9. (10 marks) Jane owns a house worth $100,000. She cares only about her wealth, which consists entirely of the house. In any given year, there is a 20 percent chance that the house will burn down. If it does, its scrap value will be $30,000. Jane's utility function is U(w) = Vw. a. Draw Jane's utility function (plotting utility against wealth). b. Is Jane risk averse or risk loving? c. What is the expected monetary value of Jane's gamble? d. How much would Jane be willing to pay to insure her house against being destroyed by fire (leaving her with the scrap value only)? e. Say that Homer is the president of an insurance company. He is risk neutral and has the utility function U(w)=w. Between what two prices (premiums) could a beneficial insurance contract be made by Jane and Homer