mt1solutions

# Mt1solutions - Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis MIDTERM EXAM Professor Orhan Torul

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis MIDTERM EXAM Professor Orhan Torul Summer I – 2010 June 21, 2010 NAME: Time: 2 Hours Exam has a total of four (4) problems and pages numbered one (1) through thirteen (13). 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, and show all your work. Problem 1 / 20 Problem 2 / 30 Problem 3 / 35 Problem 4 / 15 TOTAL / 100

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1 Problem 1: Consumption and Leisure in the One-Period Economy (20 points) Consider the economy where the representative-agent lives only for one period . She enjoys both consumption and leisure. Her utility function is defined as ( , ) 2ln( ) 4ln( ) u c l c l  where c denotes consumption, l denotes leisure (in fraction-of-the-period units), and ln is the natural logarithm function. Her only source of income is her labor income. She chooses what fraction of the period to enjoy as leisure and what fraction of the period she wants to devote to as labor. Nature imposes the following restriction: Sum of fraction she enjoys as leisure and fraction she devotes to as labor is equal to 1, i.e. 1 ln  , where n denotes fraction of the period devoted as labor. The nominal wage rate in the economy is given as \$ W (i.e. if the representative agent devotes all her time to labor, she would earn \$ W as labor income excluding taxes ). There is a proportional labor income tax, which requires the representative agent to pay n t fraction of her income as tax. (i.e. for each dollar she earns, she has to pay n t dollar as labor income tax, where 01 n t  .) The price of the consumption good in the economy is given as \$ P . There is a proportional sales tax , which requires the representative agent to pay an additional c t fraction of her expenditure as sales tax. (i.e. for each dollar she spends, she has to pay c t dollar as sales tax, where c t .) a) Construct the budget constraint for the representative agent in its general form. (2 pts) (1 ) ) ) cn P t c t W l      
2 b) Suppose that you are given the following information: \$10 W , \$2 P , 0.40 n t , 0.50 c t . Rewrite the budget constraint using this information. (2pts) 2 (1 0.5) (1 0.4) 10 (1 ) or 3 6(1 ) or 2(1 ) cl    c) Set up the Lagrangian for this problem, and derive the optimality condition. (6pts)   ( , , ) 2ln( ) 4ln( ) ) 3 L c l c l l c  First-order conditions are 2 3 0 c c  4 6 0 l l Combining the two first order conditions, optimality conditions is simply d) Using the optimality condition you find in part c, and the budget condition you find in part b, find the values for consumption c , labor n , and leisure l . (You are to find numerical values for the ,, cn

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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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Mt1solutions - Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis MIDTERM EXAM Professor Orhan Torul

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