# JHU_Fall2011_FinalExam_Solutions.pdf - Department of...

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Department of Applied Economics Johns Hopkins UniversityEconomics 602 Macroeconomic Theory and Policy Final Exam Suggested Solutions Professor Sanjay Chugh Fall 2011 NAME: The Exam has a total of four (4) problems and pages numbered one (1) through sixteen (16). 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.In particular, some of the questions state explicit WORD COUNT limits – respect these limits. You are to answer all questions in the spaces provided. You may use two pages (double-sided) of notes. You may notuse a calculator or any other aids. Problem 1 / 30 Problem 2 / 30 Problem 3 / 25 Problem 4 / 15 TOTAL / 100
1Problem 1: The Consumption-Leisure Framework (30 points). In this question, you will use the basic (one period) consumption-leisure framework to consider some labor market issues. Suppose the representative consumer has the following utility function over consumption and labor,( , )lnu c ncAn=, where, as usual, cdenotes consumption and ndenotes the number of hours of labor the individual chooses to work. The constant A > 0is outside the control of the individual. usual, ln( )is the natural log function.) Suppose the budget constraint (expressed in real, rather than in nominal, terms) the individual faces is (1)ctw n=, where tis the labor tax rate, wis the realhourly wage rate, and the number of hours the individual works. Recall that in one week there are 168 hours, hence n + l = 168 must always be true. a.(4 points) Construct the Lagrangian for the consumer’s utility maximization problem, defining any new notation you need to include. (As nis
b.(4 points) Based on the Lagrangian in part a, compute the representative consumer’s first-order conditions with respect to consumption and with respect to labor. Clearly present the important steps and logic of your analysis.
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2Problem 1 continued c.(6 points) Based on ONLY the first-order condition with respect to labor computed in part b, qualitatively sketch two things in the diagram below and briefly address one question. First, sketch the general shape of the relationship between w and n(perfectly vertical, perfectly horizontal, upward-sloping, downward-sloping, or impossible to tell). Second, sketch how changes in t affect the relationship (shift it outwards, shift it in inwards, or impossible to determine). And, briefly (in no more than 10 words!) describe the economicsof how you obtained your conclusions. (IMPORTANT NOTE: In this question, you are not to use the first-order condition with respect to consumption nor any other conditions.)
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