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 = AKαL1-α, where A = 9, α = 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∂L . It should only depend on L. Y  ( )9( )250.5( )L0.5  45L0.5 MPL  ∂Y∂L  ( )45( )0.5 L 0.5  22.5L 0.5 B) Set MPL = w and solve for L. Call this labor demand, LD. It should only depend on w. w  MPL  22.5L 0.5 L0.5  22.5w 1 LD  506.25w 2 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? LS  LD  100[ ]( )1  t w2  506.25w 2 w4  506.25100  5.0625  we  1.5 Le  100•we2  100•1.52  225 YFE  9•250.5•Le0.5  45( )2250.5  675ECON 302 Fall 2009 Assignment #2 2 Labor Income  weLe  ( )1.5( )225  337.5 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? LS  LD  100[ ]( )1  0.6 w2  506.25w 2  16w2  506.25w 2 w4  506.2516  we  31.64060.25  2.372 Le  16( )2.3722  90  YFE  45( )900.5  426.907 Labor Income  weLe  ( )2.372( )90  213.454 we¸after  tax  ( )1  t we  ( )0.4( )2.372  0.9488  we¸pre  tax  we¸after  tax Labor Incomeafter  tax  ( )1  t weLe  ( )0.4( )213.454  85.382  Labor Incomepre  tax  Labor Incomeafter  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 we  1.5  w  2 is a binding price floor  LS  LD  surplus in the labor market LS( )2  400 LD( )2  126.563  Le  LD( )2  126.563 ( )excess supply  we  2Labor Income  weLe  ( )2( )126.563  253.125 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 theECON 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. 0.00.51.01.52.02.53.00 100 200 300 400 500Labor Supply/Demand (w)Labor (L)Labor Market (w vs. L)Labor SupplyLabor DemandMinimum Wage 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 2) Let Y  AK0.3L0.5N0.2 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, ΔY, and %ΔY 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 %ΔY for t = 0, 1, 2, …, 20. Talk about the graphs qualitatively. 01020304050600 5 10 15 20Output (Y)Time (t)Output (Y) vs. 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 0%5%10%15%20%25%0 5 10 15 20Output Growth (%ΔY)Time (t)Output Growth (%ΔY) vs. Time (t) Output growth in terms of percentage change is constant around 6% except during the period when the land reclamation project is completed. Due to the discrete jump in output there, output growth is over 20% for t = 10. However, output growth returns to its constant rate after t = 10. C) What is the marginal product of capital (MPK) for this production function? Graph it for t =