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# P2solution - Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Problem Set 2 Professor Orhan Torul

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1 Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Problem Set 2 Professor Orhan Torul Summer I - 2010 1. A Backward-Bending Aggregate Labor Supply Curve? Despite our use of the backward- bending labor supply curve as arising from the representative agent’s preferences, there is controversy in macroeconomics about whether this is a good representation. Specifically, even though a backward-bending labor supply curve may be a good description of a given individual’s decisions, it does not immediately follow that the representative agent’s preferences should also feature a backward-bending labor supply curve. In this exercise you will uncover for yourself this problem. For simplicity, assume that the labor tax rate is 0 t throughout all that follows. Also assume that nominal price level P is fixed at \$1 P . a. Suppose the economy is made up of five individuals, person A, person B, person C, person D, and person E, each of whom has the labor supply schedule given below. Using the indicated wage rates, graph each individual’s labor supply curve as well as the aggregate labor supply curve (which is simply the total hours worked by all agents). Nominal Wage, W Person A Person B Person C Person D Person E \$10 20 hours 0 hours 0 hours 0 hours 0 hours \$15 25 15 0 0 0 \$20 30 22 8 0 0 \$25 33 27 15 5 0 \$30 35 30 20 15 0 \$35 37 32 25 20 6 \$40 36 31 27 25 21 \$45 35 30 26 28 30 \$50 33 29 24 25 29 Now suppose that in this economy, the “usual” range of the nominal wage is between \$10 and \$45. Solution: In the table below, the aggregate (total) number of hours worked by all persons in the economy at each wage rate is now shown (last column).

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2 Nominal Wage, W Person A Person B Person C Person D Person E Aggregate \$10 20 hours 0 hours 0 hours 0 hours 0 hours 20 hours \$15 25 15 0 0 0 40 \$20 30 22 8 0 0 60 \$25 33 27 15 5 0 80 \$30 35 30 20 15 0 100 \$35 37 32 25 20 6 120 \$40 36 31 27 25 21 140 \$45 35 30 26 28 30 149 \$50 33 29 24 25 29 140 The aggregate labor supply curve simply plots the values in the last column in the table above against the wage rate (with, recall, the labor tax rate held constant at 0 n t throughout for simplicity), as shown below. Clearly, most of the aggregate labor supply curve is upward-sloping, with only the very top portion backward- bending. For brevity, the individuals’ labor supply curves are omitted they are of course simply e ach individual’s hours worked plotted against the wage, and it should be clear even from the table that each individual in the economy has a backward- bending labor supply curve. Note that nominal wage and real wage are identical since \$1 P .
3 b. Restricting attention to this range, is the aggregate labor supply curve backward- bending? Solution: If the usual range of the nominal wage is \$10-\$45 in the economy, then clearly no (see the Figure above), the aggregate labor supply is not backward-bending.

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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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P2solution - Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Problem Set 2 Professor Orhan Torul

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