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comp2_08Jan09b

# comp2_08Jan09b - Dietrich Vollrath and Bent E Srensen...

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Dietrich Vollrath and Bent E. Sørensen January 15th, 2008 Comprehensive Exam in Macroeconomic Theory–Procedural Instructions (1) Write your answers only on the paper we will provide. (2) We will be distributing a numbered sign–in sheet in a moment. The number next to your signature will be your student number . (3) Every sheet of paper you turn in to us must have your student number written at the top–center of the sheet and circled . (4) Every sheet of paper you turn in to us must have a page number written at the top–right corner of the sheet. (5) When you have finished, or when it is 1:00 pm (whichever comes first), prepare a cover sheet for your exam. This cover sheet should not have a page number, but must have the following things on it: (a) Your student number at the top–center, circled. (b) The phrase “Macroeconomics Comprehensive Exam”. (c) The sentence “My last page is page number X”, where X is your total number of pages of answers. 1

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1. (25%) Individuals live for two periods. They earn labor income of w t in the first period of their life, and consume in both periods. Their utility function is U = (1 - β ) ln c 1 + β ln c 2 , and they take the interest rate of r as exogenous to their consumption decision. (a) What is the optimal amount of savings ( s t ) done by an individual? Production in this economy uses both physical and human capital. The production function is y t = k α t h 1 - α t . The wages of a young person are thus w t = (1 - α ) k α t h 1 - α t . There is a tax on savings at the rate of τ . The proceeds of this tax are used to finance the accumulation of human capital. There is no population growth. Physical capital accumulates as
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comp2_08Jan09b - Dietrich Vollrath and Bent E Srensen...

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