Question

An insurance company would like to offer theft insurance for renters. The policy would pay the full replacement value of any items that were stolen from the apartment. Some apartments have security alarms installed. Such systems detect a break-in and ring an alarm within the apartment. The insurance company estimates that the probability of a theft in a year is 0.07 if there is no security system and 0.02 if there is a security system (there cannot be more than one theft in any year). An apartment with a security system costs the renter an additional $100 per year. Assume that the dollar loss from a theft is $10,000 and that the insurance company is risk neutral and the renter would be willing to pay more than the expected loss to insure against the loss of theft. For a security system to be effective the renter must turn it on whenever he or she leaves the apartment. Suppose it costs the renter $20 per year in expended effort to turn on the alarm system. What is the lowest deductible amount would provide sufficient incentive for the renter to turn on the alarm system each time she leaves the apartment?

Answer 1