Productivity of the high ability type is $25, productivity of the low ability type is $20. The cost of acquiring education level y is y for the high ability type and 3 y for the low ability type. Assume that both types are equally likely (qL = 0.5 for the high ability type, qH = 0.5 for the low ability type). Employers form beliefs about which type they face when observing the education level y.

Determine the range of y where there are

a) separating equilibria

b) pooling equilibria with no education

c) pooling equilibria with non-zero education

How can you refine the separating equilibria in part a)?

This is a question on game theory!