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Chapter 3
The Firm: Production and Cost
I. Firms
The firms populating the various industries are the vehicle through which labor generates
gross domestic product. Firms can be classified along two dimensions: first, by their legal
structure; and second, by their degree of economic power. In terms of legal structure, there are
three types of firms: single proprietorships, partnerships, and corporations. In terms of economic
power, firms can be arranged along a continuum that measures power in terms of market share
and ownership of assets. In general, there is a positive relationship between the ownership of
business assets and market share. Firms that own a greater proportion of business assets tend to
control larger shares of the market; and the larger the share of the market, the greater, in general,
the flow of profits.
The most common type of firm, and the one most readily accessible to the individual of
modest means, is the single proprietorship. This type of firm is very easy to set up, and can be
found throughout the economic landscape. In fact, the ease with which anyone can create a
single proprietorship is what accounts for its predominance. The family-run day care and the
family farm are two examples of this type of firm. It need not, however, involve a small
operation. Some single proprietorships are actually quite large; yet their size is ultimately limited
by the capacity of the owner. After all, there are only 24 hours in a day, and only so many
departments and divisions that an owner can oversee.
Partnerships refer to the ownership of a firm by two or more individuals. They are the
least numerous type of business organization and tend to be found in the service industries such
as law, medicine, or consulting. This form of business organization is generally undertaken by a
group of individuals who can combine their differing talents. For this reason, partnerships are
frequently found in fields, such as medicine and law, where the owners have complementary
skills and expertise. This type of business organization has the advantage of being able to access
a larger amount of financial capital as a result of the broader pool of equity made possible by
several owners. The disadvantage is that conflicts can, and generally do, occur among the
owners. Moreover, each partner is liable for all the obligations incurred by the partnership.
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The corporate form of business is the most refined of the three legal forms that firms
might assume. A corporation is considered a legal individual capable of carrying on business in
its own name. Ownership in the corporation is obtained by purchasing shares of ownership in the
business, called corporate stock or shares. For example, if a corporation has issued ten million
shares of stock and one of the stockholders owns one million shares, then that stockholder owns
10% of the business. Each stockholder’s share in the business entitles him or her to a claim on the
company’s profits in the form of dividends.
There are two enormous advantages to this type of business organization. First, because
the corporation is legally viewed as an individual, each owner experiences only limited liability.
The corporation can hire individuals, carry on business, and buy other companies without
obligating the stockholders (the owners) to assume all of the liabilities taken on by the company.
The obligations are the sole responsibility of the individual that assumed them in the first place,
namely the corporation. Thus if the corporation were to go bankrupt, the owners would not be
liable for any more than the amount represented by their share of ownership. Creditors would not
be entitled to encumber the remaining income and wealth of the stockholders for purposes of
debt repayment.
Another advantage of the corporate form of organization is that the firm has access to a
much larger pool of financial capital than is ever possible through the single proprietorship or
partnership. Because of limited liability, the incentive to invest in this form of business is much
greater than for single proprietorships or partnerships. Each potential investor knows that he or
she is risking no more than the cost of purchasing the stock. In consequence, the corporation
does and can raise an enormous amount of financial capital from millions of potential
stockholders.
The corporation is the quintessential type of business enterprise. This type of
organization dominates the manufacturing industry as well as finance, transportation, public
utilities and energy. Indeed, the corporate form of organization can be found in every industry of
the economy. Yet, this type of business organization represents a relatively small fraction of all
firms; the vast majority of firms are single proprietorships. For example, in 2008 (the latest year
for which such data is available) there were approximately 31,607 thousand firms in the United
States; of that amount, 18.5 percent were corporations, 10 percent were partnerships and 71.5
percent were single proprietorships. But, while corporations accounted for 18.5 percent of all
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firms, they took in 81.3 percent of all business receipts and 57.7 percent of all net income. In
contrast, partnerships accounted for 14.8 percent of receipts and 26.8 percent of net income,
while single proprietorships brought in 3.9 percent of total receipts and 15.5 percent of all net
income.1
This pattern of concentration, in the capturing of business receipts and net income, is
repeated within the corporate sector. That is, just as corporations take in the lion’s share of total
business receipts and net income even though they account for a small fraction of all firms, the
lion’s share of corporate receipts and net income is taken in by a relatively small fraction of all
corporations. Thus, in 1996, 81.9 percent of all corporations generated, on an individual basis,
annual receipts less than $1 million; yet, as a group, they accounted for only 5.3 percent of all
corporate receipts. In contrast, at the other end of the spectrum, corporations large enough to
generate, on an individual basis, annual receipts in excess of $50 million were only 0.5 percent
of the total, yet they accounted for 68.6 percent of all corporate receipts. When this information
is combined with data from the previous paragraph, regarding the distribution of firms by type
and business receipts, what we find is that, in 1996, the top 0.1 percent of all firms captured 60.9
percent of all business receipts!
