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rob. Therefore buying & shares of the risky asset yields final wealth W = Wo + EX. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. ६ (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1- e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo.

rob. Therefore buying & shares of the risky asset yields final wealth W = Wo + EX. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. ६ (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1- e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The Arrow-Pratt measures of absolute and relative risk aversion respectively describe the willingness of a consumers to risk a fixed amount of wealth or a fixed fraction of their wealth. This problem will demonstrate this by setting up a simple investment problem. Suppose that consumers begin with initial wealth Wo and may buy shares of a risky asset whose payoff per share is given by 2. (1 w/ prob. P, X = 1-1 w/ prob.1– p. Therefore buying { shares of the risky asset yields final wealth W = Wo +X. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1– e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo-
Transcribed Image Text:The Arrow-Pratt measures of absolute and relative risk aversion respectively describe the willingness of a consumers to risk a fixed amount of wealth or a fixed fraction of their wealth. This problem will demonstrate this by setting up a simple investment problem. Suppose that consumers begin with initial wealth Wo and may buy shares of a risky asset whose payoff per share is given by 2. (1 w/ prob. P, X = 1-1 w/ prob.1– p. Therefore buying { shares of the risky asset yields final wealth W = Wo +X. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1– e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo-
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