Answered: Making dresses in a labor intensive…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Making dresses in a labor intensive process. Indeed, theproduction function of a dress making firm is well described by theequation Q=L - L^2/800, where Q denotes the number of dresses perweek and L is the number of labor hours per week. The firms cost ofhiring an extra hour of labor is $20 per hour (wage plus fringebenefits.) The firm faces the fixed selling price, P = $40. a.) How much labor should the firm employ? What are itsresulting output and profit? b.) Over the next 2 years, labor costs are expected to beunchanged, but dress prices are expected to increase to $50. Whateffect will this have on the firm's optimal output? Explain.Suppose that inflation is expected to increase the firm's laborcost and output price by identical (precentage) amounts. Whateffect would this have on the firm's output. c.) Finally, suppose that MCL =$20 and P=$50 but that laborproductivity (output per labor hour) is expected to increase by 25%over the next 5 years. What effect would this have on the firm'soptimal output? Explain. Answer In equilibrium MRP = MP*P = MC of labour MP = 1 "?o L/400 MRP = (1 "?o L/400)*40 = 20 So L = 200 and Q = 150 which is found by putting L value in production function profit = Tr "?oTc = 40*150 - 200*20 = 2000 Over the next two years, labor costs are expected to be unchanged, but dress prices are expected to increase to $50. What effect will this have on the firm's optimal output? Explain In equilibrium MRP = MP*P = MC of labour MP = 1 "?o L/400 MRP = (1 "?o L/400)*50 = 20 So L = 240 and Q = 96 which is found by putting L value in production function profit = Tr "?oTc =5*96 - 240*20 = 0 Suppose instead that inflation is expected to increase the firm''s labor cost and output price by identical (percentage) amounts. What effect would this have on the firms output? There will be no effect as both P and MC of labour rise in same proportion. There will be no impact on the equation (1 "?o L/400)*50 = 20 Suppose once again that MCL(small L) = $20 and P = $50 but that labor productivity (i.e. output per labor hour) is expected to increase by 25% over the next five years. What effect would this have on the firm's optimal output? Explain. There will be an effect on the MP .it will also rise by 25%. So it becomes 5/4(1-L/400) Equilibrium requires that 5/4(1-L/400)*50 = 20 So 1-L/400 = 8/25 Or L=272 Q= 179.52

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