9.5 Suppose there are two types of workers, high-ability workers and low-ability workers. Workers’ wages are determined by their ability—high ability workers earn $50,000 per year, lowability workers earn $30,000. Firms cannot measure workers’ abilities but they can observe whether a worker has a high school diploma. Workers’ utility depends on the difference between their wages and the costs they incur in obtaining a diploma.

a. If the cost of obtaining a high school diploma is the same for high-ability and low-ability workers, can there be a separating equilibrium in this situation in which high-ability workers get high-wage jobs and low-ability workers get low wages?

b. What is the maximum amount that a high-ability worker would pay to obtain a high school diploma? Why must a diploma cost more than this for a low-ability person if having a diploma is to permit employers to identify high-ability workers?