Production and cost are closely linked. The production manager strives
to produce any given level of output at minimal total cost and
continually seeks less costly ways to produce the firm’s goods and
services.
BASIC PRODUCTION CONCEPTS
Production transforms inputs into outputs. For instance, producing
automobiles requires a variety of inputs (also called factors of
production): raw material (steel, plastic, rubber, and so on), factories,
machines, land, and many different categories of workers. For analysis, it
is convenient to refer to two main categories of inputs—labor and
materials on the one hand and long-term capital on the other—with
each category broadly defined. Labor and materials includes production
workers, marketers, and managers at all levels as well as raw materials
and intermediate goods, including parts, water, and electricity. Capital
includes buildings, equipment, and inventories .
The firm’s production function indicates the maximum level of output
the firm can produce for any combination of inputs. We will start by
considering a production function with two inputs, labor and capital.1 A
shorthand description of such a production function is
Q = F(L, K).
PRODUCTION WITH ONE VARIABLE INPUT
Short-Run and Long-Run Production
Our analysis of production and cost makes an important distinction between the short run
and the long run.
In the short run one or more of the firm’s inputs is fixed; that is, they cannot be varied. In
the long run the firm can vary all of its inputs. There is no universal rule for distinguishing
between the short and long run; rather, the dividing line must be drawn on a case-by-case
basis. For a petrochemical refinery, the short run might be any period less than five years
since it takes roughly this long to build a new refinery. For a fast-food chain, six months (the
time it takes to obtain zoning approvals and construct new restaurants) may be the dividing
line between the short and long run.
Inputs that cannot be changed in the short run are called fixed inputs. A firm’s production
facility is a typical example. In the long run, the firm could vary the size and scale of its plant,
whereas in the short run the size of this plant would be fixed at its existing capacity. If a firm
operates under restrictive, long-term labor contracts, its ability to vary its labor force may be
limited over the contract duration, perhaps up to three years. In this case, labor could be a
fixed input in the short run.
MARGINAL PRODUCT let’s consider the production decisions of the auto parts firm.
Currently it is operating with a 10,000-square-foot plant. In the short run, this capital input is
fixed. However, labor is a variable input; that is; the firm can freely vary its number of
workers. Table 5.2 shows the amount of output obtainable using different numbers of
workers. (This information is reproduced from the earlier production function and expanded
slightly.) Notice that output steadily increases as the workforce increases, up to 120
workers. Beyond that point, output declines. It appears that too many workers within a
plant of limited size are counterproductive to the task of producing parts.
Numbers of workers
Total product
Marginal product
10
93
–
20
135
4.2
30
180
4.5
40
230
5.0
50
263
3.3
60
293
3.0
70
321
2.8
80
346
2.5
90
368
2.2
100
388
2.0
110
400
1.2
120
403
0.3
130
391
-1.2
140
380
-1.1
The last column of Table 5.2 lists the marginal product of labor (abbreviated MPL). This
marginal product is the additional output produced by an additional unit of labor, all other
inputs held constant. For instance, increasing labor from 20 to 30 workers increases output
by 180-135=45 units, or 45/10 = 4.5 units per worker. A further increase from 30 to 40
workers implies an MPL of 5.0 units per worker. Mathematically, labor’s marginal product is
MPL = dQ/dL. In other words, labor’s marginal product is the change in output per unit
change in labor input.
In our example, MPL first rises (for increases up to 40 workers), then declines. Why does
MPL rise initially? With a small workforce, the typical worker must be a jack-of-all-trades
(and master of none). Increasing the number of workers allows for specialization of labor—
workers devoting themselves to particular tasks—which results in increased output per
worker. Furthermore, additional workers can use underutilized machinery and capital
equipment. Figure 5.1a graphs labor’s total product. Consider the total product curve for a
10,000-square-foot plant. Initially, the total product curve increases rapidly . As the number
of workers increases, the curve’s slope becomes less steep , then reaches a peak and
declines. This reflects labor’s marginal productivity. When MPL is large (see Figure 5.1b), the
total product curve is steep. As MPL declines, the curve becomes less steep. The product
curve peaks when MPL approaches zero and begins to decline when MPL becomes negative .
Figure 5.1a also displays labor’s total product curve for a 20,000-square-foot plant (with
output rates taken from Table 5.1). As indicated, the larger plant generates an increased rate
of output for the same workforce. Finally, Figure 5.1b graphs labor’s marginal product for a
10,000-square-foot plant.
THE LAW OF DIMINISHING MARGINAL RETURNS The declining marginal product of an input
(like labor) represents one of the best-known and most important empirical “laws” of
production:
The Law of Diminishing Marginal Returns. As units of one input are added (with all other
inputs held constant), resulting additions to output will eventually begin to decrease; that is,
marginal product will decline.
Extra workers are assigned to less productive tasks. These workers generate additional
output but at a diminishing rate.
Optimal Use of an Input
The law of diminishing returns means that the firm faces a basic trade-off
in determining its level of production. By using more of a variable input,
the firm obtains a direct benefit—increased output—in return for
incurring an additional input cost. What level of the input maximizes
profits? As before, we look at the firm’s marginal profit, but this time we
look at marginal profit per unit of input. We increase the input until the
marginal profit per unit of input is zero.
In analyzing this input decision, a definition is helpful. Marginal revenue
product is the formal name for the marginal revenue associated with
increased use of an input. An input’s marginal revenue product is the
extra revenue that results from a unit increase in the input. To illustrate,
suppose the auto parts supplier is considering increasing labor from 20 to
30 workers. According to Table 5.2, the resulting marginal product is 4.5
parts per worker. Suppose further that the supplier’s marginal revenue per
part is constant. It can sell as many parts as it wants at a going market
price of $40 per part. Therefore, labor’s marginal revenue product
(MRPL) is ($40)(4.5) =$180 per worker. Similarly, the MRPL for a move
from 30 to 40 workers is ($40)(5.0) = $200 per worker. More generally,
labor’s marginal revenue product can be expressed as
MRPL = (MR)(MPL),
where MR denotes marginal revenue per unit of output.
Now consider the marginal cost of using additional labor. The marginal
cost of an input is simply the amount an additional unit of the input adds
to the firm’s total cost.4 If the firm can hire as many additional workers
as it wishes at a constant wage (say, $160 per day), then the marginal cost
of labor is MCL = $160. (In some cases, however, the firm may have to
bid up the price of labor to obtain additional workers.) Now note that the
additional profit from adding one more worker is the revenue generated
by adding the worker less the worker’s marginal cost.
MπL =MRPL –MCL.
it is important to distinguish between the marginal cost of an input and
the marginal cost of an additional unit of output. Taking labor as an
example, MCL is defined as ΔC/ΔL, the cost of hiring an extra worker. In
contrast, the added cost of producing an extra unit of output is MC
=ΔC/ΔQ.
The firm should continue to increase its labor force as long as the amount
of additional profit from doing so is positive, that is, as long as the
additional revenue (MRPL) is greater than the additional cost (MCL).
Due to diminishing marginal returns, labor’s marginal revenue product
eventually will fall. When MRPL exactly matches MCL (that is, when
MπL = 0), increasing the labor force any further will be unprofitable,
which leads to the following principle:
To maximize profit, the firm should increase the amount of a variable
input up to the point at which the input’s marginal revenue product equals
its marginal cost, that is, until:
MRPL = MCL.
