Answered: A lottery pays 0 or 108 with equal…

A lottery pays 0 or 108 with equal probability. Calculate the risk premium for an individual with a utility function given by u=vI.

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 5MC

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An individual has the utility function U(I) = I^(1/2), where I is their net income. (Note that I to the exponent/power of 1/2 is the same as the square root of I.) The individual starts with $1600 in income. The individual has a 20% probability of being very sick, 30% probability of being slightly sick, and 50% probability of being healthy. If the individual is sick, they lose net income because they need to pay healthcare costs. The healthcare costs are $1600 if they are very sick, $700 if they are slightly sick, and $0 if they are healthy. Please use this information for the following parts of this question unless otherwise specified. What is the individual's expected utility? Suppose a health insurance company offers the individual a full insurance contract. What is the actuarially fair, full insurance premium for this individual? What is the individual's expected utility if they purchase a full insurance contract at the actuarially fair, full insurance premium?
Leora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x).a) What is the expected income? What is Leora’s expected utility (you may leave in log form)? b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation?c) What is the maximum that Leora would be willing to pay for a full insurance policy?d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.
Consider a gamble/lottery in which a coin is tossed rapidly until a tail comes up. 2m rupee is given if the tail comes up at the mth toss. Let the individual be risk neutral, having u(x) = x where x is the amount of winning. Find the expected utility from the lottery.
Show that a decision maker who has a linear utilityfunction will rank two lotteries according to their expectedvalue.
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A consumer has utility u(1) = VI and income $1,000. When sick, the consumer must go to the doctor, which costs a $400 without insurance. If the consumer goes to the gym, the probability of getting sick is 20%, but if she does not go to the gym, the probability of getting sick is 90%. The cost of going to the gym is $50. An insurance company is offering a health insurance plan that will fully cover the cost of going to the doctor. The cost of this insurance is $100 Use this information to answer #16 and #17. 16. The consumer's expected utility from purchasing insurance and going to the gym is a. 24.5 b. 25.6 с. 29.2 d. 30.0 е. 30.1 17. In this situation, consumers will and the insurance company will earn Purchase insurance and go to the gym; negative profit b. Purchase insurance and stop going to the gym; negative profit Purchase insurance and go to the gym; positive profit d. Purchase insurance and stop going to the gym; positive profit e. Not purchase insurance and go to the gym; no…
Consider an individual who gets a utility of u(x) - x^1/2 from his total wealth x. Amsume that he has 160.000 AZN in the bank and owns a car with a value of 90,000 AZN. It is expected that will be stolen within the next year with 20% probability, whereas nothing will happen with. Your company tries to sell him an insurance package with the following properties; as an insurance premium now. (ii) if his car is stolen, your company will pay him a partial ation of 55,000 AZN. (iii) if his car is not stolen, there will be no paytent made by your .Should the individund buy this package, if the insurance premium in 12,500 AZN? Explain
Y5 Alfred is a risk-averse person with $100 in monetary wealth and owns a house worth $300, for total wealth of $400. The probability that his house is destroyed by fire (equivalent to a loss of $300) is pne = 0.5. If he exerts an effort level e = 0.3 to keep his house safe, the probability falls to pe = 0.2. His utility function is: U = w0.5 – e where e is effort level exerted (zero in the case of no effort and 0.3 in the case of effort).a. In the absence of insurance, does Alfred exert effort to lower the probability of fire?HINT: Calculate and compare the expected utility i) with effort, and ii) without effort. If effort is exerted, then the effort cost is paid regardless of whether or not a fire occurs.b. Alfred is considering buying fire insurance. The insurance agent explains that a home owner’s insurance policy would require paying a premium α and would repay the value of the house in the event of fire, minus a deductible “D”. [A deductible is an amount of money that the…
Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?
Catalina just inherited a vineyard from a distant relative. In good years (when there is no rain or frost during harvest season), she earns $115,000 from the sale of grapes from the vineyard. If the weather is poor, she loses $35,000. Catalina's estimate of the probability of good weather is 55%. The expected value of Catalina's income from the vineyard is $. (round your answer to the nearest dollar)
A bakery would like you to recommend how many loaves of its famous marble rye bread to bake at the beginning of the day. Each loaf costs the bakery $2.00 and can be sold for $7.00. Leftover loaves at the end of each day are donated to charity. Research has shown that the probabilities for demands of 25, 50, and 75 loaves are 30%, 20%, and 50%, respectively. Make a recommendation for the bakery to bake 25, 50, or 75 loaves each morning. Find the expected monetary value when baking 25 loaves. EMV=$(Type an integer or a decimal.) Find the expected monetary value when baking 50 loaves. EMV = $(Type an integer or a decimal.) Find the expected monetary value when baking 75 loaves. EMV = $ (Type an integer or a decimal.) Make a recommendation for the bakery to bake 25, 50, or 75 loaves each morning. The bakery should bake loaves of bread every morning. O 25 50 75 E
Suppose that a car - rental agency offers insurance for a week that costs $125. A minor fender bender will cost 34000 whereas a major accident might cost $16 comma 000 in repairs. Without the insurance, you would be personally liable for any damages. There are two decision alternatives: take the insurance, or do not take the insurance. You researched insurance industry statistics and found out that the probability of a major accident is 0.04% and that the probability of a fender bender is 0.18%. The expected payoff if you buy the insurance is $125.00. The expected payoff if you do not buy the insurance is $12.52. Develop a utility function for the payoffs associated with this decision for a risk-averse person. Determine the decision that would result using the utilities instead of the payoffs. Based on the expected payoffs, the best decision is to not purchase the insurance. Are these two decisions consistent?