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W14 MIC Problem Set 5 Solutions

100 howtoproduce100rugsusing 40hrmachines5rugshrand

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Unformatted text preview: n the optimal choice diagram. !100 How$to$produce$100$rugs$using$ $40/hr$machines$(5$rugs/hr)$and$ $10/hr$humans$(1$rug/hr) B TC$=$$1000$IsoCost !8 0 Q$=$100$IsoQuant 60 40 !20 !!!0 !!!0 TC$=$$800$IsoCost A !5 10 15 !2 0 !25 Machines,!K 2) A manufacturer of designer sweaters operates with the production function Q = K1/3L1/3M1/3. Q is the number of sweaters produced with K units of capital (machines), L units of labor (humans), and M units of raw material (cashmere). The factor price of capital is r = 27. The factor price of labor is w = 1. The factor price of raw material is m = 1. a) Determine whether there are increasing, decreasing or constant returns to scale. Explain briefly. b) Find the firm’s long run cost function. Use the numerical values of the factor prices given (as opposed to leaving them general). c) Now suppose the firm is operating in the short run, with K fixed at K=1 and M fixed at M=8. Find the firm’s short run cost function. Use the numerical values of the factor prices given. Answer: 2) a) This is a Cobb-Douglas production function, whose ex...
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