Edison 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. Edison 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 Edison 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 Edison. 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.

Edison's business has, in previous years, earned net income (before manager compensation) of $764, 75 percent of the time and net income of $0, 25 percent of the time. Edison has always worked hard (a₁) and reckons that if he did not work hard, net income would have been $764 only 20 percent of the time and zero for 80 percent of the time. He expects this earnings pattern to continue in to the future with a new manager. Edison 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.

Required

a. What proportion of net income must Edison offer Lily so that she will accept the position and work hard? Show calculations.

b. Assuming that Lily accepts Edison's offer, verify that she will in fact work hard.

c. Having accepted the position, Lily soon realizes that Edison 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 $764 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, Edison learns about the revelation principle. Design a contract t hat Lily wi ll accept and, given that she shirks, will motivate her to report net income honestly- that is, w ill remove her motivation to manage net income.

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 $764. In fact, if unmanaged net income is $764, net income can be managed only within a range [$700-$784). If unmanaged net in come is $0, net income can be managed in a range ($Q-$9). What proportion of net income must Edison offer lily as compensation so that she will accept the position and work hard? Assume that whatever unmanaged net income is, lily will manage it to the upper end of the appropriate range. Any further earnings management (i.e., beyond GAAP) will be immediately detected.