The shareholders of Blythe Ltd. are hiring a new manager whose effort in running the firm cannot be observed. If the manager shirks (i.e., he chooses action a₂) he will only put in effort amounting to about 40 hours a week. If he works hard (he chooses action a₁), he will put in 60 hours per week. Under the incentive contract being considered by the shareholders, the manager would receive a salary of $100,000 per annum plus a bonus of 25% of reported net income before salary and bonus. You are asked to analyze the expected impact of the bonus plan on the manager. You estimate that if the manager puts in about 60 hours per week (a₁), net income before manager remuneration will be $1,040,000 per annum with probability of 0.7, and $90,000 per year with probability of 0.3. If the managers effort is 40 hours per week (a₂), analysis of past profitability shows that annual net income has been $1,040,000 with probability of 0.4 and $90,000 with probability of 0.6. You also ascertain that the managers utility for money is equal to the square root of the money received, and that disutility for effort is four times the number of hours worked per week. The managers reservation utility is 160. The shareholder is risk neutral with utility equal to the amount of profit received after the manager compensation.

Which act, a1 or a2, will the manager prefer under the incentive contract? Show calculations