Assume that a principal is risk-neutral and wants to hire a manager to perform a task. The manager has a utility function u(s) = s of salary s with a disutility Page 5 of u 0 = 100, i.e. not working at all. He can exert two levels of unobservable effort, H and L, with costs ch = 500 and cl = 200. There are two possible observable outputs xh = 1, 000, 000 and xl = 60, 000 which are positively associated with effort. The high effort can have a probability of 0.8 generating the high output while the low effort has only a probability of 0.2 generating the same output. The principal cannot observe the manager's effort but can verify the output and has to think about how to make contracts to motivate him to work hard.

(a) Formulate this problem as an incentive-compatible contract model so that the principal can induce the manager to work hard. Explain in detail.

(b) Prove that working hard is indeed better for the manager than shirking. Show your process of obtaining the optimal salary for each of the two levels of output