You are given the following payoff table: State of Nature Altemative Sz 36 49 A2 144 0. A3 81 Prior probability 0.1 0.9 Assume that your utility function is the exponential utility function U(x) = R(1- e-) with a risk tolerance of R = 50. Determine the altemative.that maximizes the expected utility. %3D

You are given the following payoff table: State of Nature Altemative Sz 36 49 A2 144 0. A3 81 Prior probability 0.1 0.9 Assume that your utility function is the exponential utility function U(x) = R(1- e-) with a risk tolerance of R = 50. Determine the altemative.that maximizes the expected utility. %3D

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter17: Making Decisions With Uncertainty

Section: Chapter Questions

Problem 4MC

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Suppose that the consumer is asked to contemplate a gamble with a probability of 60% of winning Birr 10,000 with a utility of 10 utils, and a 40% probability of winning Birr 15,000 with a utility of 12 utils. A. What will be the expected income and expected utility of the consumer? B. If the utility of this consumer from a risk free alternative which gives him an income equal to the expected income of the risky alternative given above is equal to 11 utils, is this consumer risk lover or risk averse? Why? Illustrate your answer with the help of a diagram
Eunice, the industry analyst of H&M, wants to determine the propensity of Major Clothingcompanies toward risk. She was able to determine the utility distribution of H&M, Uniqloand Dickies. For H&M, If the expected payoff of a venture is a loss of 125,000, the utilityvalue is 0.00, if a loss of 75,000, the utility value is .2, if breakeven, the utility value is .5,if gain of 75,000 .8 and if gain of 125,000 utility value is 1. For Uniqlo, if loss of 125,000utility value is 0, if loss of 75,000 utility value is .1, breakeven is .4, if a gain of 75,000,utility value is .7 and if gain of 125,000 utility value is 1. For Dickies, if loss of 125,000,utility value is 0, if loss of 75,000, utility value is .3 breakeven is .6, if gain of 75,000, utilityvalue is .9 and gain of 125,000, utility value is 1. What is the propensity to risk of the threeinternet companies? Explain your graph.
An investor with capital x can invest any amount between0 and x; if y is invested then y is eitherwon or lost, with respectiveprobabilities p and 1− p. If p > 1/2, how much should be invested byan investor having a exponential utility function u(x) = 1 − e −bx ,b > 0.
Assume that Rosemarie has the following utility function: U(W) = W1/2. She is selling her homeand believes that the house will sell for $250,000 with probability ¼ and $122,500 withprobability ¾.a. What is her expected utility?b. What is the risk premium (P) Rosemarie would pay to avoid bearing this risk?
The owner of a ski resort is considering installing a new ski lift that will cost $900,000. Expenses for operating andmaintaining the lift are estimated to be $1,500 per day when operating. The U.S. Weather Service estimates thatthere is a 60% probability of 80 days of skiing weather per year, a 30% probability of 100 days per year, and a 10% probability of 120 days per year. The operators of the resort estimate that during the first 80 days of adequate snow in a season, an average of 500 people will use the lift each day, at a fee of $10 each. If 20 additional days are available, the lift will be used by only 400 people per day during the extra period; and if 20 more days of skiing are available, only 300 people per day will use the lift during those days. The owners wish to recover any invested capital within five years and want at least a 25% per year rate of return before taxes. Based on a before-tax analysis, should the lift be installed?
Deborah is at the casino and is considering playing Roulette. In Roulette, a ball drops into one of 36 slots on a spinning wheel. 17 of the slots are red, 17 are black, and 2 are green. Each slot is equally likely and occurs with probability 1/36. Deborah bets $1.00 on black. If the ball drops into a black slot she receives $2.00 and if it drops into a red or green slot, she receives nothing. a) The expected value of Deborah’s bet (after subtracting the $1.00 she bet) is $________________ b) Given that Deborah makes this bet, is she risk adverse, risk neutral, or risk loving?
Clancy has $4800. He plans to bet on a boxing match betweenSullivan and Flanagan. He finds that he can buy coupons for $6 thatwill pay off $10 each if Sullivan wins. He also finds in another storesome coupons that will pay off $10 if Flanagan wins. The Flanagantickets cost $4 each. Clancy believes that the two fighters each have aprobability of ½ of winning. Clancy is a risk averter who tries tomaximize the expected value of the natural log of his wealth. Whichof the following strategies would maximize his expected utility? (a) Don’t Gamble (b) Buy 400 S tickets and 600 F tickets(c) Buy exactly as many F tickets and S tickets (d) Buy 200 S and 300 F(e) Buy 200 S and 600 F
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?
Find the values of Absolute Risk Aversion (ARA) and Relative Risk Aversion (RRA) for all the cases below. . U(C) = C0.5. . U(C) = C2. . U(C) = 5×C. . U(C) = -C-2. . U(C) = -C-7. . U(C) = -e-7C. . U(C) = [1/(1-a)]×C1-a , where a is a constant.
Market Data Rate of Return Standard Deviation Treasury Bills 4.25% 0.00% S&P 500 12.00% 21.00% Required: Using the information in the table above and the varying risk aversions below, please calculate allocations to the risky and risk-free assets. (Use cells A5 to C6 from the given information to complete this question.) Risk Aversion Percent Allocated to the Market (S&P 500) Percent Allocated to Treasury Bills 4.00 2.00 1.50
Exercise 3: Risky Investment Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. 1 1 With probability p = 2 the project will be a success and return V > 160, 000. With probability 1 −p = 2 the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]
A manager is deciding whether to build a small or a large facility. Much depends on the future demand that thefacility must serve, and demand may be small or large. The manager knows with certainty the payoffs that willresult under each alternative, shown in the following payoff table. The payoffs (in $000) are the present values offuture revenues minus costs for each alternative in each event.What is the best choice if future demand will be low?