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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 costminimizing mix of capital
and labor? We need to compare the marginal product per dollar spent for the two inputs to see
which is more costeffective. 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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 Spring '12
 Whinston

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