Consider a contracting environment where the principal is a monopoly and he has incomplete information about any agent he considers employing. An agent’s utility function is given by 2x*1/2 - ei, where the agent’s effort can take two values eH=2e and eL=e for some e 0. The agent has a reservation utility, u = 10. If the agent puts high effort, eH, the probability of a high return state is 0.8 whereas If the agent puts low effort, eL, the probability of a high return state is 0.4. Suppose the principal earns 200 in the high return state and 50 in a low return state. Required:

a) Solve for the optimal contracts for low and high effort as a function of e.

b) For which values of e does the principal prefer high effort and for which values of e does the principal low effort?