9. A risk neutral principal hires a risk averse agent to work on a project. The agent's utility function is WW: 31') = x5 3(a): where w is wage, g(e,-} is the disutility associated with the effort level a,- exerted on the project. The agent can choose one of two possible effort levels, EH or 1, with associated disutility levels rm) 2 4, and g(eL:} = 2. i If the agent chooses effort level EH, the project yields 80 with probability 12" 2, and l] with probability If 2. i If the agent chooses 81, the project yields 80 with probability LE4 and I} with probability Iii-4. The reservation utility of the agent is 0. Let {WI{JUL} be an output-contingent wage contract, where an}; is the wage paid if the project yields 80, and 10,: is the wage if the yield is U. The agent receives a fixed wage if am 2 am. [a] If effort is observable, which effort level should the principal implement? What is the best wage contract that implements this effort? [5 marks] u ose e ort is not o serva e. at is t e tlma contract at t e b 3 pp ff ' b bl Wh ' h 0p ' 1 th h 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. [5' marks]