# Question: Arnold is the successful owner and operator of a small

Arnold is the successful owner and operator of a small business. He plans to take a one-year vacation and is interviewing Minnie for the position of manager while he is away.

On the basis of extensive past experience, Arnold 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 0.8. Payoffs are before any manager compensation.

However, cash flow will not be known until some time after Arnold 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, Minnie demands to be paid at year- end.

Arnold decides to base compensation on net income, a performance measure available at year- end. Due to random effects of states 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 Minnie, Arnold finds that her reservation utility is 2.6, that her utility for money equals the square root of the amount of money received, and that her disutility of effort if she works hard is 8. If she shirks, her effort disutility is 7. Arnold decides to offer Minnie a one- year contract with compensation based on a percentage of audited net income before compensation. Minnie accepts.

Required

a. What percentage of net income before compensation did Arnold offer Minnie? Verify that Minnie will work hard.

b. Why did Arnold specify that net income be audited?

c. Suppose instead that if Minnie shirks, net income will be $ 625 with probability 0.3 and $ 400 with probability 0.7 (i. e., moving support). What contract would Arnold now offer Minnie so that she works hard? Explain.

On the basis of extensive past experience, Arnold 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 0.8. Payoffs are before any manager compensation.

However, cash flow will not be known until some time after Arnold 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, Minnie demands to be paid at year- end.

Arnold decides to base compensation on net income, a performance measure available at year- end. Due to random effects of states 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 Minnie, Arnold finds that her reservation utility is 2.6, that her utility for money equals the square root of the amount of money received, and that her disutility of effort if she works hard is 8. If she shirks, her effort disutility is 7. Arnold decides to offer Minnie a one- year contract with compensation based on a percentage of audited net income before compensation. Minnie accepts.

Required

a. What percentage of net income before compensation did Arnold offer Minnie? Verify that Minnie will work hard.

b. Why did Arnold specify that net income be audited?

c. Suppose instead that if Minnie shirks, net income will be $ 625 with probability 0.3 and $ 400 with probability 0.7 (i. e., moving support). What contract would Arnold now offer Minnie so that she works hard? Explain.

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