Question from Past Microeconomics Qualifying ExamEdit
Fall 2005 - Section I, Question eight, 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 use a graph if it helps clarify your answer.
Under expected utility theory, U($2000)<2*U($1000).
Uncertain, but typically true. If an agent experiences diminishing marginal utility, the value of each additional dollar gained is less than the one before. This means that the first $1,000 brings greater utility than the second $1,000. Doubling the utility of the first $1,000 brings implies greater value than the utility of $2,000. The exception to this would be an agents with utility curves with constant or increasing marginal utility curves (Utility Monster).
Another, more probable exception would be a risk seaker such as
$ EU(w)=w^2 $
Then $ EU(2000)=4000000>2*EU(1000)=2000000 $
MORE PRECISE ANSWER: False. The inequality is only true for risk-averse agents. For risk-neutral agents, the inequality becomes an equality. For risk-loving agents, the "less than" sign needs to be reversed.