Question - Micah is the owner and operator of a small business. He plans to take a one-year vacation and is interviewing Sarah for the position of manager while he is away. Based on past experience, Micah knows that if the manager works hard (a1), the cash flow (payoff) from the year's operations will be $505 with probability 0.8 and $345 with probability 0.2. If the manager shirks (a2), cash flow will be $505 with probability 0.2 and $345 with probability of 0.8. Payoffs are before any manager compensation. However, cash flow will not be known until sometime after Micah returns, since all sales are on long-term credit, and advertising costs incurred in the year continue to generate sales well after year-end. However, Sarah demands to be paid at year-end.
Micah decides to base compensation on net income, a performance measure available at year-end. Due to random effects of state of nature, he knows that if the payoff is going to be $505, net income will be $625 with probability 0.7 and $225 with probability 0.3. If the payoff is going to be $345, net income will be $625 with probability 0.3 and $225 with probability 0.7. Net income is before any manager compensation.
Upon interviewing Sarah, Micah finds that her reservation utility is 2.6, that her utility for money equals the square root of the amount of money received, and her disutility of effort if she works hard is 8. If she shirks, her effort disutility is 7. Micah decides to offer Sarah a one-year contract with compensation based on a percentage of audited net income before compensation. Sarah accepts.
a. What percentage of net income before compensation did Micah offer Sarah? Verity that Sarah will work hard.
b. Why did Micah specify that net income be audited?
c. Suppose instead that if Sarah shirks, net income will be $625 with probability 0.3 and $400 with probability 0.7. What contract would Micah now offer Sarah so that she works hard? Explain.