Marcus is an expected utility maximizer with the Bernoulli utility functionu(w) = √w. He faces a gamble in his wealth. In a good state he gets 81 and in a bad state hegets 9. He can take out an insurance plan which will leave him with a wealth of 49 in eachstate.(a)(b)(c)state?Is Marcus risk averse?Will he purchase the insurance if the probability of the states is ½ for eachLet p denote the probability of the good state. For what value(s) of p willMarkus be just indifferent between taking out the insurance and not taking it out? Showyour working.

Risk Aversion is the theory that a person or investor is willing to choose an option or alternative…

Answered: Marcus is an expected utility maximizer…

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 17.2IP

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Please explain in detail about expected utility to get a positive upvote. An individual has a utility function U = W¼, where W is her total wealth. She has one safe asset worth Rs 5,000, and another risky asset whose value can be either Rs 5,000 or Rs 1,400 with equal probabilities. What is her expected utility? (a) Rs 11,400 (b) Rs 100 aw lo boeoqmoo vmonoos to on g cubire cou s o iva alagos ad a adWnooni lanou lo OAuti (c) Rs 2,580 (d) Rs 90
8 An investor with initial wealth $20000 and utility function U(x) = ln(x) is considering an investment that has a 80% chance of gaining r% and a 20% chance of losing s%. (1) Find in terms of r and s the certainty equivalent of this investment. (2) If s = 10, find the range of values of r for which the investor will avoid this investment.,
A risk-averse expected-utility maximizer has initial wealth w0 and utility function u. She facesa risk of a financial loss of L dollars, which occurs with probability π. An insurance companyoffers to sell a policy that costs p dollars per dollar of coverage (per dollar paid back in theevent of a loss). Denote by x the number of dollars of coverage.(a) Give the formula for her expected utility V (x) as a function of x.(b) Suppose that u(z) = −e−zλ, π = 1/4, L = 100 and p = 1/3. Write V (x)using these values. There should be three variables, x, λ and w. Find the optimal value of x,as a function of λ and w, by solving the first-order condition (set the derivative of the expectedutility with respect to x equal to zero). (The second-order condition for this problem holds butyou do not need to check it.) Does the optimal amount of coverage increase or decrease in λ,where λ > 0?(c) Repeat exercise (b), but with p = 1/6.(d) You should find that for either (b) or (c), the optimal coverage…
4. $1000 with of $325. (a) (b) Adam is risk averse. He is offered a choice between a gamble that pays a probability of 25% and $100 with a probability of 75%, or a sure payment What is the expected payment of the gamble? Will Adam prefer gamble over sure payment? Would he change his mind if the sure payment is $320 instead of $325? (c) If this individual has a utility function u(x) = lnx, would he prefer the payment of $320 or the gamble? (d) In the CRRA utility family u(x) = x¹-7. If this individual has a utility where y = 0.01, would he prefer the payment of $320 or the gamble?
Economics Shawn's consumption is subject to risk. With probability 0.75 he will enjoy 10000 in consumption, but with probability 0.25 he will have only 3600. His utility function for consumption is given by v(c) = Vc. -What is the expected value of Shawn's consumption? -What is his expected utility? -What is his certainty equivalent of having 10000 with probability 0.75 and 3600 with probability 0.25?
↑ Consider the following FIRE INSURANCE PROBLEM where fire destroys a $300 (thousand) house.< INSURANCE PAYOUT INSURANCE PREMIUM 200 0 EVENT FIRE → NO FIRE PROBABILITY 0.02 0.98 OUTCOME 100 300 10 10 (a) What do we mean when we say an agent is Risk Averse? (b) Assume utility is U(x) = √(x). What is the expected payoff and expected utility of having no insurance? Show your work. (c) Suppose the Insurance Premium was $10. Would this risk averse agent buy insurance? Show your work and explain. (d) Suppose the probability of a fire rose to 5%. Would the agent buy insurance now? Show your work and explain.
Many decision problems have the following simplestructure. A decision maker has two possible decisions, 1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utility
Suppose Grace and Lisa are to go to dinner. Lisa is visiting Grace from outof town, and they are to meet at a local restaurant. When Lisa lived in town,they had two favorite restaurants: Bel Loc Diner and the Corner Stable. Ofcourse, Lisa’s information is out of date, but Grace knows which is betterthese days. Assume that the probability that the Bel Loc Diner is better isp > 1/2 and the probability that the Corner Stable is better is 1 - p. Naturedetermines which restaurant Grace thinks is better. Grace then sends amessage to Lisa, either “Let’s go to the Bel Loc Diner,” “Let’s go to theCorner Stable,” or “I don’t know [which is better].” Lisa receives the message, and then Grace and Lisa simultaneously decide which restaurant to go to. Payoffs are such that Grace and Lisa want to go to the same restaurant, but they prefer it to be the one that Grace thinks is better. More specifically, if, in fact, the Bel Loc Diner is better, then the payoffs from theiractions are as shown in the…
A man purchased a $22,500, 1-yr term-life insurance policy for $695. Assuming that the probability that he will live for another year is 0.995, find the company's expected gain. (Round your answer to the nearest cent.) $
2 Consider the two investments listed below with possible outcomes and probabilities: INVESTMENT (in $1000) SAFE RISKY INVESTMENT AMOUNTⓇ 40+ 40+ GOOD SCENARIO OUTCOME 45+ 80+ AVERAGE+ SCENARIO PROB OUTCOME 0.40* 0.40€ 42+ 45+ BAD+ SCENARIO PROB OUTCOME PROB 0.20 35+ 0.20 10+ 0.40€ 0.40+ b) a) Suppose I have utility function U(*) = (x)2. What is the expected utility from each investment? Which investment will I choose, if any? Show and explain your work and provide the intuition. c) What is the value of the risk premium for the SAFE investment? Show and explain your work and provide the intuition. d) What is the value of the risk premium for the RISKY investment? Show and explain your work and provide the intuition.< +
Johnny is "paid" by his parents $2o if he gets a grade A, $10 if he gets a grade B, whereas he has to pay his parents back $5 if he gets a grade other than A or B. On average 20% of the grades he gets are A, and 30% are grades B. What is the expected value of what he "earns" per grade ? What is the expected value of what he "earns" at school weekly if on average he gets five grades a week ? How long should Jim save until he collects enough money to buy a pair of brand new Hi-Fi headphones that cost $225?
1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…

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