Please focus on part c, d and e. An insurance company would like to offer theft

Question

Please focus on part c, d and e.

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 .05 if there is no security system and .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 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.

a. What is the insurance company's breakeven price for a one year theft insurance policy for an apartment without a security system?

b. Does a renter have incentive to pay for a security system if he does not have insurance? To answer this question you must calculate the expected cost to the renter with and without a security system.

c. 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. What is the insurance company's breakeven price for a one year theft insurance policy for an apartment with a security system? (HINT: Moral Hazard)

d. What deductible amount would provide sufficient incentive for the renter to turn on the alarm system each time he or she leaves the apartment?

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

Explanation / Answer

Loss of amount in theft condition = $10,000

There can be four outcomes: 1) Theft with security Alarm (TS)

2) Theft without security Alarm (TWS)

3) No theft with security Alarm (NTS)

4) No theft without security Alarm (NTWS)

Probability of theft with security Alarm (a) = 0.01

Probability of theft without security Alarm (b) = 0.05

A) Breakeven price with out security Alarm = expected loss of renter without security Alarm= $(0.05 * 10000)= $500

B) Matrix of all four possible outcomes is represented as:

Here from above table it is clear that if renter doesnot install security Alarm then his expected cost = $500

and if renter install security Alarm then expected cost = $150

So renter has an incentive to install security Alarm without insurance and by doing so he can minimise the expected costs equal to $350.

C) Cost of turning on the security system = $10

Matrix of all possible outcomes in the case of security alarm and also turning on and not decission for Insurance company:

Above table clearly depits that breakeven price of risk neutral insurance company is = $160. Because renter doesnot have any incentives to swith on the alarm.

D) lGreater than equals to $10 will incentivies the renter to switch on the alarm.

E) $150

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