An economy's aggregate production function is given by Y = A.K-N - N-. The marginal product of labor for this production function is MPN = A.K - 2N. (a) (5 points) Assume that A = 8 and K.= 12. Suppose that the labor supply function for this economy is given by N' = 3 + w. Find the equilibrium real wage rate, the full employment level of employment, and the full employment level of output for this economy. SHOW ALL WORK OR POINTS WILL BE TAKEN OFF Draw a production function and labor market diagram vertically as we did in class and label this initial equilibrium point as point A. A correct and completely labeled diagram is worth 10 points (b) (5 points) Suppose that A falls to 6 and labor supply is now given by: N' - 6 + w Find the equilibrium real wage rate, the full employment level of employment, and the full- employment level of output for this economy and label on your diagrams as point B. (c) (8 points) Explain exactly why the profit maximizing level of labor has changed given the increase in total factor productivity. Again be very specific with your answer as in using numbers. Begin your answer with: At the same level of labor input N' = (what it was at point A). the firm is no longer ......- d)(2 points) Are workers better off or worse off due to the changes above?Mallings Help tell me what you want in da el(5 points) Why would we expect labor supply to change the way it did? KEY An economy's aggregate production function is given by Y - A K.N- N'. The marginal product of labor for this production function is MPN. = A.K- 2N. (a) (10 points) Assume that A = 10 and K = 10. Suppose that the labor supply function for this economy is given by NS = 5 + 2w. Find the equilibrium real wage rate, the full employment level of employment, and th's full-employment level of output for this economy. w = 10 x 10 - 215 + 2w] 5w =90 W = 18, N = 41, Y =2419 Y = 10 x 10 1 41 - 412 Draw a production function and labor market diagram vertically as we did in class and label this initial equilibrium point as point A. PK [A = 12, K = 12] 4988 PF [ A= 10, K = 10] 2419 41 58 NS [ a' ] NS [ a ] 28 a > a 18 ND [A = 12, K = 121 ND [ A=10, K=10] 41 58(b) (10 printa) We discussed numerous times the possible impact of the recent cut in the corporate tax rate down to 2196. We also discussed how good the economy is doing and how the stock market is at near record highs. Suppose that the corporate tax cut results in firms investing in more capital so that capital (K) LOL: N' = 2 + 2w goes up to equal 12 and A also goes up to equal 12. At the same time, labor supply changes and Find the equilibrium real wage rate. the full employment level of employment, and the fall- employment level of output for this economy and label on your diagrams as point B. w = 12 x 12 - 2[2 + 2w] Sw = 140 w =28, N =58, Y = 4985 Y = 12 x 13 x 58-58 (c) (10 points) Explain exactly why the profit maximizing level of labor has changed given the increase in total factor productivity. Again be very specific with your answer as in using punibers. Begin your answer with: At the same level of labor input N* = (what it was at point A), the firm is no longer ... 2 N- 41, MPN - 12 = 12 - 2 (41) - 67 and we needed to attract 41 workers is 19.5 so MPX- w.. 62 - 19.5 (note 19.5 is the wage you need to pay to attract 41 workers since N'- 2+ 2w -HIKE! for every worker you hire MPM falls by 2 - in order to hire one more worker you need to increase the price of leisure - for every 1/2 increase in w, one more worker is willing to work You hire 17 more workers, MEN falls by 17 x 2 = 34 to 28.(from 62)... and in order to hire 17 more workers, you need to raise the wage by 8.5 from 19.5 to 28 which equals the MIN, back to profit maximization D(10 points) Are workers better off or worse off due to the increase in the capital stock (K) What has happened to the government's income tax revenue and why" Workers are better off for two reasons: more of them are working = 58 vs. 41 and their REAL WAGE went up from 18 to 25. Government's income tax revenue has gone up for two reasons: more people are working 58 va 41, (more tax revenue) and they are making more money, real wages went up from 18 to 28 (more tax revenue)