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)
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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Question
![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-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc937b847-9c00-4fc7-8573-69bfc53484ee%2F5ed6f138-ff5c-4016-b408-4db212f6e3dc%2Fnoymc_processed.jpeg&w=3840&q=75)
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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