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Uncertainty and Insurance:
Assume that you own an office building in the Bay Area. Your utility is given by U = V1/2, where V is the value of the office building. Suppose all of your wealth is invested in the value of the office building. The probability of a strong earthquake occurring this year is 1%. If it does occur the value of the building will fall from $9,000,000 to $1,000,000.
a) Given the chances of an earthquake, what is the expected value of the building?
b) If you buy enough insurance to guarantee yourself wealth equal to the expected value. How much insurance coverage will you buy and what will be the "fair insurance" premium for such coverage?
c) What is your expected utility without insurance?
d) What is the reservation price (a.k.a., highest premium you will pay) for the insurance coverage you would have bought in response to (b) above?
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