Pierre is negotiating with Yvonne as a-possible manager. He wants the manager to work hard, since his past experience is that hard work generates a net income (before any manager compensation) of $2,000 90% of the time, and $900 10% of the time. Pierre's recent experience, when he has not worked hard, is that the $2,000 net income is generated only 10% of the time, otherwise net income is $900.

During the negotiations, Pierre 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 4 if she works hard and 1.1 if she shirks. Her reservation utility is 11.

Pierre decides that Yvonne is ideal for the job. He quickly offers her annual cash compensation of a $100 salary plus 10% of net income before manager compensation. Yvonne immediately accepts.

Required

a. Show calculations to demonstrate why Yvonne accepts the position.

b. After two years, Pierre is worried because net income has been $900 each year. He decides to change Yvonne's compensation contract. After consulting a compensation specialist, he offers her a salary of $52.30 plus a profit share of 9.

21% of net income before manager compensation. Yvonne hesitates, but decides to accept. Show calculations to demonstrate why she hesitates but accepts.

Note: Take calculations to two decimal places.

c. Pierre is risk-neutral, with utility equal to the amount of profit received after manager compensation. Is Pierre's expected utility higher or lower under the new contract in part

b, compared to the original contract | in pat a Show calculations and explain why there is a difference.