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

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 .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

A) Breakeven price for Insurance company

Break even price:

Break even pricing is the practice of setting a price point at which a business will earn zero profits on a sale.

here, break even price for insurance company for an apartment without security system is as follows,

= $ 10000

( Apaartment without security is not required to pay additional amount or incentive so price that is to be charged by company is the loss that incurred by the renter .)

B. Incentive to be paid by renter :

Here renter is not required to pay any incentive if he does not have insurance.

cost to be paid by renter without security is $ 10000

cost to be paid by renter with secutiy is $10050

C) Break even price with effective security system :

security system to be effective the renter must turn it on whenever a person leaves apartment and it costs renter $10 per year.

now the Break even price for Insurance company with security system = $ 10060

(here renter has to pay $ 50 for security and $10 for turning on the security sysem so it comes to $ 10060 inclusing loss of $10000 by theft)

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