Question

13. There are two types of workers: the fast workers, who have a constant marginal product of $20 and the slow workers, who have a constant marginal product of $10. There are equal numbers of each type of worker, and they always receive a competitive wage. A firm cannot tell the difference between the two types of workers. Suppose that there is an opportunity for the workers to get a college degree, which the firm can observe. The cost of each year of college for the fast workers is equivalent to a $2 wage cut, and for the slow workers is equivalent to a $4 wage cut. Which of the following is true about a separating equilibrium in which the fast workers all get a degree and the slow workers all choose not to go to college?

A) There is a separating equilibrium in which it takes 2 years of college to obtain a degree.

B) There is a separating equilibrium in which it takes 4 years of college to obtain a degree.

C) There is a separating equilibrium in which it takes 6 years of college to obtain a degree.

D) There is a separating equilibrium regardless of how many years of college it takes to obtain a degree.

E) There is never a separating equilibrium in this model.

Answer 1

Answer is option B)

two types of workers , High type ( H)

& Slow type (S)

Then, MP shows the wages

Then WH = 20, WS = 10

Per year college education, CH = 2, & CS = 4

So, let e years of education

Then, for separating eqm, only H type should obtain college education

so, WH-WS > e*CH

rise in wages should exceed the total cost of obtaining education for H type

& WH-WS < e*CS

rise in wages for slow type should be less than total cost of obtaining education for S type

so, 10> 2e & 10< 4e

so , e < 5, & 2.5< e

thus , 2.5< e < 5

so B is right, 4 years of education could lead to separating eqm