3. (40 marks) Jane owns a house worth $100,000. Assume that her wealth consists entirely of the house. In any given year, there is a 2% 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) = 2Jv_v . a. Draw Jane's utility function (plotting utility against wealth). b. Show whether Jane is risk averse. c. If the insurance premium is 2.5 cents per dollar insured, how much insurance will Jane buy? (1. Heidi, Jane's sister, owns a house with the same value ($100, 000) and with the same chance (2%) of burning down. The scrap value of the burned house is also $30,000. Find the expected utility foe Jane if the two sisters share the losses equally. Assume the accidents of re for the two houses are independent