12. A risk neutral principal hires a risk averse agent to work on a project. The agent's utility function is = g(ei), where w is wage,g@'i) is the disutility associated with the effort level ei exerted on the project. The agent can choose one of two possible effort levels, en or et., with associated disutility levels g(eu) = 2, and g@l.) = 1. If the agent chooses effort level en, the project yields 20 with probability 3/4, and O with probability 1/4. If he chooses et., the project yields 20 with probability 1 / 4 and O with probability 3/4. The reservation utility of the agent is 0. Let WI.} be an output-contingent wage contract, where WII is the wage paid if the project yields 20, and WI, is the wage if the yield is O. The agent receives a fixed wage if WH = (a) If effort is observable, which effort level should the principal implement? What is the best wage contract that implements this effort? [8 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? 18 marks] (c) Explain in words why the principal's payoff differs across the cases con- sidered in parts (a) and (b) above. [4 marks]