A farm household in rural Mexico consists of five adult brothers and no other dependents. Total annual income depends on the number of brothers working on the farm through the year and is given by the following schedule:

Each brother, at the beginning of the year, can decide to migrate to Mexico City, where a typical job, commensurate with his skills, pays $1,300 per annum, but the unemployment rate is as high as 50%. A person who migrates to the city cannot come back and work on the farm that year. Furthermore, all city jobs are temporary one-year appointments. Also assume, for all questions that follow, that the brothers are risk-neutral and there is no difference in the cost of living between the city and the countryside. Now consider three different scenarios.

(a) Suppose the family is completely individualistic: those brothers who work on the farm share the farm income equally among themselves. There are no remittances to or from any family member who goes to the city. Find the number of brothers who will migrate.

(b) Now suppose the family is completely altruistic: the total family income, whether from a city job or from the farm, is pooled and shared equally. How many brothers will this family send off to Mexico City to look for jobs?

(c) Here is a third possibility. Those brothers who migrate to the city become selfish and never send home any remittances, even if they are employed (maybe those in the countryside have no way to verify whether their brothers in the city have a job). However, the family sits down and makes the following arrangement: those brothers who try out their luck in the city will each be sent $200 a year from the farm income, to insure against possible joblessness (assume that this contract is always honored). Find how many brothers will decide to migrate. (Assume that if a brother is indifferent between migrating and not migrating, he does migrate.)

(d) Compare the numbers in parts (a)–(c). In light of the comparison, discuss the following assertion. “The extent of rural urban migration depends, ceteris paribus, on the nature and degree of altruistic links within families.”

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Number of brothers 1 2 3 4 Total farm output (in $) 1,000 1,800 2,400 2,800 5 3,000