Let's denote a lottery as (X₁, P1; X2, P2; ... ; Xm, Pm), where Xi and Pi indicate the reward magnitude and probability of each potential outcome. A decision-maker prefers B = ($5000, 1.00) to A = ($0, 0.01; $25000, 0.04; $5000, 0.95) and prefers C = ($25000, 0.04; $0, 0.96) to D = ($5000, 0.05; $0, 0.95). Prove that Expected Utility Theory cannot account for the preference. Note: you can assume that the initial endowment is $0 and the utility of $0 is zero.
Let's denote a lottery as (X₁, P1; X2, P2; ... ; Xm, Pm), where Xi and Pi indicate the reward magnitude and probability of each potential outcome. A decision-maker prefers B = ($5000, 1.00) to A = ($0, 0.01; $25000, 0.04; $5000, 0.95) and prefers C = ($25000, 0.04; $0, 0.96) to D = ($5000, 0.05; $0, 0.95). Prove that Expected Utility Theory cannot account for the preference. Note: you can assume that the initial endowment is $0 and the utility of $0 is zero.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Let's denote a lottery as (X₁, P1; X2, P2; ….. ; Xm, Pm), where X₁ and Pi indicate the reward magnitude
($5000, 1.00) to A = ($0,
=
and probability of each potential outcome. A decision-maker prefers B
0.01; $25000, 0.04; $5000, 0.95) and prefers C = ($25000, 0.04; $0, 0.96) to D= ($5000, 0.05; $0, 0.95).
Prove that Expected Utility Theory cannot account for the preference.
Note: you can assume that the initial endowment is $0 and the utility of $0 is zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e7c282-b8ba-43ba-8a6b-2448afdf9cd4%2Fa9028d96-f8f7-49ac-8ea5-206f41e6666b%2Fn02ii7w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let's denote a lottery as (X₁, P1; X2, P2; ….. ; Xm, Pm), where X₁ and Pi indicate the reward magnitude
($5000, 1.00) to A = ($0,
=
and probability of each potential outcome. A decision-maker prefers B
0.01; $25000, 0.04; $5000, 0.95) and prefers C = ($25000, 0.04; $0, 0.96) to D= ($5000, 0.05; $0, 0.95).
Prove that Expected Utility Theory cannot account for the preference.
Note: you can assume that the initial endowment is $0 and the utility of $0 is zero.
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