Midterm_Spring2019.pdf - 1 Econ 139 Midterm Instructor Stephen Bianchi 12 March 2019 Be sure to write your name and student ID on your blue/green book(s

# Midterm_Spring2019.pdf - 1 Econ 139 Midterm Instructor...

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1 Econ 139 Midterm Instructor: Stephen Bianchi 12 March 2019 Be sure to write your name and student ID on your blue/green book(s). You may use one double sided sheet of handwritten notes. Do not turn the page until instructed to do so.

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3 As a general rule for exams, you may use any theorems stated in lecture without proof, unless you are explicitly directed otherwise. Problem 1. True or false. For each statement, please carefully justify your answer (no credit without justification). (22 points) 1. Consider an economy with two agents trading three goods, where the agents have increasing and concave utility functions U 1 and U 2 over all three goods. A Pareto op- timal allocation in this economy is an allocation where the marginal rate of substitution (MRS) between any pair of goods is the same for both agents. (8 points) 2. A VNM expected utility investor, with a strictly increasing and strictly convex utility function u over payoffs, and initial wealth W 0, considers an investment in an asset with uncertain payoff ˜ X . For this investor, the certainty equivalent of the investment CE ( ˜ X ) is less than or equal to the expected payoff E [ ˜ X ]. (7 points) 3. If is rational, then is transitive, that is, x y and y z imply x z . (7 points)

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4 Problem 2. Evaluating risky investments. (21 points, 7 points each) Consider an economic environment in which there are two possible future states: a good state that occurs with probability π = 1 /
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