A decision-maker faces a lottery that gives her a final wealth of 1 dollar with probability 1/4, 3 dollars with probability 1/2, and 8 dollars with probability 1/4. (a) Suppose this decision-maker is an expected utility maximizer with von Neumann-Morgenstern utility u₁(x)=√x+1, where x is her final wealth. Find the risk premium associated with this lottery. (b) Now suppose that a second decision-maker who maximizes expected utility with von Neumann-Morgenstern utility u2(x)=√x faces the same lottery. Without calculating this decision-maker's risk premium, determine whether it is higher than, lower than, or the same as that for the decision-maker in part (a).

A decision-maker faces a lottery that gives her a final wealth of 1 dollar with probability 1/4, 3 dollars with probability 1/2, and 8 dollars with probability 1/4. (a) Suppose this decision-maker is an expected utility maximizer with von Neumann-Morgenstern utility u₁(x)=√x+1, where x is her final wealth. Find the risk premium associated with this lottery. (b) Now suppose that a second decision-maker who maximizes expected utility with von Neumann-Morgenstern utility u2(x)=√x faces the same lottery. Without calculating this decision-maker's risk premium, determine whether it is higher than, lower than, or the same as that for the decision-maker in part (a).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.10P

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