A family owns a house worth USD 2 mln. In any given year, there is a 1% chance that the house will burn down. If it does, its scrap value will be USD 600,000.

a) What is the expected value of this lottery?

b) Suppose that the family is risk-averse and its preferences over lotteries is described by utility function u(w) = w^. How much would this family be willing to pay at maximum to insure its house against being destroyed by fire (i.e. what is the reservation demand price for insurance)? Hint: First find the expected utility, certainty equivalent, risk premium, expected loss, and then the reservation demand price.

c) Now suppose that the family is risk loving and its preferences over lotteries is described by a utility function u(w) = w^2. How much would this family be willing to pay at maximum to insure its house against being destroyed by fire? Hint: First find the expected utility, certainty equivalent, risk premium, expected loss, and then the reservation demand price.