2. You are building your dream house and have to make a lot of design deci- sions, but one decision regards infrastructure and risk. You are deciding if you want to install a French drain in your basement. With probability there will be heavy enough rain to flood your basement causing damage $D. With probability 1 -* there will be no flooding. The cost of the French drain is $C, and your budget is B. The value of the house is H. If there is no damage your total wealth is W = H + B. If there is damage W =H + B -D. Your utility from wealth is U(W) = In(W). a. What is your expected utility if you do not pay for the French drain? b. What is your expected utility if you pay for the French drain, and it is always effective at preventing damage from flooding? c. If the probability of flood damage is 20%, What is the cost of the French drain that would leave you indifferent between installing one or not? Normalize the value of your house to unity H = 1, and suppose your budget if twenty percent of the value of the house so that B = .2. The damage is 10% of the value of the house D = .1.d. What is your expected utility if the drain is effective at preventing flood damage 90% of the time? e. What would the price of flood insurance have to be to leave you indif- ferent between insuring against a flood after purchasing the French drain