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comp1_07 - Dietrich Vollrath and Bent E Srensen...

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Dietrich Vollrath and Bent E. Sørensen June 27, 2005 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. (30%) People live for two periods and maximize their lifetime utility of U = ln c 1 + ln c 2 . They have a discount rate of zero and there is a positive interest rate of r. Individuals have two options for their time. They can work or they can go to school. The time spent in school is denoted n , and the time they spend working is (1 - n ). Time spent in school creates human capital that can be used in the next period, according to the following formula, h t +1 = ( n t h t ) α x 1 - α , where x represents public education spending. Note that human capital in
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