Suppose the typical Florida resident has wealth of $500,000, of which his or her

Question

Suppose the typical Florida resident has wealth of $500,000, 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 (a loss of $100,000). However, it is possible to retrofit the house with various protective devices (shutters, roof bolts, etc.) for a cost of $2,000. This reduces the 10 percent chance of a loss of $100,000 to a 5 percent chance of a loss of $50,000. The homeowner must decide whether to retrofit and thereby reduce the expected loss. The problem for an insurance company is it does not know whether the retrofit will be installed 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 $1,500.

The typical homeowner has a utility function equal to the square root of wealth.

Will the homeowner retrofit the house, and which insurance policy will the homeowner buy?

Will the insurance company make a profit (on average) given the homeowner%u2019s choice?

Please show work and answer all questions asked

Explanation / Answer

Risk aversion and expected utility

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