Practice question. please help me do it. Do as much as you can and i will give you full rating.

9. A risk neutral principal hires a risk averse agent to work on a project. The agent's utility function is V( w. a) = W7 no). where (a is wage, guy} is the disutility associated with the effort level 6, exerted on the project. The agent can choose one of two possible effort levels, 9;; or q, with associated disutility levels (ag) 2 4, and gfq) = 2. 0 If the agent chooses effort level ('11, the project yields 80 with probability 1/2, and 0 with probability 1/2. 0 If the agent chooses q, the project yields 80 with probability 1/4 and 0 with probability 3/4. The reservation utility of the agent is 0. Let {7:13, 27);} be an output-contingent wage contract, where mg is the wage paid if the project yields 80, and w; is the wage if the yield is 0. The agent receives a fixed wage if My 2 rub (a) If effort is observable, which effort level should the principal implement? What is the best wage contract that implements this effort? [5 marks] (b) Suppose effort is not observable. What is the optimal contract that the principal should offer the agent? What effort level does this contract im- plement? [3 marks] (c) Compare the optimal contract in part (a) with that in part (b) and provide intuition for any similarity or difference in the income risk they impose on the agent and in the principal's payoff. [7 marks]