HW chap 7

# Substituting120l2 forl1 andsolvingforl2 250120l2 50l2

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Unformatted text preview: o production plants that use finely divisible labor toproduce its output. The marginal product of labor at plant 1 is and the marginal product of labor at plant 2 is Beta Inc. wants to find the best assignment of 120 workers between the two plants. What is it? Instructions: Enter your answers as whole numbers. Beta Inc. should assign 100 workers to plant 1 and 20 workers to plant 2. rev is ed jrl 08­09­2011 Explanation: The marginal product of labor with L workers equals the extra output produced due to the ΔL marginal units of labor, per unit of labor added. A production method is efficient if there is no other way for the firm to produce a larger amount of output using the same amounts of inputs. First, the assignment of workers at the two plants should sum to 120: L1 + L2 = 120. To find the optimal allocation, set the marginal product of labor at plant 1 equal to the marginal product of labor at plant 2: MP1 = MP2 http://e z to.mhe c loud.mc gr a w- hill.c om/hm.tpx? todo= pr intvie w 4/7 1/21/2014 Assignme nt Pr int Vie w 250/L1 = 50/L2 . Substituting 120 – L2 for L1 and solving for L2 , 250/(120 – L2 ) = 50/L2 250L2 = 50(120 – L2 ) 250L2 = 6,000 – 50L2 250L2 + 50L2 = 6,000 300L2 = 6,000 L2 = 6,000/300 L2 = 20. In turn, L1 = 120 – 20 L1 = 100. Therefore, Beta Inc. should assign 100 workers to plant 1 and 20 workers to plant 2. 14. awar d: 4 out of 4.00 points Jason has a boat­building firm. It uses labor L, capital K, and materials M, to build its boats. Its production function is . For what values of α, β, and γ does Jason's technology have constant returns to scale? Increasing returns to scale? De...
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