There are two types of workers, Type I and Type II, and there are equal numbers of each of these two types in the labor market. Workers know their own type, and they can choose whether or not to get a college education. The marginal value to an employer of a Type I worker is 1 if this worker does not have a college education, and it is 2 if this worker has a college education. The marginal value to an employer of a Type II worker without a college education is 2, and the marginal value of a Type II worker with a college education is 5. The cost of a college education is e for a Type I worker, and 2 3 e for a Type II worker. Employers are not able to observe whether a worker is of Type I or of Type II, but are able to observe whether the worker has a college education. 5 The labor market is competitive and employers will pay a wage equal to what they believe to be the expected marginal product, given that worker’s education level. The net payoff to a worker who does not get a college education is equal to his or her wage. The net payoff to a worker with a college education is equal to that worker’s wage minus his or her cost of a college education. 

A) For what values of e will there be a separating equilibrium in which firms believe that all of the Type II’s and none of the Type I’s will get college educations? Explain your answer. 

B) For what values of e will there be a pooling equilibrium in which everyone goes to college and firms believe that anybody who would not go to college must be a Type I? 

C) Suppose that e = 4 and that the fraction π of all workers are Type I’s and the fraction 1 − π are Type II’s. For what values of π will there be a pooling equilibrium, in which everyone goes to college and firms believe that anybody who would not go to college must be a Type I?