Arthur's small business has grown to the point where he plans to hire a full-time manager. Arthur, an architect, has
Arthur's small business has grown to the point where he plans to hire a full-time manager. Arthur, an architect, has little inclination and ab il ity to manage a medium-sized, fast-growing business himself. He plans to semi-retire, devoting his working hours to consulting on issues of design and project management. Arthur's accounting system is quite simple. There is no R&D or other recognition lags. Consequently, the firm's payoff and its net income for the year are equal.
Arthur is negotiating with Yvonne as a possible manager. He wants the manager to work hard, since his past experience is that 90 percent of the time, hard work generates a net income (before any manager compensation ) of $2,250, while 10 percent of the time it generates $600. Arthur's recent experience, when he has not worked hard, is that the $2 ,250 net income is generated only 10 percent of the time; otherwise, net income is $600.
During the negotiations, Arthur ascertains that Yvonne is both risk and effort-averse. Her utility for money is equal to the square root of the amount of money received. Her disutility for effort is 6 if she works hard and 1.5 if she shirks. Her reservation utility is 9.5. Arthur decides that Yvonne is ideal for the job. He quickly offers her a series of one-year contracts, with annual cash compensation of a $100 salary plus 10 percent of net income before manager compensation. Yvonne immediately accepts.
Take calculations to two decimals.
a . Show calculations to demonstrate why Yvonne accepts the position. Will she work hard or shirk?
b. After two years, Arthur is worried because net income has been $600 each year. He decides to change Yvonne's next year's compensation contract. After consulting a compensation specialist, he offers her a salary of $52.30 plus a profit share of 9.21 percent of net income before manager compensation. Yvonne hesitates, but decides to accept. Show calculations to demonstrate why she hesitates, and why she nevertheless accepts.
c. Arthur is risk-neutral, with utility equal to the amount of profit received after manager compensation. Is Arthur's expected utility higher or lower under the new contract in part b, compared to the original contract in part a? Show calculations and explain why there is a difference.
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