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 percent chance of 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, and do on) 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 that 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 homeowner buy?
Will the insurance company make a profit (on average) given the homeowner’s choice?