3. Markets with Asymmetric Information I (32 points)

Suppose employers follow a strategy in which they hire workers and pay salaries depending on the course work completed according to the following conditions:

Course Work	Annual Income
Not completed (y=0 weeks)	$ 20,000
Completed at intermediate level (y= 4weeks)	$ 85,000
Completed at advanced level (y= 6 weeks)	$ 108,000

There are two types of candidates: high-ability (H) and low-ability (L). Each candidate is choosing whether to complete an intermediate level course or an advanced level course, relative to not completing any. The intermediate and advanced courses differ in content, so one year of intermediate level work is not the same as one year of advanced level work. The costs of completing course work for each type of candidates are:

C_H(y) = $10, 000y;

C_L(y) = $15, 000y.

(a) ( 1 Point) Calculate the benefit (additional income) of completing the course work at the intermediate level.

(b) ( 1 Point) Calculate the benefit (additional income) of completing the course work at the advanced level.

(c) ( 4 Points) Will a high-ability candidate complete the advanced course work?

(d) ( 4 Points) Which course work will a low-ability candidate complete?

(e) ( 2 Points) Will y = 4 allow firms to identify candidates correctly? What about y = 6?

(f) ( 5 Points) Find the range of y for which the signaling equilibrium arises for the intermediate course work (such that only the high-ability candidate will complete the intermediate course work).

(g) ( 5 Points) Find the range of y for which the signaling equilibrium arises for the advanced course work (such that only the high-ability candidate will complete the advanced course work).

(h) (6 points) Draw a diagram with weeks of course work on the horizontal axis. On this diagram, show the benefits to education, B(y), the costs of education for each type of candidates, and the signaling equilibrium for each type of course work.

(i) ( 4 Points) Suppose firms cannot distinguish between the two types of candidates and no other solutions to the problem of adverse selection exist. What are the consequences of adverse selection in the labor market?