Question
Question 6 Assume that home owners who finance their homes are required by the lender to carry fire insurance, and that statistical studies show that
Question 6
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]
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