Question

6) Davy Metal Company produces brass fittings. Davy's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions. Q = 500L0.6 0.8 where Q- annual output measured in pounds, L-labor measured in person hours, K=capital measured in machine hours. Davy's employees are relatively highly skilled and earn $15 per hour. The firm estimates a rental charge of $50 per hour on capital. Davy forecasts annual costs of $500,000 per year, measured in real dollars. a. Write an expression for the marginal product of labor. b. Write an expression for the marginal product of capital. c. Determine the firm's optimal capital-labor ratio, given the information in the question, and your answers to parts (a) and (b). d. How much capital and labor should the firm employ, given the $500,000 budget? Calculate the firm's output at those levels of labor and capital. Davy is currently negotiating with a newly organized union. The firm's personnel manager indicates that the wage may rise to $22.50 under the proposed union contract. Analyze the effect of the higher union wage on the optimal capital-labor ratio and the firm's employment of capital and labor. What will happen to the firm's output?

Answer 1

0.560 10.6 x 08 6 Marginal 2. dust of leber (NPL) 6P APL = dolo2 HPL - (5w) (0.6 0.6-1 MPL = 300 -0.4 68. MPL - 30 (+8 (20-4 6. p 6) Mergina paded of capita) Chpx). 2MPX - Dolak MyK. (sav) (0.8) 100 x03- HPK - 40 2006 .2 - HPX 400 / 2°6 O w = 815, 8 - 150. cH ubhmal point; MPL . HPK 5 30 K08/204) 40 (20.0/x+2) 15 50

6 Cost foi c= wL+ OK Joouw = 15L + 5ok We have k = 2 TK = 0.42 K = 0.4L - put (11 in (1) - 50000o = 15L +50(0.42) 500 uro = 151 +20L Juo uw = 35L L = 50000 35 - L = 14235.71 and K = 0.4 L K = 0.4 (14285,71) K = 5114.28 = 500 Lob K.8 Q 5o (14235-72) 06(5734.23)0-8 te = 157572460.2

. Now we $23.50. Die cu cyhoed bangl. op MIL 31 MPK 5 3 x 21.50 (4) 1 .3 (New abitel Ialor roha) (K = 0.6L 7 Sou o = 22.50 Lt sok su wo = 22.50 L + 50 (0.6L). sono = 22.50L +3.L 50 voo : 52.50L -- (suwow sa su 12= 25. 95 23.8 (New Number of Inter compland and ka 0.6L K v.6 (9523.3) a 5714.28] New cepted numbed. a = 500 Lob AB Q: Sw (9523.3) "6 (5714,28393 123345 058 from output fall.