Problem 4 Insurance Ben is a proud owner of a romantic mansion facing the lake Mendota worth $500, 000. The location attractive as it is, however has one drawback. Occasionally in the spring heavy rains raise the water level in the lake, flooding the house. When this happens, the value of the house drops to $50, 000. The flood occurs with probability 1/10. Ben finds the situation too stressful and therefore he is going to sell the house in the summer (after the potential flood). By cF and CAF denote his wealth when there is, and there is no flood respectively. a) In the commodity space (CF, CNF) show the affordable bundle if there is no insurance (the endowment point). b) Ben can buy insurance that pays x dollars when there is a food, paying premium 0.1x (for given premium rate y = 0.1 he can choose any x.) - find analytically and show on the graph his budget constraint. c) Suppose Ben's Von Neumann Morgenstern expected utility function is given by U(CF, CNF) = 0.1V(CF) + 0.9V(CNF) . Is Ben risk averse (argue using a graph of his Bernoulli utility function)? d) What is his MRS at the endowment point (no insurance)? e) Find the optimal insurance and wealth levels under two contingencies. Does he insure fully? f) On the graph show how your answer changes if the insurance premium is 0.2x (that is insurance premium rate is y = 0.2)