# UW-Madison ECON 302 - ECON 302 Assignment 2 (14 pages)

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## ECON 302 Assignment 2

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## ECON 302 Assignment 2

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Econ 302 - Intermediate Macroeconomic Theory and Policy
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ECON 302 Fall 2009 Assignment 2 1 Homework will be graded for both content and neatness Sloppy or illegible work will not receive full credit This homework requires the use of Microsoft Excel 1 The following question is concerned with the effect of personal income taxes and minimum wage laws on labor market outcomes for workers You are provided with an aggregate production function of the form Y AK L1 where A 9 0 5 and K 25 are fixed throughout the problem The equation LS 100 1 t w 2 describes labor supply where t is level of taxes and w is the real wage Therefore we can write 1 t w as the after tax real wage Firms are assumed to hire labor until the marginal product of labor equals the real wage MPL w This defines equilibrium in the labor market A Compute the marginal product of labor MPL Recall that MPL Y 9 25 MPL 0 5 0 5 L Y It should only depend on L L 0 5 45L 0 5 0 5 Y 45 0 5 L 22 5L L B Set MPL w and solve for L Call this labor demand LD It should only depend on w 0 5 w MPL 22 5L 0 5 L 1 22 5w 2 L 506 25w D C Let t 0 find the equilibrium levels of w L and Y the full employment level of output What is the total factor payment received by labor i e labor income 2 2 L L 100 1 t w 506 25w S 4 D w 506 25 5 0625 w 1 5 e 100 2 2 L 100 w 100 1 5 225 e e 0 5 Y FE 9 25 L 0 5 e 45 225 0 5 675 ECON 302 Fall 2009 Assignment 2 2 Labor Income w L 1 5 225 337 5 e e D Repeat part C under the assumption that t 0 6 Is labor better or worse off in terms of the after tax real wage and after tax labor income 2 2 L L 100 1 0 6 w 506 25w S 4 w D 2 2 16w 506 25w 0 25 506 25 w 31 6406 2 372 e 16 2 L 16 2 372 90 Y e FE 45 90 0 5 426 907 Labor Income w L 2 372 90 213 454 e e w e after tax 1 t w 0 4 2 372 0 9488 w Labor Income e pre tax e after tax w e after tax 1 t w L 0 4 213 454 85 382 Labor Income e e pre tax Labor Income after tax The real wage increases but the post tax real wage is less than the pre tax real wage As both the real wage after tax and labor income decrease after the tax on labor is imposed labor is worse off Fewer people are working due to the effect of the tax on labor supply and those that are still in the labor force are receiving a lower after tax wage E Repeat part C with t 0 and a minimum wage of w 2 Draw a rough graph showing the intersection of the labor demand and labor supply curves the minimum wage price floor the equilibrium level of employment and the equilibrium real wage Is labor better or worse off in terms of the after tax real wage and after tax labor income Previous w 1 5 w 2 is a binding price floor L L surplus in the labor market e S D L 2 400 S L 2 126 563 L L 2 126 563 excess supply w 2 D e D e Labor Income w L 2 126 563 253 125 e e The real wage has increased but fewer workers can find employment under the binding price floor of w 2 As a result total labor income has decreased so workers as a whole are worse off under the ECON 302 Fall 2009 Assignment 2 3 minimum wage However if you are able to find employment your personal income has improved at the expense of your fellow workers who can t find a job In that sense the policy is arbitrarily redistributive Labor Market w vs L Labor Supply Demand w 3 0 2 5 2 0 1 5 Labor Supply Labor Demand 1 0 Minimum Wage 0 5 0 0 0 100 200 300 400 500 Labor L F Taking into account your answers to parts C through E should the government intervene in the labor market Why or why not If the government imposes an income tax t 0 or sets a minimum wage above the market clearing wage without intervention workers as a group are made worse off However if the government gives an earned income tax credit t 0 to workers labor is better off This analysis assumes perfect competition in the labor market homogeneity across workers all workers are the same and can t be differentiated by their level of human capital or skill and doesn t account for regulations like workplace safety requirements that might decrease total employment slightly but make the remaining workers in the labor force much better off Also note that output decreases under government intervention which implies that labor market regulations can potentially cause a slowdown in economic activity and recession ECON 302 Fall 2009 Assignment 2 4 0 3 0 5 0 2 2 Let Y AK L N be a Cobb Douglas production function that uses the level of technology A capital K labor L and land N to produce output Y Technological progress makes all other factors more productive and land is used in combination with labor and capital Time is represented by t and takes on values t 0 1 2 20 The next four equations describe how technology and the factors of production change over time e is the exponential function Excel is required for this problem A t 2e0 03t technology K t 10e0 05t capital L t 5e0 02t labor N t 10 if 0 t 9 20 if t 9 land land reclamation project completed at time t 10 A Compute Y Y and Y for t 0 1 2 20 HINT for this question see Excel file Q2 tab EXP x returns e to the power x in Excel See Excel B Graph Y and Y for t 0 1 2 20 Talk about the graphs qualitatively Output Y vs Time t 60 Output Y 50 40 30 20 10 0 0 5 10 15 20 Time t Output seems to be growing at a constant rate with a discrete jump at t 10 when the land reclamation project is completed This project doesn t seem to affect the growth rate afterwards however ECON 302 Fall 2009 Assignment 2 5 Output Growth Y Output Growth Y vs Time t 25 20 15 10 5 0 0 5 10 15 20 Time t Output growth in terms of percentage change is constant around 6 except during the period when the land reclamation project …

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