Heavy rains caused serious flooding in Lake Ontario and the St. Lawrence River in spring 2017 and severe damage to properties on both sides of the border between Canada and the United States. Does the expectation that the government will subsidize the cost of rebuilding a home that is destroyed by flooding affect the probability that risk-averse people will buy insurance or the amount that they actually buy? To consider these questions, let the utility function for a risk-averse person be \(U(W)=2 W^{0.5}\) and the probability that the person's house will be completely destroyed be \(0.3 \%\).

a. If there is no subsidy, the loss in wealth is \(\mathrm{C} \$ 500,000\). Will a prospective client buy insurance if the cost of insurance is \(\mathrm{C} \$ 2,000\) ?

b. If the government provides a subsidy equal to \(25 \%\) of the cost of rebuilding the house so that the loss in wealth is reduced to \(\mathrm{C} \$ 375,000\), will the client buy insurance if the cost of insurance is still \(\mathrm{C} \$ 2,000\) ?

c. If the government provides a subsidy equal to \(25 \%\) of the cost of rebuilding the house so that the loss in wealth is reduced to \(\mathrm{C} \$ 375,000\), will the client buy insurance if the cost of insurance is reduced to \(\mathrm{C} \$ 1,000\) ?