Johnny owns a house that would cost $100,000 to replace should it ever

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. Johnny’s utility function is U = W0.5.

How much would fair insurance cost that completely replaces the house if destroyed by fire? Assuming that Johnny has no other wealth, how much would Johnny be willing to pay for such an insurance policy? Why the difference?

ANSWER

Fair insurance would cost (0.001 ∗ $100,000 ) = $100. Johnny’s expected utility without insurance equals (.001 ∗ 00.5 ) + (.999 ∗ 100,0000.5 ) = 315.91. He can receive this level of utility with certainty if he had risk-free wealth of $99,800.10. Thus he is willing to pay $199.90 for insurance. He is willing to pay more than the fair price because he is risk averse.