Slim owns a small business. He wants to retire from active management but retain ownership. He plans to hire a manager to run the business for him. However, Slim is concerned that a manager might not put sufficient effort into the business, which will result in a reduction of expected profits. The following table shows annual net incomes (before management remuneration) and associated probabilities under two levels of manager effort:

Manager's Effort

Work Shirk

Probability Net Income Probability Net Income

High Net Income 0.8 $25,000 0.2 $25,000

Low Net Income 0.2 $16,000 0.8 $16,000

Work: represents the manager working 60 hours per week during the year.

Shirk: represents the manager working 40 hours per week during the year.

Slim is interviewing Dim, a prospective manager. Dim's utility function for remuneration equals 4 times the square root of his annual total remuneration. Like most people, Dim is effort-averse. His (annual) disutility of effort is 0.1 times the number of hours he works per week. Dim's reservation utility is 150.

REQUIRED

1. Slim offers Dim remuneration of 10% of net income before manager remuneration. Determine if Dim would be willing to work for Slim and give your reasoning. Also, if he does decide to work for Slim, determine whether he would work or shirk and give your reasoning. Show all your calculations.
2. Suppose that Slim offers Dim an annual salary of $2,304, rather than a share of net income. Will he now choose to work or shirk? Explain and show all your calculations.
3. Suppose that low net income if Dim shirks is $12,250, rather than $16,000 as in the table above, and low net income if he works is the same as that shown in the table. Slim offers Dim a salary of $2,304 unless net income is $12,250, in which case he receives zero. Which decision will Dim now make? Show all your calculations.