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a) Verify that these two lotteries have the same expected value but that lottery B has a bigger variance than lottery A. b) Suppose that your utility function is U = √(I+ 10), where I is expected value of the lottery. Compute the expected utility of each lottery. Which lottery has the higher expected utility? If you have this utility function, are you risk-averse, risk neutral, or risk loving? c) Suppose that your utility function is U = 1001. Compute the expected utility of each lottery. If you have this utility function, are you risk-averse, risk neutral, or risk loving? d) Suppose that your utility function is U = 10P. Compute the expected utility of each lottery. If you have this utility function, are you risk-averse, risk neutral, or risk loving?

a) Verify that these two lotteries have the same expected value but that lottery B has a bigger variance than lottery A. b) Suppose that your utility function is U = √(I+ 10), where I is expected value of the lottery. Compute the expected utility of each lottery. Which lottery has the higher expected utility? If you have this utility function, are you risk-averse, risk neutral, or risk loving? c) Suppose that your utility function is U = 1001. Compute the expected utility of each lottery. If you have this utility function, are you risk-averse, risk neutral, or risk loving? d) Suppose that your utility function is U = 10P. Compute the expected utility of each lottery. If you have this utility function, are you risk-averse, risk neutral, or risk loving?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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2. Consider two lotteries, A and B. With lottery A, there is a 11% chance that you receive a payoff of $10, 10% chance that you receive $100,9, 28% chance that you receive $1 1% chance that you receive $28, and 50% of receive nothing. With lottery B, there is a 1% chance that you receive a payoff of $1000, 1% chance that you receive $100, 3% chance that you receive a payoff of S10, 45% chance that you receive a payoff of $1, and 50% chance that you receive a payoff of nothing. Further, you must pay $1 to raffle. a) Verify that these two lotteries have the same expected value but that lottery B has a bigger variance than lottery A. b) Suppose that your utility function is U = v(1 + 10), where I is expected value of the lottery. Compute the expected utility of each lottery. Which lottery has the higher expected utility? If you have this utility function, are you risk-averse, risk neutral, or risk loving? c) Suppose that your utility function is U = 1001. Compute the expected utility of each lottery. If you have this utility function, are you risk-averse, risk neutral, or risk loving? d) Suppose that your utility function is U = 10/". Compute the expected utility of each lottery. If you have this utility function, are you risk-averse, risk neutral, or risk loving?
Transcribed Image Text:2. Consider two lotteries, A and B. With lottery A, there is a 11% chance that you receive a payoff of $10, 10% chance that you receive $100,9, 28% chance that you receive $1 1% chance that you receive $28, and 50% of receive nothing. With lottery B, there is a 1% chance that you receive a payoff of $1000, 1% chance that you receive $100, 3% chance that you receive a payoff of S10, 45% chance that you receive a payoff of $1, and 50% chance that you receive a payoff of nothing. Further, you must pay $1 to raffle. a) Verify that these two lotteries have the same expected value but that lottery B has a bigger variance than lottery A. b) Suppose that your utility function is U = v(1 + 10), where I is expected value of the lottery. Compute the expected utility of each lottery. Which lottery has the higher expected utility? If you have this utility function, are you risk-averse, risk neutral, or risk loving? c) Suppose that your utility function is U = 1001. Compute the expected utility of each lottery. If you have this utility function, are you risk-averse, risk neutral, or risk loving? d) Suppose that your utility function is U = 10/". Compute the expected utility of each lottery. If you have this utility function, are you risk-averse, risk neutral, or risk loving?
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