602_Spring2009_MidtermExam

602_Spring2009_MidtermExam - Department of Applied...

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Department of Applied Economics Johns Hopkins University Economics 602 Macroeconomic Theory and Policy Midterm Exam Professor Sanjay Chugh Spring 2009 March 9, 2009 NAME: The Exam has a total of four (4) problems and pages numbered one (1) through twelve (12) (followed by three blank pages for any scratch work). 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 1 / 20 Problem 2 / 30 Problem 3 / 20 Problem 4 / 30 TOTAL / 100

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1 Problem 1: Consumption and Savings in the Two-Period Economy (20 points). Consider a two-period economy (with no government and hence no taxes), in which the representative consumer has no control over his income. The lifetime utility function of the representative consumer is () 12 1 2 ,l n l n ucc c c =+ , where ln stands for the natural logarithm. We will work here in nominal terms: suppose the consumer’s present discounted value of ALL lifetime NOMINAL income is 52. For part a of this problem, suppose also the following: 1. The nominal interest rate between period 1 and period 2 is zero (i.e., i = 0, which is roughly what the nominal Federal Funds interest rate is currently). 2. The consumer begins period 1 with zero net assets. 3. Nominal prices of consumption in the two periods are 1 2 P = and 2 2 P = . a. (14 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 nominal asset position at the end of period 1? If so, compute it; if not, explain why not.
2 Problem 1a continued (if you need more space)

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3 Problem 1 continued. b. (6 points) Now ignore all numerical values presented at the beginning of this problem (that is, suppose you were given no numerical information whatsoever) . To demonstrate how important the concept of the real interest rate is in macroeconomics, an interpretation of it (in addition to the couple of different interpretations we have already discussed in class) is that it reflects the rate of consumption growth between two consecutive periods. Based on the consumption-savings optimality condition for the given utility function 12 1 2 (, ) l n l n uc c c c =+ , 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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This note was uploaded on 03/08/2011 for the course ECON 602 taught by Professor Chugh during the Spring '11 term at Johns Hopkins.

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602_Spring2009_MidtermExam - Department of Applied...

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