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Risk and Uncertainty

Carmen has bought a house. Her wealth including the house is $640,000 and her utility function is U(W) = W1/2. There is a 20% chance that her house burns down, in which case her wealth would be reduced to $160,000.

(a) What is Carmen's expected utility? What is the expected value of her wealth?

(b) What is the certainty equivalent of this risky situation? What is the risk premium?

(c) What is the expected loss? What is the maximum amount Carmen would be willing to pay to fully insure her house?

(d) An insurance company offers her insurance against a ?re which costs 25 cents per dollar (the insurance premium has to be paid no matter whether the house burns down or not). How much insurance should she buy? [The result should be as a fraction of 57. Round to the next full number.]

(e) What are the expected pro?ts of the insurance company? [Round to the next full number.]

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