Consider the following moral hazard game, with a risk-neutral principal hiring a risk averse agent. The principal's payoff is given by 7 = q - w and the agent's payoff is given by U = Vw - e. The agent's reservation utility is given by U - 1, and the agent can choose between an effort level, , of either 0 or 10. Output is equal to either 0 or 400 and depends in part on effort and in part on luck. The probabilities of the output levels conditional upon effort are shown below: Probability (q=0) Probability (q=400) e= 0 0.5 0.5 e=10 0.1 0.9 (a) Write an expression for the agent's participation constraint (PC) and an expression for their incentive compatibility constraint (ICC). Explain why these are necessary conditions that need to hold if the principal is effectively resolving the moral hazard problem. (b) Assuming that principals are scarce and agents compete to work for them, what would the optimal contract be if the principal can observe output but not effort? What would be the principal's expected profits? What about the agent's expected utility