BAYLOR UNIVERSITY HANKAMER SCHOOL OF BUSINESS DEPARTMENT OF FINANCE, INSURANCE 35 REAL ESTATE Problem Set #5 Name: Dr. Garven 1. Suppose the typical Florida resident has wealth of$5001000, of which his or her home is worth $100,000. Unfortunately: Florida. is in hurricane alley, and it is believed there is a 10 percent chance of a hurricane that could totally destroy the house (i.e., a loss of $100,000). However, it is possible to retrot the house with various protective devices (shutters, roof bolts. etc.) for a cost of $2,000. This reduces the size of loss from a 10 percent chance of loss of $100,000 to a 5 percent chance of a loss of $50,000. The homeowner must decide whether to retrot and thereby reduce the expected loss. The problem for an insurance compan}r is that it does not know whether the retrot will be chosen and therefore cannot quote a premium conditioned on the policyholder choosing this action. Nevertheless, the insurance company offers the following two policies from which the homeowner can choose: (1) The premium for insurance covering total loss is $12,000 or (2) the premium for insurance covering only 50 percent of loss is $11500. The typical homeowner has a utility function equal to the square root of wealth; i.e.., U( W) : W "'ith this information, answer the following questions: A. Assume that the purchase of homeowners insurance is mmpulsom. Which insurance policy will the homeowner buy? Will the insurance company make a prot (on average) given the homeowners choice? Will the homeowner retrot the house? . Now assume that the purchase of homeowners insurance is not compulsory. Show that in this case. the homeowner will uni purchase insurance: but nevertheless choose to retrot the house. . Find the maximum price which the insurer can charge for the coinsurance contract such that prot can still be earned while at the same time providing the typical Florida homeowner with higher expected utility from insuring and retrotting. How much prot will the insurer expect to earn on a per policy basis