Suppose the agent has a utility function of U= we, where e can assume the levels 0 or 7, and a reservation utility of U=4. The principal is risk neutral. Denote the agent's wage, conditioned on output, as w if output is 0 and wif output is 1,000. Only the agent observes his effort. Principals compete for agents. Table 6 shows the output. Table 6: Output from Low and High Effort Probability of output of X Effort 0 1,000 Total Low(e = 0) 0.9 0.1 1 High (e = 7) 0.2 0.8 1 220 (a) What are the incentive compatibility, participation, and zero- profit constraints for obtaining high effort? (b) What would utility be if the wage were fixed and could not depend on output or effort? (c) What is the optimal contract? What is the agent's utility? (d) What would the agent's utility be under full information? Under asymmetric information, what is the agency cost (the lost utility) as a percentage of the utility the agent receives?