Assume U(x, y) = √4 xy. a) Derive the indirect utility function v(p, Y ). b) Now assume a consumer is considering a gamble that has a 50% chance of returning 121% of the initial investment (a gain of 21%) and a 50% chance of returning 81% (a loss of 19%). If a consumer’s initial budget is 100, what is the expected outcome of this gamble? c) Now using the indirect utility function from a), the gamble from b) and assuming prices are equal to 1, find an optimal allocation of consumer’s initial wealth between risky asset from gamble in b) and a risk-free asset. Assume the return on risk-free assets is 1 (no gain/loss).
Assume U(x, y) = √4 xy. a) Derive the indirect utility function v(p, Y ). b) Now assume a consumer is considering a gamble that has a 50% chance of returning 121% of the initial investment (a gain of 21%) and a 50% chance of returning 81% (a loss of 19%). If a consumer’s initial budget is 100, what is the expected outcome of this gamble? c) Now using the indirect utility function from a), the gamble from b) and assuming prices are equal to 1, find an optimal allocation of consumer’s initial wealth between risky asset from gamble in b) and a risk-free asset. Assume the return on risk-free assets is 1 (no gain/loss).
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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Assume U(x, y) = √4 xy.
a) Derive the indirect utility
b) Now assume a consumer is considering a gamble that has a 50% chance of returning 121% of the initial investment (a gain of 21%) and a 50% chance of returning 81% (a loss of 19%). If a consumer’s initial budget is 100, what is the expected outcome of this gamble?
c) Now using the indirect utility function from a), the gamble from b) and assuming prices are equal to 1, find an optimal allocation of consumer’s initial wealth between risky asset from gamble in b) and a risk-free asset. Assume the return on risk-free assets is 1 (no gain/loss).
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