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Fall 2009 Final Exam

# Fall 2009 Final Exam - 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 2009 December 17, 2009 NAME: The Exam has a total of four (4) problems and pages numbered one (1) through nine (9). 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 / 25 Problem 3 / 25 Problem 4 / 25 TOTAL / 100

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1 Problem 1: Consumption and Savings in the Two-Period Economy (25 points). Consider a two-period economy (with no government), in which the representative consumer has no control over his income. The lifetime utility function of the representative consumer is !" 1 2 1 2 , ln ln u c c c c #\$ , where 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 income is 26. 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.
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 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. For your reference, the definition of the rate of consumption growth rate between period 1 and period 2 is 2 1 1 c c

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Fall 2009 Final Exam - Department of Economics University...

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