Y5

Problem 1 Miss Jones has all her wealth m invested in her house, and she considers the coverage, q, of her fire insurance for the house. There are two states of the world: fire, f, with a probability p and no fire, n, with a probability (1-p). There is a fair premium of a per $ coverage, i.e., 1= p. If she has no insurance and there is a fire her wealth will be my = 0. If she has no insurance and there is no fire her wealth will be me = m. If she has some insurance, the wealth in the two states of the world will be m, = m - mq and my = q - nq. Miss Jones cannot take more than full coverage q - m. c) Assume that Miss Jones is an expected utility maximizer with the utility function u = m. Show that her expected utility is independent of the chosen level of coverage, d) Assume that Miss Jones is an expected utility maximizer with the utility function u = m'. Solve her maximization problem. This utility function is neither concave nor strictly quasiconcave so you have to check all the three possible solutions: no coverage, some coverage, and full coverage. How large is the expected utility associated with each of these solutions? Which solution has the highest expected utility, and what coverage will she choose? Show your calculations.Problem 1 Miss Jones has all her wealth m invested in her house, and she considers the coverage, q, of her fire insurance for the house. There are two states of the world: fire, f, with a probability p and no fire, n, with a probability (1-p). There is a fair premium of a per $ coverage, i.e., 1= p. If she has no insurance and there is a fire her wealth will be my = 0. If she has no insurance and there is no fire her wealth will be me = m. If she has some insurance, the wealth in the two states of the world will be m, = m - mq and my = q - nq. Miss Jones cannot take more than full coverage q - m. c) Assume that Miss Jones is an expected utility maximizer with the utility function u = m. Show that her expected utility is independent of the chosen level of coverage, d) Assume that Miss Jones is an expected utility maximizer with the utility function u = m'. Solve her maximization problem. This utility function is neither concave nor strictly quasiconcave so you have to check all the three possible solutions: no coverage, some coverage, and full coverage. How large is the expected utility associated with each of these solutions? Which solution has the highest expected utility, and what coverage will she choose? Show your calculations