# Suppose the function u(x) = x^0.5 where x is consumption represents your

September 29, 2018

Suppose the function u(x) = x^0.5 where x is consumption represents your preference over gambles using an expected utility function.You have a probability ? of getting consumption xB (bad state) and a probability 1-? of getting xG (good state).(a) Calculate the certainty equivalent xCE of the gamble.(b) Calculate the risk premium of the gamble.Now let ? = 0.1, xB = 10 and xG = 100.An insurance company allows you to choose an insurance contract (b, p), where b is the insurance benefit the company pays you if bad state occurs and p is the insurance premium you pay the company regardless of the state.Suppose the company’s offer is p = 0.2b. You may choose any combination of (b, p).(c) Is the insurance contract actually fair? How much will you insure (i.e. find your optimal p and b)?(d) What will your consumptions be in the two states with the insurance. Are you fully insured?(e) What is the expected profit of the insurance company from the contract?

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