325_Fall2009_MidtermExamPart2 - Department of Economics...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Midterm Exam – Part 2 Professor Sanjay Chugh Fall 2009 October 15, 2009 NAME: Part 2 of the Exam has a total of two (2) problems and pages numbered one (1) through eight (8). Each problem’s total number of points is shown below. Your solutions should consist of some appropriate combination of mathematical analysis, graphical analysis, logical analysis, and economic intuition, but in no case do solutions need to be exceptionally long. Your solutions should get straight to the point – solutions with irrelevant discussions and derivations will be penalized. You are to answer all questions in the spaces provided You may use one page (double-sided) of notes. You may not use a calculator. Problem 3 / 28 Problem 4 / 22 TOTAL PART 2 / 50
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1 Problem 3: “Hyperbolic Impatience” and Stock Prices (28 points). In this problem you will study a slight extension of the infinite-period economy from Chapter 8. Specifically, suppose the representative consumer has a lifetime utility function given by 23 123 () ( ) ( ). . . . tt t t uc JE ±±± ±± ± ± , in which, as usual, u ( . ) is the consumer’s utility function in any period and ȕ is a number between zero and one that measures the “normal” degree of consumer impatience. The number J (the Greek letter “gamma,” which is the new feature of the analysis here) is also a number between zero and one, and it measures an “additional” degree of consumer impatience, but one that ONLY applies between period t and period t+1. 1 This latter aspect is reflected in the fact that the factor Ȗ is NOT successively raised to higher and higher powers as the summation grows. The rest of the framework is exactly as studied in Chapter 8: 1 t a ² is the representa tive consumer’s holdings of stock at the beginning of period t, the nominal price of each unit of stock during period t is t S , and the nominal dividend payment (per unit of stock) during period t t D . Finally, the representative consumer’s consumption during period t is c t and the nominal price of consumption during period t is P t . As usual, analogous notation describes all these variables in periods t +1, t +2, etc. The Lagrangian for the representative consumer’s utility-maximization problem (starting from the perspective of the beginning of period t ) is 1 11 1 1 1 1 1 1 2 22 2 2 1 2 2 2 2 3 33 3 32 . . . t t t t t t t t ttt t t t t t t t t t YSD a P c S a YS D a P c S a D a P c S a D a P O JEO JE O ² ± ± ± ± ± ± ± ± ± ± ± ± ± ± ªº ± ² ² ¬¼ ± ² ² ± ² ² ± ² ...
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325_Fall2009_MidtermExamPart2 - Department of Economics...

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