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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
MPL 1 rug
= 0.1 rugs per dollar
The marginal product per dollar spent on labor is
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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- Spring '12