comp2_07Jan08 - Dietrich Vollrath and Bent E Srensen...

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Dietrich Vollrath and Bent E. Sørensen January 10, 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. (10%) Consider an IS/LM framework. The demand for money is M d = 0 . 5 Y - 0 . 5 i where Y is output and i = r + π where r is the real rate of interest and π is the rate of inflation. Further assume that output demand is Y = C + G + I where C = 0 . 8 Y and I = 0 . 1 Y - 0 . 1 r . a) Derive the IS-curve (you need to find the exact coefficients implied by the information you are given). b) If G = 1, M = 4, and π = 0 find Y . c) Derive the aggregate demand curve; i.e., a relation between Y and π . (Again, you need to find the exact function implied by the information given.) 2. (30%) Consider the case of 2 agents, each living for 2 periods. Output is deterministically given in period 0, while there are 2 states-of-the-world ( a and b ) in period 1. We will refer to one agent as “home” and one as “foreign” and mark the variables for “foreign” with a star. Assume ini-
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