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PROBLEM (10) A risk averse decision maker with u(x) equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ? (b) Now suppose that he can buy "2 copies" of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this "bundled lottery" or a sure reward of 2 x $901 = $1802? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many "idiosyncratic risks". = √x faces a lottery L that delivers $2500 or $100 with

PROBLEM (10) A risk averse decision maker with u(x) equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ? (b) Now suppose that he can buy "2 copies" of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this "bundled lottery" or a sure reward of 2 x $901 = $1802? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many "idiosyncratic risks". = √x faces a lottery L that delivers $2500 or $100 with

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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PROBLEM (10) A risk averse decision maker with u(x) Vx faces a lottery L that delivers $2500 or $100 with equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ? (b) Now suppose that he can buy "2 copies" of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this "bundled lottery" or a sure reward of 2 x $901 = $1802 ? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many "idiosyncratic risks".
Transcribed Image Text:PROBLEM (10) A risk averse decision maker with u(x) Vx faces a lottery L that delivers $2500 or $100 with equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ? (b) Now suppose that he can buy "2 copies" of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this "bundled lottery" or a sure reward of 2 x $901 = $1802 ? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many "idiosyncratic risks".
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