Question
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
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
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started