A farm household in rural Mexico consists of five adult brothers and no other de

Question

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:  

Number of brothers

1

2

3

4

5

Total farm output (in $)

1000

1800

2400

2800

3000

Each brother, at the beginning of the year, can decide to migrate to Mexico City, where a typical job, commensurate with his skills, pays $1300 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 jobless (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) to 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.”

Number of brothers

1

2

3

4

5

Total farm output (in $)

1000

1800

2400

2800

3000

Explanation / Answer

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.

As per The HarrisTodaro Model someone will migrate if the expected wage in the urban area is larger than the expected wage in the rural area. Here, if all 5 brothers live on the farm there earning are ZMK600 each. If 1 brother migrates to the city then his earnings will be ZMK1300*0.5=ZMK650>600, thus, at least 1 brother will migrate to the city.

Now with 1 brother migrated in the city there are 4 brothers on the farm, and are earning 700 each. If 1 brother were to migrate to the city he would make 650<700 so 1 brother will migrate.

Therefore in this situation only 1 brother will migrate to the city and 4 brothers will stay and work on the farm.

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?

If 5 brothers are on the farm then they are earning 600 each. Now, If 1 brother moves to the city the total earnings among all brothers will be 1300*0.5+2800=3450, that means each brother will be earnings 690>600. Thus at least 1 brother will migrate to the city.

If four brothers are working on the farm and 1 migrate the city then each brother is earning 690. If 1 more brother migrate to the city then the total earnings to share is 2(1300*0.5)+2400=3700. That means each brother will be earning 740>690 so at least two brothers will migrate to the city.

If three brothers are working on the farm and 2 migrates to the city than each brother is earning 740. If 1 more brother migrates to the city then the total earnings to share is 3(1300*0.5)+1800=3750, that means each brother will be getting 750>740 so at least 3 brothers will migrate to the city.

If 2 brothers are working on the farm and 3 are in the city then each brother is earning 750. If 1 more brother moves to the city then the total earnings to share is 4(1300*0.5)+1000=3600, that means each brother will be earning 720<750 so ONLY 3 brothers will move to the city.

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