Question

7. 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 (wm) with their potential earnings in the United States (wus). The wage skill relationship in the two countries is given by: Wm = 690+.55 Wus = 670+ 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 proportion of the population migrating to the US

The process of migration will stop when the wage in Sodor will be equal to wage in the US.

The wage in Sodor = Wage in the US.

690 + .5s = 670 + s

s - .5s = 690 - 670

.5s = 20

s = 40

The workers whose efficiency is greater than 40 will migrate to the US. There are 60 workers in Sodor whose efficiency is greater than 40. These 60 workers will migrate to the US.

The immigrant with the highest efficiency is 100 and the immigrant with the lowest efficiency is 40. Therefore, the average number of efficiency units among the migrants is

(40+100)/2= 70.

As the immigrants have above average skills, the immigrants are positively selected.

b) when the workers pay $20 weekly wages in migration cost, the wage skill line drops by $20 and becomes

w_us = 650 + s

The wage in Sodor = Wage in the US.

690 + .5s = 650 + s

s - .5s = 690 - 650

.5s = 40

s = 80

The workers whose efficiency is greater than 80 will migrate to the US. There are 20 workers in Sodor whose efficiency is greater than 80. These 20 workers will migrate to the US.

The average number of efficiency units is [(80+100)/2] 90. The immigrant population is positively selected.