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(Moral Hazard) The owner of a company has to hire a manager for a new project. If the project succeeds, it brings $2 million profit to the company. If fails, the profit is zero. The owner first offers a base salary, $w and a bonus $b if the project is successful to the manager. Then the manager decides whether to accept or reject it. If the manager accepts the job, he needs to choose whether to expend good supervisory effort or to expend poor supervisory effort. The disutility is 0.4 if he expends good supervisory effort and 0 if poor good supervisory effort. The project will succeed with probability 0.7 if he provides good effort and succeed only with probability 0.2 if he provides poor effort. If the manager rejects the owner’s offer, he can get an outside job, which pays him $90,000. The owner is risk neutral, and the manager is risk averse. The owner’s utility function is u(y) = y. The manager’s utility function is u(y) = ?y, where y is dollar income in millions.
(a) Draw the game tree for the situation above. Write down payoffs for the players in the order of (Owner, Manager).
(b) What is the incentive compatibility constraint for the manager to choose good supervisory effort?
(c) What is the participation constraint for the manager to work for this company than to accept the outside job?
(d) Find the pair of (w, b) that maximizes the owner’s expected profit.
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