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Unformatted text preview: Econ 6344 – Macroeconomics I Midterm Examination October 4 th , 2007 Read each problem carefully and make sure you answer all the questions asked within each problem. 1. [50 points] A person lives for 2 periods. They have a certain income of W in each period. They have a zero discount rate. Their utility function is U(C), and you don’t know the actual form of this utility function. There is uncertainty for this person in the form of interest rate volatility (you can think of them facing an adjustable rate mortgage or using an adjustable rate money market fund). Specifically, there is a 50% chance that the actual interest rate is 1 r δ + + and a 50% chance that the actual interest rate is 1 r δ +- . A. Set up this person’s expected utility function and derive the first order condition that you would solve to find their optimal first period consumption. B. Using the FOC, show under what conditions 1 / C δ ∂ ∂ < . [Hint: you use the implicit function theorem]....
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