Suppose there are two types of professors - Type 1 and Type 2. Students are motivated to work harder with Type 1 professors and learn more. Hence, their value to the university is $10. The value of Type 2 to the university is $4. Cost of education for Type 1 professors is 0.5c and for Type 2 is c where c is cost of getting education. There are 15% of Type 1 in the population. Type 1 professors like their jobs more, and hence, have a lower cost of getting their education to be a professor. Assume PhD is used as a signal.

a) What will be the wage paid if the university cannot separate out Type 1 from Type 2 professors? What is the problem if this happens and why?

b) Define separating equilibrium in this context. What values of c would lead to a separating equilibrium? Why is this a signaling equilibrium?

c) Define pooling equilibrium in this context. What values of c would lead to the two different types of pooling equilibrium that we talked about in class? Why are they signaling equilibrium?