A firm’s board of directors wants to maximize its profits. If the firm’s manager puts in a high effort, the firm gets a high profit of 9 with probability 80%, but if the manager puts in a low effort, the firm gets a low profit of 4 with probability 80%. The utility functions of both the board of directors and the manager are identical and are simply u(b)=b. High effort for the manager costs 2. The manager has an outside wage of 1. Calculate the optimal wage schedule under high and low realized profits.
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- A firm’s board of directors wants to maximize its profits. If the firm’s manager puts in a high effort, the firm gets a high profit of 9 with probability 80%, but if the manager puts in a low effort, the firm gets a low profit of 4 with probability 80%.
The utility functions of both the board of directors and the manager are identical and are simply u(b)=b. High effort for the manager costs 2. The manager has an outside wage of 1.
Calculate the optimal wage schedule under high and low realized profits.
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- A firm's board of directors wants to maximize its profits. If the firm's manager puts in a high effort, the firm gets a high profit of 9 with probability 80%, but if the manager puts in a low effort, the firm gets a low profit of 4 with probability 80%. The utility functions of both the board of directors and the manager are identical and are simply u(b)-b. High effort for the manager costs 2. The manaаger has an outside wage of 1. Calculate the optimal wage schedule under high and low realized profits.A firm wants to maximize its expected profit. The firm must choose the production quantity q. The production cost is C=2q2 . However, the firm is uncertainty about the price consumers will be willing to pay for the product. With probability 75% the consumers will be willing to pay $24 per unit of output q. With probability 25% consumers will only be willing to pay $8. The firm must choose q before it learns if the price will be high or low. a) Compute the quantity q that maximizes the firm’s expected profit. Find the expected profit given this optimal quantity. b) Suppose that a consulting company knows exactly how much consumers are willing to pay. How much would the firm be willing to pay for this information?BPO Services is in the business of digitizing information from forms that are filled out by hand. In 2006, a big client gave BPO a distribution of the forms that it digitized in house last year, and BPO estimated how much it would cost to digitize each form. Form Type Mix of Forms Form Cost A 0.5 $3.00 B 0.5 $1.00 The expected cost of digitizing a form is . Suppose the client and BPO agree to a deal, whereby the client pays BPO to digitize forms. The price of each form processed is equal to the expected cost of the form that you calculated in the previous part of the problem. Suppose that after the agreement, the client sends only forms of type A. The expected digitization cost per form of the forms sent by the client is . This leads to an expected loss of per form for BPO. (Hint: Do not round your answers. Enter the loss as a positive number.)
- Jacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a premium. Jacob’s utility function for wealth is given by U(w) = In (w). (A) What is the maximum amount Jacob is willing to pay for this insurance? Show work and explain.Max Pentridge is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $10,000. With probability p = 0.9 the palace will succeed and Max's wealth will grow from $10,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $5,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $10,000 with certainty? ____ (Please round your final answer to the whole dollar, if necessary)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 Low or High investment in safety. Low Investment in Safety_ Cost for firm= $0 Probability of an Accident = 80% Probability of No Accident =20% High Investment in Safety Cost for firm= $150 Probability of an Accident = 20% Probability of No Accident = 80% The Government wants to reduce the risk of an accident, but the Government cannot observe the fir m'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 occurs, then the firm does not have to…
- Farmer Brown faces a 25% chance of there being a year with prolonged drought, with zero yields and zero profit, and he faces a 75% chance of a normal year, with good yields and $100,000 profit. These probabilities are well-known. Suppose that an insurance company offered a drought insurance policy that pays the farmer $80,000 if a prolonged drought occurs. Assume that the farmer’s utility function is u(c) = ln(c). He has initial wealth of $25,000. a Let Y be the expected amount of money that the insurance company will pay Farmer Brown, in the case that Farmer Brown is insured. Compute Y. b. Let X be the most amount of money X Farmer Brown is willing to pay for the insurance. Set up the equation that defines X. Either carefully explain in words what your equation says or put short captions explaining the different parts of your equation. c Determine X to the nearest dollar. d What is the economic intuition on why X > Y?Suppose that a firm offers an infinite warranty on a product that breaks down with probability 1/3 (if it is replaced after a breakdown, then it again breaks down with the same probability and can be replaced again under an infinite warranty, and so on). With probability 1/4 the buyer is lazy and never asks for a replacement. With the remaining probability the buyer always asks for a replacement when the product breaks down. The marginal cost of production is 8. What is the expected cost of selling the product with this infinite warranty?Amy likes to go fast in her new Mustang GT. Their utility function over wealth is v(w) where w is wealth. If Amy goes fast she gets an increase in utility equal to F. But when Amy drives fast, she is more likely to crash: when she drives fast the probability of a crash is 10%, but when she obeys the speed limit, the probability of a crash is only 5%. Amy's car is worth $2000 unless she crashes, in which case it is worth $0. If Amy doesn't have insurance, driving fast isn't worth the risk, so she will alway obey the speed limit. If Amy is offered an insurance contract with full insurance for a premium P with the deductible D, which of the inequalites below is her incentive compatibility constraint that makes sure that she will still obey the speed limit even when she is fully insured? 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.05U(0 – P – D + 2000) + 0.95U(2000 – P) 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.1(U(2000 – P – D) + F) + 0.90(U(2000 – P) + F) 0.05U(2000 – P – D) + 0.95U(2000)…
- A client (the principal) is trying to determine the best possible contract to enter into with her favoring the client is x and the probability of winning is 8. lawyer (the agent). The principal makes the following assumptions: the dollar amount of a judgment The lawyer has offered to () work for a fixed fee of F. (i) pay the client a fixed fee of F and keep the remainder of the judgment, and (ii) work for a contingent fee or a share of the contract with t lawyer's share being a If the principal is highly risk-averse and is interested in production efficiency she will choose option i option i option iA consumer has the following utility function u(x)= root x where x is the consumer’s total wealth. The consumer's total wealth is the consumer’s cash plus the value of her house. The consumer has $400 in cash (risk free) plus a house. The house is currently worth $756. With probability 70% nothing happens, and the value of the house stays the same. With probability 30%, high winds will cause $580 in damages to the house (in which case, the house value becomes $176). An insurance company offers to fully insure the house at an insurance premium p. What is the maximum insurance premium that the consumer is willing to pay? The consumer is willing to pay at most p=. The fair insurance premium is . In this example, the associated risk premium is .A drug company is considering investing $100 million today to bring a weight loss pill to the market. At the end of one year, the firm will know the payoff; there is a 0.50 probability that the pill will sell at a high price and generate $37 million per year of profit forever and a 0.50 probability that the pill will sell at a low price and generate $1 million per year of profit forever. The interest rate is 10%. Suppose the firm decides to wait one year to determine whether the pill will sell at a high or low price. The firm will not invest if it learns that the pill will sell at a low price. What is the net present value of waiting one year to make the investment? $122.72 million $64.5 million $201.22 million $88 million