W14 MIC Problem Set 5 Solutions

# Answer laborl 60 mins 1 rug 5 rugs the marginal

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Unformatted text preview: nswer: Labor,!L ! 60 mins \$! 1 rug \$ ! 5 rugs \$ The marginal product of a machine is 5 rugs per hour: MPK = # &# &=# & " hour %" 12 mins % " hour % The marginal product of a worker is 1 rug per hour. What is our cost-minimizing mix of capital and labor? We need to compare the marginal product per dollar spent for the two inputs to see which is more cost-effective. In other words, we need to compare MPK/PK to MPL/PL, where we use the rental price (r) and wage (w) to refer to the prices of capital and labor, respectively. MPK 5 rugs = = 0.125 rugs per dollar The marginal product per dollar spent on machines is r \$40 MPL 1 rug = = 0.1 rugs per dollar The marginal product per dollar spent on labor is w \$10 Thus, the producer gets a bigger “bang for the buck” with machines. Because machines and workers are perfect substitutes, the firm should hire only machines. At a rate of 5 rugs per hour, it would take 20 hours to produce 100 rugs. Thus, the total cost will be (\$40/hr)(20 hrs) = \$800. The optimum is illustrated at point A o...
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## This homework help was uploaded on 03/03/2014 for the course ECON 310 taught by Professor Whinston during the Spring '12 term at Northwestern.

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