Suppose that education does not increase an individuals marginal productivity and that there are two types of people in the world: over-achievers and slackers. Overachievers dont really mind going to school and for them the cost of y years of school is y/2 . Slackers, on the other hand, find school more burdensome, and for them the cost of y years of school is y. Consider two different firms. Firm 1 offers to pay workers such that the present discounted value of their lifetime earnings is $12 if workers have at least 6 years of schooling, and $8 to all other workers. Firm 2 offers to pay workers such that the present discounted value of their lifetime earnings is $12 if workers have at least 2 years of schooling, and $8 to all other workers.

(a) For each firm separately, analyze whether its educational requirements will enable them to distinguish between over-achievers and slackers.

(b) What is the minimum educational requirement a firm can offer and still expect to be able to distinguish between over-achievers and slackers?