Suppose that your wealth is $250,000. You buy a house worth $200,000 and invest the remainder of your wealth in a riskfree asset paying an annual interest rate of 5%. There is a probability of 0.001 that your house will be damaged by a fire during the year and its value would be reduced to $100,000. If the house is not damaged by the fire, its value remains at $200,000 at the end of the year. Assume that your expected utility of end-of-year wealth is equal to the expectation of end-of-year wealth minus 100 multiplied by the ratio of variance of end-of-year wealth to the expectation of end-of-year wealth, that is, E[U(W)]=E[W]-100*(Var(W)/E[W]).

a) Calculate the expectation of your wealth at the end of the year.

b) Calculate the variance of your wealth at the end of the year.

c) Calculate your expected utility of end-of-year wealth.

d) How much would you be willing to pay for complete fire insurance (100% of the house value) at the start of the year?

e) Even though insurance is almost always actuarially unfair, why should a person owning a home still purchase insurance?