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2. Preferences under uncertainty Suppose Felix is offered the opportunity to take part in one of two gambles. Gamble A pays $100 with probability 0.92, $500 with probability 0.04, and nothing with probability 0.04. Gamble B pays $100 with certainty. Which of the following inequalities reflects a preference for gamble B over gamble A if Felix's utility from earning X dollars is given by U(X)? ○ U(100) > U(0.92 × 100) + U(0.04 × 500) + U(0.04 × 0) OU(100) U(0.92 x 100) + U(0.04 x 500) + U(0.04 x 0) ⒸU(100)>0.92U(100) +-0.04U (500) +0.04U(0) OU(100) <0.92U (100) +0.04U (500) + 0.047(0) Now suppose he is offered a second set of gambles. Gamble C pays $100 with probability 0.44, $500 with probability 0,04, and nothing with probability 0.52. Gamble D pays $100 with probability 0.52 and nothing with probability 0.48. If Felix's preferences are consistent, he should prefer gamble

2. Preferences under uncertainty Suppose Felix is offered the opportunity to take part in one of two gambles. Gamble A pays $100 with probability 0.92, $500 with probability 0.04, and nothing with probability 0.04. Gamble B pays $100 with certainty. Which of the following inequalities reflects a preference for gamble B over gamble A if Felix's utility from earning X dollars is given by U(X)? ○ U(100) > U(0.92 × 100) + U(0.04 × 500) + U(0.04 × 0) OU(100) U(0.92 x 100) + U(0.04 x 500) + U(0.04 x 0) ⒸU(100)>0.92U(100) +-0.04U (500) +0.04U(0) OU(100) <0.92U (100) +0.04U (500) + 0.047(0) Now suppose he is offered a second set of gambles. Gamble C pays $100 with probability 0.44, $500 with probability 0,04, and nothing with probability 0.52. Gamble D pays $100 with probability 0.52 and nothing with probability 0.48. If Felix's preferences are consistent, he should prefer gamble

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. Preferences under uncertainty Suppose Felix is offered the opportunity to take part in one of two gambles. Gamble A pays $100 with probability 0.92, $500 with probability 0.04, and nothing with probability 0.04. Gamble B pays $100 with certainty. Which of the following inequalities reflects a preference for gamble B over gamble A if Felix's utility from earning X dollars is given by U(X)? ⒸU (100) > U(0.92 × 100) + U(0.04 x 500) + U(0.04 x 0) U(100) U(0.92 x 100) + U(0.04 x 500) + U(0.04 x 0) ⒸU(100) > 0.92U (100) +0.04U (500) + 0.040(0) OU(100) <0.927/(100) + 0.047(500) + 0.047(0) Now suppose he is offered a second set of gambles. Gamble C pays $100 with probability 0.44, $500 with probability 0,04, and nothing with probability 0.52. Gamble D pays $100 with probability 0.52 and nothing with probability 0.48. If Felix's preferences are consistent, he should prefer gamble
Transcribed Image Text:2. Preferences under uncertainty Suppose Felix is offered the opportunity to take part in one of two gambles. Gamble A pays $100 with probability 0.92, $500 with probability 0.04, and nothing with probability 0.04. Gamble B pays $100 with certainty. Which of the following inequalities reflects a preference for gamble B over gamble A if Felix's utility from earning X dollars is given by U(X)? ⒸU (100) > U(0.92 × 100) + U(0.04 x 500) + U(0.04 x 0) U(100) U(0.92 x 100) + U(0.04 x 500) + U(0.04 x 0) ⒸU(100) > 0.92U (100) +0.04U (500) + 0.040(0) OU(100) <0.927/(100) + 0.047(500) + 0.047(0) Now suppose he is offered a second set of gambles. Gamble C pays $100 with probability 0.44, $500 with probability 0,04, and nothing with probability 0.52. Gamble D pays $100 with probability 0.52 and nothing with probability 0.48. If Felix's preferences are consistent, he should prefer gamble
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