Question

Suppose that a worker's skills can be summarized by the number of efficiency units she owns and that the distribution of efficiency units in the population is such that worker 1 has 1 efficiency unit, worker 2 has 2 efficiency units, and so on. Suppose that there are 100 workers in the country of Sodor. In deciding whether or not to migrate to the U.S., the residents of Sodor compare their weekly earnings at home (w.) with their potential earnings in the United States (W..). The wage skill relationship in the two countries is given by: W = 690 + 5s w = 670+ s where s gives the number of efficiency units that the worker has. a. Assume that there are no migration costs. What proportion of the population in Sodor immigrates to the US? What is the average number of efficiency units among the immigrants? Is the immigrant flow positively or negatively selected? b. Suppose that workers who migrate from Sodor to the United States must pay a migration cost that is equivalent to $20 in weekly wages. What proportion of the population in Sodor immigrates to the US? What is the average number of efficiency units among the immigrants? Is the immigrant flow positively or negatively selected?

Answer 1

A. The workers will migrate till their earnings in the US are greater than or equal to their earnings at home. Using the relationship given above, we get

670+s>=690+.5s

.5s>=20

s>=40.

All of the workers who have efficiency units of 40 or more will migrate to US.

For average efficiency units, lets assume that the worker with 40 units will also migrate (he/she is indifferent to moving). So, average efficiency

(40+41+42+.....+100)/61

The formula for calculating sum of n consecutive numbers is- (first number+last number)*n/2. Using this formula we get

average efficiency=4270/61=70.

There is positive selection since the average efficiency of workers moving to US is higher than the overall average efficiency.

B. Since everyone is now paying $20 a week to move to the US, effectively the new US wage line is

670+s-20=650+s

Using the same method as above,

650+s>=690+.5s

.5s>=40

.s>=80.

So workers with s>=80 will move to US now. Which means 21 (or 20, if the worker with s=80 decides not to move as he/she is indifferent to moving) will move. Giving us proportion=21/100=21%.

Average efficiency=(80+81+...+100)/21=90.

There will still be positive selection bias since the average efficiency of workers moving to the US is higher.