The Cost of Production 241table, we observe that the firm’s marginal cost rises steadily with increases in
output. Expanding output starting from a level of 40,000 units per month is
much more expensive than starting from 20,000 units.
What factors underlie the firm’s increasing short-run marginal cost (SMC)?
The explanation is simple. With labor the only variable input, SMC can be
expressed as[6.1]
where PLdenotes the price of hiring additional labor (i.e., wage per hour) and
MPLdenotes the marginal product of labor.^5 To illustrate, suppose the pre-
vailing wage is $20 per hour and labor’s marginal product is .5 unit per hour
(one-half of a typical repair job is completed in one hour). Then the firm’s
marginal (labor) cost is 20/.5 $40 per additional completed job. According
to Equation 6.1, the firm’s marginal cost will increase if there is an increase in
the price of labor or a decrease in labor’s marginal product. Moreover, as the
firm uses additional labor to produce additional output, the law of diminishing
returnsapplies. With other inputs fixed, adding increased amounts of a vari-
able input (in this case, labor) generates smaller amounts of additional out-
put; that is, after a point, labor’s marginal product declines.As a result, marginal
cost rises with the level of output. (Clearly, material costs are also variable and,
therefore, are included in SMC. However, because these costs typically vary in
proportion to output, they do not affect the shape of SMC.)
Now we can explain the behavior of short-run average cost (SAC). When
output is very low (say 5,000 units), total cost consists mainly of fixed cost
(since variable costs are low). SAC is high because total cost is divided by a
small number of units. As output increases, total costs (which are mostly
fixed) are “spread over” a larger number of units, so SAC declines. In the
graph in Figure 6.2, notice that SAC lies well above SMC for low levels of out-
put. As long as extra units can be added at a marginal cost that is lower than
the average cost of the current output level, increasing output must reduce
overall average cost. But what happens to average cost as marginal cost con-
tinues to rise? Eventually there comes a point at which SMC becomes greater
than SAC. As soon as extra units become more expensive than current units
(on average), the overall average begins to increase. This explains the upward
arc of the U-shaped SAC curve. This argument also confirms an interesting
result: The firm’s marginal cost curve intersects its average cost curve at the minimum
point of SAC.SMCPL/MPL,
(^5) The mathematical justification is as follows. Marginal cost can be expressed as MC C/
Q (C/L)/(Q/L) PL/MPL. As the notation indicates, here we are looking at discrete
changes in output and input. The same relationship holds with respect to infinitesimal changes,
(dC/dQ).
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