w I =the wage per hour paid in the informal sector. 5

It is sensible to assume that migration continues as long as urban incomes are significantly higher than rural incomes. Or in other words migration occurs when Now think about u, the rate of unemployment in the formal sector (1) The higher u is, the more people there are actively seeking formal sector employment that are unable to find it. (2) The higher u is the lower the probability of a new migrant from the country finding a formal sector job. (3) Without a social safety net, a migrant has to “create” a job for themselves in the informal sector. Because of the preceding LHS in the above expression can be thought of as the wage one can expect if they move to the city. Thus, the lower is u, the higher the expected wage where, k, is a measure of the degree of risk aversion. 6

The main point of Harris-Todaro is that if the expected urban wage equals rural income there is no incentive to migrate. 2. is greater than rural income there is a great incentive to move from country to city 3. were less than rural incomes there would be an incentive to move in the other direction. (South Korea in recent years) The expected urban wage depends on what type of job you land, that depends on probabilities and these are linked to current urban unemployment rate as defined above. Therefore to understand the model set rural and expected urban incomes equal and solve the above for u, the urban unemployment rate 7

One failing of the Harris-Todaro model assumes migrants are risk- neutral. This means that the utility of a gamble where the payoff is $6000 is the same as the utility of $6000 guaranteed. From this result we can show the following: 1. u will increase if w F increases! 2. u will increase if n increases---i.e the number of hours worked per period per worker ! 3. u will increase if k drops i.e. less sensitivity to risk 4. u will increase if Q T A /N T R falls, i.e. agricultural output per rural worker falls 5. u will increase if w I increases—i.e. the wage per hour paid in the informal sector ! 6. u will increase if P A /P decreases due to either P A falling or general inflation, P 8 Given the urban unemployment rate, u

This is not realistic. Especially poor migrants will be risk averse This means that to the degree potential migrants are risk-averse. The less net migration out of rural areas will be, given the gap between rural and urban wages. Consider k a measure of the degree of risk aversion. 9

Debraj’s discussion of social capital Debraj raises an interesting point in relation to this issue of risk aversion. 1. He begins by pointing out that information availability is high and mobility is low in rural areas 2. In other words, every one knows your business in a small village and it is hard to move. This means that 1. In terms of insurance and credit, rural areas provide a strong support network for the poor (this is his “social capital”) 2. If someone runs into trouble,the community knows why.(If not due to own negligence, individual receives some support) 3. Low mobility also gives rise to “reciprocity”. One helps others in their time of need knowing that they will help them in return. Once migration starts however This social capital will be eroded and thus, all else equal, lowers the cost of migrating since local rural support breaks down. 10