Bea is an expected utility maximizer with von Neumann-Morgenstern utility u(x) = x². She has an initial wealth of w≥ 3. A colleague offers her a bet that has a 50-50 chance of winning 2 or losing 3 (giving final wealth of w+2 and w-3, respectively). (a) For each w, find the risk premium associated with taking the bet. (b) For what values of w (if any) is Bea willing to accept the bet? Is she more inclined to accept when her wealth is lower or when it is higher? (c) Calculate the Arrow-Pratt measure of absolute risk aversion as a function of w.
Bea is an expected utility maximizer with von Neumann-Morgenstern utility u(x) = x². She has an initial wealth of w≥ 3. A colleague offers her a bet that has a 50-50 chance of winning 2 or losing 3 (giving final wealth of w+2 and w-3, respectively). (a) For each w, find the risk premium associated with taking the bet. (b) For what values of w (if any) is Bea willing to accept the bet? Is she more inclined to accept when her wealth is lower or when it is higher? (c) Calculate the Arrow-Pratt measure of absolute risk aversion as a function of w.
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:Bea is an expected utility maximizer with von Neumann-Morgenstern utility u(x) = x². She
has an initial wealth of w≥ 3. A colleague offers her a bet that has a 50-50 chance of winning
2 or losing 3 (giving final wealth of w+ 2 and w-3, respectively).
(a) For each w, find the risk premium associated with taking the bet.
(b) For what values of w (if any) is Bea willing to accept the bet? Is she more inclined to
accept when her wealth is lower or when it is higher?
(c) Calculate the Arrow-Pratt measure of absolute risk aversion as a function of w.
(d) How are your answers to parts (b) and (c) related?
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