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Assume that home owners who finance their homes are required by the lender to carry fire insurance, and that statistical studies show that such home

Assume that home owners who finance their homes are required by the lender to carry fire

insurance, and that statistical studies show that such home owners face a 3.8% chance of

suffering from a fire annually. Further studies have documented that when smoke detectors are

installed (at a cost of $650), the average losses arising from a fire fall from $450,000 to $90,000.

Further, assume that the average home value is $450,000, and the home owners' utility function

takes the form U=WW0.5

Hello Insurance Company offers a policy with a 15% home owner copayment for

damages with a premium of $600.

a) Calculate homeowner's utility with no smoke detectors. Hint: You need to combine two

possibilities: if there is fire and if there is no fire. [4]

b) Calculate homeowner's utility with smoke detectors installed. Hint: You need to combine

two possibilities: if there is fire and if there is no fire. [4]

c) Compare your answers to a) and b) to decide whether home owners will install smoke

detectors or not. Explain your answer. [1]

d) Would such a policy be profitable for the insurance company?

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