G601: Problem Set 7: Moral Hazard and Adverse Selection

G601: Problem Set 7: Moral Hazard and Adverse Selection, March 7, 1999

A. Problems 7.1 from Games and Information .

B. A high-tech firm is trying to develop the game Wizard 1.0. It will have revenues of $200,000 if it succeeds, and $0 if it fails. Success depends on the programmer. If he exerts high effort, the probability of success is .8. If he exerts low effort, it is .6. The programmer requires wages of at least $50,000 if he can exert low effort, but $70,000 if he must exert high effort. (Let's just use payoffs in thousands of dollars, so 70,000 dollars will be written as 70.)

(a) Prove that high effort is first-best efficient.

(b) Explain why high effort would be inefficient if the probability of success when effort is low were .75.

(c) Let the probability of success with low effort go back to .6 for the remainder of the problem. If you cannot monitor the programmer and cannot pay him a wage contingent on success, what should you do?

(d) Now suppose you can make the wage contingent on success. Let the wage be S if Wizard is successful, and F if it fails. S and F will have to satisfy two conditions: a participation constraint and an effort-choice constraint. What are they?

(e) What is a contract that will achieve the first best?

(f) What is the optimal contract if you cannot pay a programmer a negative wage?

C. Problem 9.2 in Games and Information .

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