4) Luke is planning an around-the-world trip on which he plans to spend $10,000. The utility from the trip is a function of how much she spends on it (Y), given by U(Y) = InY a). If there is a 25 percent probability that Luke will lose $1000 of his cash on the trip, what is the trip's expected utility. b). Suppose that Luke can buy insurance to fully against losing the $1,000 with a actuarially fair insurance. What is his expected utility if he purchase this insurance. Will he purchase the insurance? c). Now suppose utility function is U(Y) = Y/1000 What is his expected utility if he purchase the insurance in b). Will he purchase the insurance?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.5P
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4) Luke is planning an around-the-world trip on which he plans to spend $10,000.
The utility from the trip is a function of how much she spends on it (Y ), given by
U(Y) = InY
a). If there is a 25 percent probability that Luke will lose $1000 of his cash on the trip,
what is the trip's expected utility.
b). Suppose that Luke can buy insurance to fully against losing the $1,000 with a
actuarially fair insurance. What is his expected utility if he purchase this insurance.
Will he purchase the insurance?
c). Now suppose utility function is
U(Y) = Y/1000
What is his expected utility if he purchase the insurance in b). Will he purchase the
insurance?
Transcribed Image Text:4) Luke is planning an around-the-world trip on which he plans to spend $10,000. The utility from the trip is a function of how much she spends on it (Y ), given by U(Y) = InY a). If there is a 25 percent probability that Luke will lose $1000 of his cash on the trip, what is the trip's expected utility. b). Suppose that Luke can buy insurance to fully against losing the $1,000 with a actuarially fair insurance. What is his expected utility if he purchase this insurance. Will he purchase the insurance? c). Now suppose utility function is U(Y) = Y/1000 What is his expected utility if he purchase the insurance in b). Will he purchase the insurance?
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