Tom operates a small, fast- growing electronics business. His workload has expanded to the point where he decides to hire a full- time manager. He will then take one year off to travel, and on his return he will concentrate on the technical aspects of the business.
Tom is negotiating with Lily for the manager job. He ascertains that Lily is risk averse, with utility for money equal to the square root of the dollar compensation received. Lily advises Tom that she already has a job offer, which yields her an expected utility of 6. She is not willing to work for less than this, but would accept an expected utility of 6 from Tom. Lily also advises that she is effort averse, with disutility of effort of 2 if she works hard, and 1 if she does not work hard.
Tom’s business has, in previous years, earned net income (before manager compensation) of $ 725 75% of the time and net income of $ 0 25% of the time. Tom has always worked hard (a1) and reckons that if he did not work hard, net income would have been $ 725 only 20% of the time and zero for 80% of the time. He expects this earnings pat-tern to continue into the future with a new manager. Tom realizes that he must motivate Lily to work hard, and he offers her a one- year contract, with compensation based on a proportion of reported net income before manager compensation.

a. What proportion of net income must Tom offer Lily so that she will accept the position and work hard? Show calculations.
b. Assuming that Lily accepts Tom’s offer, verify that she will in fact work hard.
c. Having accepted the position, Lily soon realizes that Tom cannot observe the firm’s unmanaged net income— he can only observe the net income she reports. She is tempted to opportunistically manage earnings so as to ensure that net income of $ 725 is reported, even if she does not work hard. Calculate whether or not, in a one- year contract, Lily is better off to work hard and not manage earnings or to not work hard and manage earnings.
d. Concerned that Lily may manage earnings, Tom learns about the revelation principle. Design a contract that Lily will accept and, given that she shirks, will motivate her to report net income honestly— that is, will remove her motivation to manage net income. Note: If net income is reported as zero, Lily must receive a salary in order to attain reservation utility.
e. New GAAP rules make it impossible to manage earnings from $ 0 up to $ 725. In fact, if unmanaged net income is $ 725, net income can be managed only within a range [$ 700–$ 784]. If unmanaged net income is $ 0, net income can be managed in a range [$ 0–$ 9]. What proportion of net income must Tom offer Lily as compensation so that

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