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

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 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.

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

What is the renter’s expected loss if she has no insurance and does not use the security system?

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

What is the renter’s expected gain from using the security system if she has no insurance?

What is the additional benefit for fully insured renter of turning the security system on?

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

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Answer #1

1) Expected Loss when there is no insurance as well as no security. :

To calculate the Expected loss , we need to multiply the loss amount of one theft with the probability of loss.

Thus: 10,000*.05=500

2) The break even price for insurance company is the price at which insurance company will neither be at loss nor at profit at the end of the year even after paying for the loss.

Taking the number of apartments as 100 . Taking Probability as 0.05 , there would be 5 houses having theft. Total loss is 5*10,000=50,000.

Thus BEP is 50,000/100=500.

3) Loss if no security is 500.

Loss after security maximum is 10,000*.01=100.

Thus loss saved is 400.

Security cost is 50.

Thus net gain is 350.(400-50)

4) Price of insurance is 500.

Extra cost of security is 50.

Thus here having security will cost renter 50 extra.

However , one point to be noted is the insurance company will make good for loss as per the replacement price of the theft items. However , renter won't get the new item from the market at such price . She will have to pay for the new item.

Thus , the net benefit will be :

(Difference between the market price of the items lost- replacement price of the items)*(0.05-0.01) -50 = Net benefit of installing security system.

5) The Break even price is 10,000*0.01=100.

As the renter having security system will have loss probability of 1%.

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