3. Peter owns just his car and has £2,500 in cash. The car is worth £7,500. The probability that the car will be stolen (and never recovered) is 0.1. If his vNM utility function is two times the square root of his wealth, what is the maximum amount he would pay for a full-coverage insurance on his car?

Question

3.	Peter owns just his car and has £2,500 in cash. The car is worth £7,500. The probability that the car will be stolen (and never recovered) is 0.1. If his vNM utility function is two times the square root of his wealth, what is the maximum amount he would pay for a full-coverage insurance on his car?

(A)	£975.
(B)	£199.
(C)	£1000.
(D)	£900.
(E)	£1164.

(Solution is A, 975)

economyst · Answer

Without insurance, Pete's expected utility is .9*sqrt(2*10000) + .1*sqrt(2*2500) = 134.3502884 utils So, what wealth give him equal amount of utility. Well, work the utility formula backwards. That is (134.3502884^2)/2 = 9025. Take it from here.