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Fall 2010 Problem Set 1 solutions

Fall 2010 Problem Set 1 solutions - Department of Economics...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Problem Set 1 Suggested Solutions Professor Sanjay Chugh Fall 2010 Instructions : Written (typed is strongly preferred, but not required) solutions must be submitted no later than 2:00pm on the date listed above. You must submit your own independently-written solutions. You are permitted (in fact, encouraged) to work in groups to think through issues and ideas, but you must submit your own independently-written solutions. Under no circumstances will multiple verbatim identical solutions be considered acceptable. Your solutions, which likely require some combination of mathematical derivations, economic reasoning, graphical analysis, and pure logic, should be clearly, logically, and thoroughly presented; they should not leave the reader (i.e., your TAs and I) guessing about what you actually meant. Your method of argument(s) and approach to problems is as important as, if not more important than, your “final answer.” Throughout, your analysis should be based on the frameworks, concepts, and methods we have developed in class. There are three problems in total, each with multiple subparts.
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2 Problem 1: Elasticity of Labor Supply and Fiscal Policy. (40 points). Consider the static (i.e., one-period) consumption-leisure framework. In quantitative and policy applications that use this framework, a commonly-used utility function is ! " 1 1/ 168 1 1/ ( , ) ln u l c l c # $ # % & % & , in which c denotes consumption, l denotes the number of hours (in a week) spent in leisure, and # and $ (the Greek letters “psi” and “theta,” respectively) are constants (even though we will not assign any numerical value to them) in the utility function. The representative individual has no control over either # or $ , and both 0 # ( and 0 $ ( . Labor is measured as n = 168 – l , the real wage is denoted by w , and the labor-income tax rate is denoted by t. The take-home rate (the fraction of labor income that an individual keeps) can thus be defined as S = (1- t ). Finally, expressed in real terms, the representative individual’s budget constraint is (1 ) c t wn & . Thus, this is exactly the consumption-leisure framework studied in Chapter 2, with now a particular functional form for u ( c,l ). a. (5 points) For the given utility function, set up the consumption-leisure optimality condition, and then solve it for n , expressing the solution in terms of (among other things) S , rather than t . (that is, your final expression here should be of the form n = …, and on the right-hand side the take-home rate S should appear, but the tax rate t should not appear.). ( Note: You do not need to set up a Lagrangian in order to analyze this problem; you may go straight to the consumption-leisure optimality condition. Be very careful in deriving the result, because the rest of the analysis is based on this.) Clearly present the steps and logic of your work.
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Fall 2010 Problem Set 1 solutions - Department of Economics...

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