Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars.  Suppose that this person has a 40% chance of wealth of $100,000 and a 60% chance of wealth of $2,000,000 as summarized by P(0.40, $100,000, $2,000,000). a. What is the expected value of wealth? b. Construct a graph of this utility function . c. Is this person risk averse, risk neutral, or a risk seeker? d. What is this person’s certainty equivalent for the prospect?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.1P
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Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars.  Suppose that this person has a 40% chance of wealth of $100,000 and a 60% chance of wealth of $2,000,000 as summarized by P(0.40, $100,000, $2,000,000).

a. What is the expected value of wealth?

b. Construct a graph of this utility function .

c. Is this person risk averse, risk neutral, or a risk seeker?

d. What is this person’s certainty equivalent for the prospect?

 

 

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