An individual has a vNM utility function over money of u(x) Vx, where x is final wealth. She currently has $8 and can choose among the following three lotteries. Which lottery will she choose? • Lottery 1: Give up her $8 and face the gamble (0.1, 0.5, 0.4) over final wealth levels ($1, $8, $27). • Lottery 2: Keep her $8. • Lottery 3: Give up her $8 and face the gamble (0.2, 0.8,0.0) over final wealth levels ($1, $8, $27) O Lottery 1 O Lottery 2 O Lottery 3 O They are indifferent between lotteries 1 and 2 O They are indifferent between lotteries 2 and 3 O They are indifferent between lotteries 1 and 3 O They are indifferent between all three lotteris

An individual has a vNM utility function over money of u(x) Vx, where x is final wealth. She currently has $8 and can choose among the following three lotteries. Which lottery will she choose? • Lottery 1: Give up her $8 and face the gamble (0.1, 0.5, 0.4) over final wealth levels ($1, $8, $27). • Lottery 2: Keep her $8. • Lottery 3: Give up her $8 and face the gamble (0.2, 0.8,0.0) over final wealth levels ($1, $8, $27) O Lottery 1 O Lottery 2 O Lottery 3 O They are indifferent between lotteries 1 and 2 O They are indifferent between lotteries 2 and 3 O They are indifferent between lotteries 1 and 3 O They are indifferent between all three lotteris

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.2P

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A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and if it does not. Assume that the Bernoulli utility function takes the form u(x) = with r > 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA? Alex plays football for a local club in Kumasi. If he does not suffer any injury by the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coach worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = Assume he could buy insurance at price P that could pay $9,900 in case of injury. What is the highest value of P that makes it worthwhile for Alex to purchase insurance? What is the certainty…
Draw a utility function (with income on the horizontal axis) for an individual who is risk-loving at low levels of income, risk-neutral at moderate levels of income, and risk-averse at high levels of income (with each of these three regions clearly labeled). How would someone who looked at this graph (and had no other information about the individual) be able to figure out the individual’s attitude toward risk (averse/loving/neutral) in each region?
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