3. Principal-Agent Problem (from Eric Rasmusen's textbook) (30 points) Suppose the agent has a utility function of LI : e, where H 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 10;; if output is 1, 000. Only the agent observes his effort. Principals compete for agents. The following table summarizes the production technology: 1 l Probability of Output of l Effort 0 1000 e = 0 0.9 0.1 e = 7 0.2 0.8 a. Write out the incentive compatibility, participation, and zero-prot constraints for obtaining high effort. (5 points) b. Suppose the wage were fixed at If! 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)