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W14 MIC Problem Set 5 Solutions

W14 MIC Problem Set 5 Solutions - ECON 310-1 Microeconomic...

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How to produce 100 rugs using $40/hr machines (5 rugs/hr) and $10/hr humans (1 rug/hr) A Q = 100 IsoQuant TC = $800 IsoCost TC = $1000 IsoCost 5 1 0 15 2 0 0 Labor,L Machines, K 25 20 4 0 60 8 0 0 10 0 B ECON 310-1: Microeconomic Theory Northwestern University, Winter 2014 Professors James A. Hornsten and Ronald R. Braeutigam Solutions to Problem Set #5. Production and Cost Instructions: This problem set is to be handed in (to the appropriate TA Section box during class) on Monday, February 17. Solutions will be posted at that time, so late submissions will not be accepted. We encourage you to work in a group. Each person must submit a hard copy of the assignment with only his or her name on it (i.e., group submissions will not be accepted.) The teaching assistants will go over some of the solutions in sections in Week 7. 1) A firm can produce woven rugs using weaving machines (K), labor (L), or a combination of the two. Workers and machines are perfect substitutes in production. A machine can produce a rug in 12 minutes. A person can produce a rug in an hour. The wage rate is w = $10 per hour and the rental price of a machine is r = $40 per hour. Determine the cost minimizing way to produce 100 rugs, and then illustrate your answer on an optimal choice diagram with K on the horizontal (x-) axis and L on the vertical (y-) axis. Answer: The marginal product of a machine is 5 rugs per hour: MP K = 60 mins hour ! " # $ % & 1 rug 12 mins ! " # $ % & = 5 rugs 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 MP K /P K to MP L /P L , where we use the rental price (r) and wage (w) to refer to the prices of capital and labor, respectively. The marginal product per dollar spent on machines is MP K r = 5 rugs $40 = 0.125 rugs per dollar The marginal product per dollar spent on labor is MP L w = 1 rug $10 = 0.1 rugs per dollar Thus, the producer gets a bigger “bang for the buck” with machines.
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