An insurance company would like to offer theft insurance for renters. The policy would pay the full

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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 0.05 if there is no security system and 0.01 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 $50 per year. Assume that the dollar loss from 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.

a. What is the insurance company's break-even price for a one-year theft insurance policy for an apartment without a security system?
b. What is the renter’s expected loss if she has no insurance and does not use the security system? c. What is the renter’s expected loss if she has no insurance and uses the security system?

d. How much is the renter’s incentive to pay for the security system if she has no insurance? Express this incentive in dollar amount.

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 $10 per year in expended effort to turn on the alarm system.

e. What is the additional benefit for the renter of turning the security system on? Express in dollar amount.
f. In view of your answer in part “e”, what is the insurance company's break-even price for a one year theft insurance policy for an apartment with a security system?
g. What deductible amount would provide sufficient incentive for the renter to turn on the alarm system each time he or she leaves the apartment? The deductible amount has to be greater than or equal to ____.

h. What is the insurance company's break-even price for a one year theft insurance policy with that deductible amount for an apartment with a security system?