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? Hint: Expected profit

equals premium minus expected loss. [4]