Suppose there are two types of persons: high-ability and low-ability. The schooling required to obtain a particular diploma costs a high-ability person $8,000 per year, and it costs a low-ability person $10,001 per year. Firms wish to use this diploma as a signal of an individual’s ability. The firms intend to pay workers such that the present value of lifetime earnings for a worker without the diploma is $250,000 and the present value of lifetime earnings for a worker with the diploma is $450,000.
(a) What range of years of education must be required to obtain this diploma in order for the diploma to be an effective signal of worker ability?
(b) In a competitive labor market, how many years of education will be required to obtain this diploma in equilibrium? Briefly explain why in this case.