A firm earns gross profit (profit not including the wage) of 100 from a low-ability worker and 200 from a high-ability worker. A quarter of the workers are low-ability and the rest are high-ability.
a. If competitive firms have no signals available, what is the equilibrium wage they would pay?
b. Under what conditions on the cost of getting an education for each type, cL and cH, is there a separating equilibrium?
c. Suppose cL = 50 and cH = 0. Outline a pooling equilibrium in which both types get an education. Be sure to specify the firm's out-of equilibrium beliefs if it were to meet an uneducated worker. Similarly, outline a pooling equilibrium in which neither type gets an education.