Suppose the typical Florida resident has wealth of $500,000, of which his or her home is worth $100,000. Unfortunately Florida is infamous for its hurricanes, and it is believed there is a 10% chance of a hurricane that could totally destroy a 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 loss of $100,000 to a 5% 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 that it does not know whether the retrofit will be installed and therefore cannot quote a premium condition 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% of loss is $1,500.
a. The typical homeowner has a utility function equal to the square root of wealth. Will the homeowner retrofit the house, and if so, which insurance policy will the homeowner buy?
b. Will the insurance company make a profit (on average) given the homeowner's choice?