Extra Practice 12

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School

University of Southern California *

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351X

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Economics

Date

Feb 20, 2024

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pdf

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Uploaded by SuperGoatPerson992

Econ 351x Extra Practice Chapter 12 1 1. Consider the following example. A risk-neutral worker can choose Low or High effort. The manager cannot observe the worker’s action, but the manager can observe the realized revenue for the firm (either $300 or $500). Low Effort High Effort Cost for worker= $0 Cost for worker= $12 Probability Low Revenue ($300) = 80% Probability Low Revenue ($300) = 60% Probability High Revenue ($500) = 20% Probability High Revenue ($500) = 40% Instead of offering a flat wage, the manager is trying a new payment scheme. The manager is currently offering to the worker a payment equal to x% of the revenue of the firm. Compute the minimum x such that the worker prefers to exert high effort. a. x = 30% b. x = 15% c. x = 20% d. x = 25% e. x = 35% 2. Consider the following example. A risk-neutral worker can choose Low or High effort. The manager cannot observe the worker’s action, but the manager can observe the realized revenue for the firm (either $300 or $500). Low Effort High Effort Cost for worker= $0 Cost for worker= $40 Probability Low Revenue ($300) = 75% Probability Low Revenue ($300) = 25% Probability High Revenue ($500) = 25% Probability High Revenue ($500) = 75% Instead of offering a flat wage, the manager is trying a new payment scheme. The manager is currently offering to the worker a payment equal to 30% of the revenue of the firm. Given this payment, the firm’s expected profit will be a. $205 b. $325 c. $315 d. $335 e. $245 3. Zack sells cars. The number of cars he is able to sell depends on his own effort “ e ’ . Zack's production function is Q = 3e. Zack's employer promises to pay him a bonus b for each car sold. However, there is a risk that the company will go bankrupt and will not be able to pay its employees. That is, with probability 0.6 the company will survive and will pay the promised bonus; and with probability 0.4 the company will go bankrupt and will pay nothing. Zack is risk-neutral, and when he chooses his effort, he does not know if the company will go bankrupt or not; he only knows the probabilities. For Zack, his effort cost is 3e 2 . Zack's expected utility equals his expected income minus the cost of effort. What is the bonus b that induces Zack to choose an effort e*=6?

Econ 351x Extra Practice Chapter 12 2 4. Ultimate Shoe Company (USC) is a new firm that produces handmade shoes. Let Q be the number of shoes produced. Each worker is able to produce shoes according to the following production function: Q = 2√𝑒 , where the variable e represents the effort of the worker. For the worker, his personal cost of exerting effort is simply Effort cost = 𝑒 2 . The worker receives from USC a payment b for each shoe produced. The worker’s utility equals his income minus his effort cost. The worker chooses the effort that maxim izes his utility. Find the worker’s optimal effort choice. a. 𝑒 ∗ = 4𝑏 2 b. 𝑒 ∗ = 2√𝑏 c. 𝑒 ∗ = 2𝑏 d. 𝑒 ∗ = 4√𝑏 e. 𝑒 ∗ = 𝑏 2 5. Eye-Kya is a new furniture company. It hires workers to produce chairs. Let Q be the number of chairs produced. Each worker is able to produce chairs according to the following production function: Q = 4𝑒 , where the variable e represents the effort of the worker. For the worker, his personal cost of exerting effort is simply Effort cost = 𝑒 2 4 . The worker receives from Eye-Kya a payment b for each chair produced. The worker’s utility equals his income minus his effort cost. The worker chooses the effort t hat maximizes his utility. Find the worker’s optimal effort choice. If b=1, then we have a. 𝑒 ∗ = 16 b. 𝑒 ∗ = √2 c. 𝑒 ∗ = 4 d. 𝑒 ∗ = 2 e. 𝑒 ∗ = 8 6. Consider the information from the previous question and suppose that Eye-Kya only has one worker. Eye-Kya pays to the worker b for each chair produced. Suppose Eye-Kya has market power; that is, Eye- Kya faces a downward sloping demand curve. If Eye-Kya sells Q chairs, then it can charge a price P = 520 – 2Q (inverse demand). Eye- Kya’s profit from the production of chairs equals its revenues minus the labor costs. Find the payment b that maximizes the firm’s profit. The firm’s profit is a. Profit = 33,050 b. Profit = 33,160 c. Profit = 33,280 d. Profit = 33,230 e. Profit = 33,190

Econ 351x Extra Practice Chapter 12 3 7. A risk-neutral firm produces chemical products, and its objective is to maximize expected profit. There is a risk that there will be an accident during the production process, and dangerous chemical products will be released into the ocean, polluting the water. To reduce the risk of an accident, the firm can choose the level of investment “s” in safety . If the firm invests “s” in safety, the probability of an accident is 1 -s, while the probability of no accident is s. For the firm, the cost of investing “s” in safety is s 2 . The firm has no direct cost or benefit from the accident (the accident does not directly impact the profit of the firm). The government wants to reduce the risk of an accident, but the government cannot observe the firm ’s investment in safety. Therefore, there is a moral hazard problem. However, the government can observe whether an accident occurred or not. So the government decides to create a fine (penalty): if an accident occurs, the firm must pay a fine F to the government. If an accident does not occur, then the firm does not have to pay anything. Compute the fine F that the government must impose, so that in the SPE the probability of an accident is 10%.

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