1. Assume Johnny\'s utility function is U (W ) = W ^a . a. For what values of a
ID: 1249401 • Letter: 1
Question
1. Assume Johnny's utility function is U (W ) = W ^a .a. For what values of a is he risk averse, risk neutral, and risk loving? From now on, assume that a = 1/2. Johnny owns a house that would cost $100,000 to replace should it ever be destroyed by fire. There is a 0.1% chance that the house could be destroyed during the course of a year. b. How much would fair insurance cost that completely replaces the house if destroyed by fire? c. Assuming that Johnny has no other wealth, how much would Johnny be willing to pay for such an
insurance policy?
Explanation / Answer
Johnny is risk averse if the second derivative is negative, risk seeking if the second derivative is positive, and risk neutral if the second derivative is 0. U = Q^a U' = aQ^(a-1) U''=a(a-1)Q^(a-2) Johnny is risk averse if: a(a-1) a a > 1 Johnny is risk neutral if: a(a-1)=0 a^2 - a=0 a^2 = a a = 1 a=1/2, so johnny is risk averse. If Johnny were risk neutral, he would be willing to pay: $100,000*0.001=$100. I guess this is what your professor is calling "fair." But Johnny is risk averse with a=1/2 If there were no risk, Johnny would have a utility of: U = (100000^1/2) = 316.22 But with a 0.1% risk, he only has U = 316.22*(1-0.001)=315.90 And this much utility is only worth 315.90 = W^1/2 W = 315.90^2 W= 99792.81 So, for insurance, he is willing to pay: 100000-99792.81=207.19 This is over double what a risk-neutral individual would pay.Related Questions
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