midterm_solutions.pdf - 1 Econ 139 u2013 Midterm Suggested...

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1Econ 139 – MidtermSuggested SolutionsFall 2019As a general rule for exams, you may use any theorems stated in lecture without proof, unlessyou are explicitly directed otherwise.Problem 1. True or false.For each statement, please carefully justify your answer (nocredit without justification). (28 points)1. SupposeU((x, y, πx)) =πu(x) + (1-π)u(y), where the Bernoulli utility functionuisstrictly increasing and concave, representson the space of simple lotteriesL. ThenV((x, y, πx)) =πv(x)+(1-π)v(y), wherev(x) =f(u(x)) andfis a strictly increasingfunction, also represents. (9 points)
2. The following situation is an arbitrage opportunity:StateAsset 1Asset 2Asset 3State 11.05.00.0State 20.19.01.0Price0.36.90.6(9 points)
3. LetXrepresent current wealth and consider an investment that pays off +θXwithprobabilityπand-θXwith probability 1-π, whereθ(0,1).Letπ=π(X, θ)represent the probability that makes an investor indifferent between taking on theinvestment or not. Thenπ(X, θ)12+14rR(X)θwhererR(X) is the relative risk aversion coefficient. (10 points)[Hint: you may appeal to a result that was derived in lecture.]
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