There are two types of workers in an economy: half are high productivity workers (H) and half are low productivity workers (L). Type H's have a constant marginal product of ! = 20 and type L's have a constant marginal product of ! = 10. Firms do not observe a worker's type. Assume this is a competitive market, so in equilibrium, firms pay workers their expected marginal productivity.

a) Without any further information about workers, what wage will firms pay?

Suppose workers are interviewed before being hired, and firms use their performance in the interview to gather additional information about the workers. Specifically, firms expect workers' marginal productivity to be: ! ! = 0.5! + 0.5!, where ! is the average level of productivity among all workers and s is the worker's "score" in the interview. This can either be 10 or 20.

b) What will a worker be paid if he scores a 20 in the interview? What will he be paid if he scores a 10?

Now, suppose workers come from two distinguishable groups, A and B, and there are no systematic productivity differences between the two groups. However, firms believe that ¾ of A workers are type H and only ¼ of B workers are type H.

c) What will an A worker who scores 20 in the interview be paid? What will a B worker who scores 20 in the interview be paid?

Now, suppose firms believe that half of both A and B workers are type H; however, they have difficulty interpreting interview scores for B workers. This causes them to put less "weight" on the information from the interview when determining the expected productivity of B workers. Specifically, firms expect MP of B workers to be: ! ! ! = 0.67! + 0.33!. Expectations about MP of A workers are the same as above.

d) What will a B worker who scores 20 in the interview be paid? What will a B worker who scores 10 be paid? How do these values compare with the corresponding values for A workers?