You are engaged by the owner of a small firm to recommend a one-year compensation contract for the firm's top manager. She is concerned about cash flow and feels that in previous years the manager may have been shirking.

You ascertain that if the manager works hard (a₁), the firm's ultimate cash flow from current year operations will be one of $338 or $142 (before manager compensation) with probability 0.6 or 0.4, respectively. If the manager shirks (a₁), cash flow will be $338 or $142 with probability 0.2 or 0.8, respectively. Cash flow, however, will not be known until after the manager's one-year contract has expired.

As an expert in GAAP. you know that if cash flow will be $338, net income for the year will be $456 with probability 0.7 and $63 with probability 0.3. If cash flow will be $142, net income will be $456 with probability 0.2 and $63 with probability 0.8. You recommend that the manager's contract be based on reported net income. 

You interview the manager and find that he is rational, risk-averse with utility for money equal to the square root of the amount of money received, and effort-averse with disutility of effort of 2.5 if he works hard and 1.8 if he shirks. The manager's reservation utility is 4.

Required

a. What percentage of net income must the manager be offered so that he will accept the contract and work hard?

b. Suppose that all information given in the question is unchanged except that if the manager shirks, and cash flow will be $142, net income will be $456 with probability 0.3 and $30 with probability 0.7. What contract would you then recommend? Show calculations and explain your contract choice.

c. The owner is risk-neutral, with utility equal to the dollar amount of the payoff, net of the manager's compensation. What is the agency cost of the contract in part a? Show calculations.