325_Fall2010_FinalExam

325_Fall2010_FinalExam - Department of Economics University...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Final Exam Professor Sanjay Chugh Fall 2010 December 16, 2010 NAME: The Exam has a total of four (4) problems and pages numbered one (1) through twelve (12). 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 two pages (double-sided) of notes. You may not use a calculator. Problem 1 / 25 Problem 2 / 20 Problem 3 / 15 Problem 4 / 40 TOTAL / 100
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1 Problem 1: Consumption and Savings in the Two-Period Economy (25 points). Consider a two-period economy in which the government co l l e c t s on ly lump - sum t ax e s f rom the representative consumer, and in which the representative consumer has no control over his pre- tax income. The lifetime utility function of the representative consumer is ±² 12 1 2 ,l n l n ucc c c ³ , where, as usual, ln (.) stands for the natural logarithm. We will work here in purely real terms: suppose the consumer’s present discounted value of ALL lifetime REAL pre-tax income is 26, and the present discounted value of ALL lifetime tax payments is 6. Suppose that the real interest rate between period 1 and period 2 is zero (i.e., r = 0), and also suppose the consumer begins period 1 with zero net assets. a. (17 points) Set up the lifetime Lagrangian formulation of the consumer’s problem, in order to answer the following: i) is it possible to numerically compute the consumer’s optimal choice of consumption in period 1? If so, compute it; if not, explain why not. ii) is it possible to numerically compute the consumer’s optimal choice of consumption in period 2? If so, compute it; if not, explain why not. iii) is it possible to numerically compute the consumer’s real asset position at the end of period 1? If so, compute it; if not, explain why not.
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2 Problem 1 continued b. (8 points) To demonstrate how important the concept of the real interest rate is in macroeconomics, an interpretation of it (in addition to the several different interpretations we have already discussed in class) is that it reflects the rate of consumption growth between two consecutive periods. Using only the consumption-savings optimality condition for the given utility function, briefly describe/discuss (rambling essays will not be rewarded) whether the real interest rate is positively related to, negatively related to, or not at all related to the rate of consumption growth between period one and period two.
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325_Fall2010_FinalExam - Department of Economics University...

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