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Economics

11. a) Mrs. Smith owns a house that constitutes her wealth. In the current period, the house is worth 144. In the future period, with a probability of 5%, the house can catch on fire, which would cause a major accident and a loss of 80 in its value. Mrs. Smith's utility function is = , where denotes her wealth. Suppose that she can buy insurance with partial cover at the risk premium rate = 6%. What coverage will she optimally choose? b) Suppose now that there is also a possibility of a leak in the pipes of the house, which would cause a minor accident and loss of 23 in the value of the house. The probability of a leak is 10%. However, major and minor accidents cannot happen at the same time. i) Compute the expected price of the house and the expected utility of Mrs. Smith. ii) Suppose that she can buy insurance to fully cover future losses for both minor and major accidents. What is the maximum insurance premium that she would pay for this type of insurance? Show your answer. iii) Suppose that she is offered two insurance options. Insurance A offers full coverage for a minor accident and a fixed 57.5% coverage for a major accident. Insurance B offers full coverage for a major accident and no coverage for a minor accident. Both insurances cost the same fixed amount of money. Which insurance would Mrs. Smith would choose? Show your answer. iv) Suppose that she can buy insurance at a risk premium rate , which offers a partial cover D for both accidents. Mrs. Smith can choose the size of D. Determine the maximum premium rate at which she would prefer to buy the insurance.