Your employer, 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,

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'sbreak-even pricefor a one-year theft insurance policy for an apartment without a security system?

The break-even price is

P = $10,000x0.05 = $500, the dollar loss multiplied by the probability of a theft.

b.Does a renter have an 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.

The expected cost without insurance and without a security system:

$10,000x0.05 = $500

The expected cost without insurance but with a security system:

$10,000x0.01 + $50 = $150

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 break-even price for a one year theft insurance policy for an apartment with a security system? (HINT: Moral Hazard)

The losses with a security system that is turned off:

$50 + $10,000x0.05 = $550, cost of the security system plus the losses multiplied by the probability of a theft without insurance and without a security system since they have it but it's not on.

The losses with a security system that is turned on:

$50 + $10,000x0.01 + $10 = $160, cost of the security system plus the probability of a theft with a security system, which in this case is on, so we add the cost to keep it on, $10.

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?

Deductible amount should be at least $500 - $150 = $350 (numbers from b.)

e.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?

$10,000x0.01 = $100

f.Based on the information and answers above, your boss has asked you to evaluate and state your assessment of this product.

I recommend the insurance to my boss based on the numbers above.

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I would like to see if my answers for d., e., and f. are correct and that is all I need help with.