Question from Past Microeconomics Qualifying Exam[]
Spring 2005 - Section I, Question seven, George Mason University
T,F,U. State first whether the following statements are true, false or uncertain. Then briefly explain your reasoning in four or five sentences. You may sue a graph if it helps clairify your answer.
Under expected utility theory, U($2000)<2*U($1000).
Answer[]
Uncertain. It depends on the underlying utility function.
If U=W, then U($2000) = 2*U($1000) = 2000.
If U=W^.5, then U($2000)=44.7 < 2*U($1000)=63.2.
If U=W^2, then U($2000)=4,000,000 > 2*U($1000)=2,000,000
(Alternative) False. If we assume that the utility of wealth function is strictly concave, then the above inequality is true. But EU theory requires multiple payoffs with probabilities summing to 1. You must linearly weight outcomes according to their probabilities; the problem makes no mention of probabilities or alternative payoffs.
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