Assume that the cost to rent, operate, and maintain a self-checkout station for a
month is $1,000 and hiring a cashier costs $1,600 per month. The cost of each input
combination from Table 72.1 is shown below.a. cost of capital 20 ×$1,000 =$20,000
cost of labor 4 ×$1,600 =$ 6,400
TOTAL $26,400
b. cost of capital 10 ×$1,000 =$10,000
cost of labor 10 ×$1,600 =$16,000
TOTAL $26,000Clearly, your firm would choose the lower cost combination, combination b, and
hire 10 cashiers and put in 10 self-checkout stations.
When firms must choose between alternative combinations of inputs, they evaluate
the cost of each combination and select the one that minimizes the cost of produc-
tion. This can be done by calculating the total cost of each alternative combination of
inputs, as shown in this example. However, because the number of possible combina-
tions can be very large, it is more practical to use marginal analysis to find the cost-
minimizing level of output–which brings us to the cost-minimization rule.The Cost-Minimization Rule
We already know that the additional output that results from hiring an additional unit
of an input is the marginal product (MP) of that input. Firms want to receive the high-
est possible marginal product from each dollar spent on inputs. To do this, firms ad-
just their hiring of inputs until the marginal product per dollar is equal for all inputs.
This is thecost-minimization rule.When the inputs are labor and capital, this
amounts to equating the marginal product of labor (MPL) per dollar spent on wages to
the marginal product of capital (MPK) per dollar spent to rent capital:(72-1) MPL/Wage =MPK/Rental rateTo understand why cost minimization occurs when the marginal product per dollar
is equal for all inputs, let’s start by looking at two counterexamples. Consider a situa-
tion in which the marginal product of labor per dollar is greater than the marginal
product of capital per dollar. This situation is described by Equation 72-2:(72-2) MPL/Wage >MPK/Rental rateSuppose the marginal product of labor is 20 units and the marginal product of cap-
ital is 100 units. If the wage is $10 and the rental rate for capital is $100, then the mar-
ginal product per dollar will be 20/$10 = 2 units of output per dollar for labor and
100/$100= 1 units of output per dollar for capital. The firm is receiving 2 additional
units of output for each dollar spent on labor and only 1 additional unit of output for
each dollar spent on capital. In this case, the firm gets more additional output for its
money by hiring labor, so it should hire more labor and less capital. Because of dimin-
ishing returns, as the firm hires more labor, the marginal product of labor falls and as
it hires less capital, the marginal product of capital rises. The firm will continue to sub-
stitute labor for capital until the falling marginal product of labor per dollar meets the
rising marginal product of capital per dollar and the two are equivalent. That is, the
firm will adjust its hiring of capital and labor until the marginal product per dollar
spent on each input is equal, as in Equation 72-1.
Next, consider a situation in which the marginal product of capital per dollar is greater
than the marginal product of labor per dollar. This situation is described by Equation 72-3:(72-3) MPL/Wage <MPK/Rental rate708 section 13 Factor Markets
Self-checkout lines have reduced the
need for many stores to hire extra
cashiers.© Ilene MacDonald / Alamy
A firm determines the cost-minimizing
combination of inputs using the
cost-minimization rule:hire factors so
that the marginal product per dollar spent on
each factor is the same.