Uncertainty and Insurance: You own a house and have a utility function equal to in which x1 represents your total wealth in a state of nature in which your house is still standing, and x2 represents your total wealth in a state of nature in which your house has burned down. Assume all of your total wealth is related to the value of your house (and its property) in each state of nature. If your house is still standing, it is worth $1,000,000. If it is all burned down, it is worth $200,000 (land value). The probability of a fire is pf = 0.02. a) (2pts) What is your current level of utility without fire insurance? b) (2pts) If the insurance company offers “fair insurance” how much coverage will you buy and what will be your insurance premium? (show work) c) (2pts) What is your level of utility with insurance? d) (2pts) What is the highest price you would be willing to pay for the insurance policy?