4. 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-Morgensternutility u₁(x) = √x+1, where z is her final wealth. Find the risk premium associatedwith this lottery.Solution: The expected value of the lottery is 1/4+3/2+8/4 = 15/4. The certaintyequivalent, CE, solves√CE+1=√2 √4 √9 7+√2+Hence CE = (35+ 14√2)/16 and the risk premium is (25-14√/2)/16.(b) Now suppose that a second decision-maker who maximizes expected utility with vonNeumann-Morgenstern utility u₂(x) = √faces the same lottery. Without calculatingthis decision-maker's risk premium, determine whether it is higher than, lower than, orthe same as that for the decision-maker in part (a).Solution: The first decision-maker has Arrow-Pratt measureu₁(x)1u₁(x) 2(x + 1)r₁(x) =and the second has Arrow-Pratt measurer₂(x):==u(x) 1u₂(x) 2x-Since r₂(x) > r₁(x) for every x>0, the second decision-maker is more risk averse thanthe first and therefore has a higher risk premium.

A probability distribution refers to a statistical function that encompasses all of these…

1. 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(2) = √2+1, where r is her final wealth. Find the risk premium associated with this lottery.

1. 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(2) = √2+1, where r is her final wealth. Find the risk premium associated with this lottery.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.10P

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