3. Consider an individual with initial wealth W = $1,000 and utility function over money given by u(w) = w. The individual faces loss of L = $800 with probabil- ity . Suppose an insurance is available at price Sp per unit, where one unit of insurance pays the insured $1 if loss occurs and $0 otherwise. (a) What is the fair price for this insurance, and how much insurance will the individual buy at this price? (b) Suppose p= $0.3. How much insurance will the individual buy? (c) Suppose p = $0.3, but now the individual's utility function over money is u(w) = w?. How much insurance will the individual buy? As clarified in the class, assume that the individual cannot insure more than the amount of loss.

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
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Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
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3. Consider an individual with initial wealth W = $1,000 and utility function over
money given by u(w) = w}. The individual faces loss of L = $800 with probabil-
ity . Suppose an insurance is available at price $p per unit, where one unit of
insurance pays the insured $1 if loss occurs and $0 otherwise.
(a) What is the fair price for this insurance, and how much insurance will the
individual buy at this price?
(b) Suppose p = $0.3. How much insurance will the individual buy?
(c) Suppose p = $0.3, but now the individual's utility function over money is
u(w) = w². How much insurance will the individual buy? As clarified in
the class, assume that the individual cannot insure more than the amount
of loss.
Transcribed Image Text:3. Consider an individual with initial wealth W = $1,000 and utility function over money given by u(w) = w}. The individual faces loss of L = $800 with probabil- ity . Suppose an insurance is available at price $p per unit, where one unit of insurance pays the insured $1 if loss occurs and $0 otherwise. (a) What is the fair price for this insurance, and how much insurance will the individual buy at this price? (b) Suppose p = $0.3. How much insurance will the individual buy? (c) Suppose p = $0.3, but now the individual's utility function over money is u(w) = w². How much insurance will the individual buy? As clarified in the class, assume that the individual cannot insure more than the amount of loss.
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