3. Principal-Agent Problem (from Eric Rasmusen's textbook) (30 points) Suppose the agent has a utility function of U = (/1572 7 e, where B can assume the lev- els 0 or 7, and a reservation utility of U = 4. The principal is risk neutral. Denote the agent's wage, conditioned on output, as wL if output is 0 and am if output is 1, 000. Only the agent observes his effort. Principals compete for agents. The following table summarizes the production technology: 1 Probability of Output of Effort 0 1000 e = O 0.9 0.1 e : 7 0.2 0.8 a. Write out the incentive compatibility, participation, and zero-profit constraints for obtaining high effort. (5 points) b. Suppose the wage were xed at {b and could not depend on output or effort. What would the agent's utility be? (5 points) c. What is the optimal contract? (10 points) d. Calculate the agent's utility under full information and the agent's utility under moral hazard. (5 points) e. Under moral hazard, what is the agency cost (the lost utility) as a percentage of the utility the agent receives? (5 points)