The above evidence suggests that the organization of the U.S. economy is bifurcated into
two spheres; a dual structure characterized by a core consisting of a small number of very large
firms, and a periphery composed of a large number of relatively small firms. The core of the
economy consists of that small proportion of firms, almost all of them corporations, which own
the largest share of the nation’s business assets and generate most of GDP. These are the firms
that dominate economic activity and have considerable impact on the behavior of GDP. The
periphery consists of that larger group of small firms, generally, though not exclusively, single
proprietorships and partnerships, that own a smaller fraction of the nation’s business assets and
generate a smaller proportion of GDP. These are the smaller firms that populate the economy and
whose fortunes can change without having, on a per firm basis, much of an impact on the
economy. While most industries tend to have a mixture of core and peripheral firms, there are
some industries that are controlled exclusively by core firms while others are overwhelmed by
peripheral firms.
1 Table 863 of “Business Enterprise,” in Statistical Abstract of the United States, 1999,
http://www.census.gov/statab/www.
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It should be noted that the dominance that core firms exercise over assets and the
production of GDP, does not translate into dominance over the employment of labor. That is,
core firms do not employ the majority of the nation’s civilian labor force; instead, it’s the
periphery that employs most of the workers, even though, on a per firm basis, the labor force of
most peripheral firms is small, often numbering less than 20 employees. Though, by the
standards of the Small Business Administration, a firm with a labor force less than 500 is
considered small.2 In contrast, the labor force of most core firms is quite large, generally
numbering in the thousands, even though, on a national basis, the total number of workers
employed by such firms is less than the amount employed by the periphery. Finally, while core
firms, as a group, may not employ as many workers, it is the case that they tend to provide better
employment conditions. Wages and benefits are often better in core firms than they are within
peripheral firms.3
The firms within the core have managed to gain control over their environment by
expanding their area of economic activity in the hope of minimizing the hazards of the
marketplace. One of the most common techniques by which this control is accomplished is
through horizontal integration; a situation in which one firm buys another firm in the same
industry allowing it to capture a larger share of the market. Rather than having two firms
competing against each other selling the same good, there is now one firm selling the product.
Another method of gaining control involves buying suppliers or buyers. This is called vertical
integration, and involves one firm buying another firm that provides inputs to the original firm or
purchases its output. The motivation for either horizontal or vertical integration is the obvious
one of greater profits; obtained through the development of a more predictable economic
environment, one with less competition in the output market and a more predictable flow and
price of inputs and outputs.
The firms that have managed to achieve a certain amount of vertical integration have also
generally achieved a significant amount of horizontal integration. The classic example of such a
firm was U.S. Steel during the period from 1890 to 1975. This firm not only managed to
consolidate its position within the steel industry by buying up or squeezing out the competition,
2 See Table No. 877 in Business Enterprise, Statistical Abstract of the United States, 1999,
http://www.census.gov/statab/www. 3 This is discussed in chapter 10.
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allowing it to dominate an increasingly large share of the steel market, it also expanded its
operations into mining and railroads, the inputs needed in the production and delivery of steel.
A phenomenon that has become increasingly significant since World War II involves the
emergence of the conglomerate form of corporate organization. This term refers to a firm that
has achieved not only a certain degree of horizontal and vertical integration, but has also
managed to move into industries that are quite unrelated to its original business. This
phenomenon is common in the core of the economy. The core is populated by corporations with
business interests in numerous, sometimes quite unrelated, industries. The most powerful version
of the conglomerate is the multinational corporation, which, as its name implies, has business
interests in several countries in addition to numerous industries.
It’s important to keep in mind that while most businesses are single proprietorships and
usually confined to one physical location (a plot of land, as in a farm, or a building as in a factory
or retail outlet), a significant number of businesses – particularly those in the core of the
economy – have more than one establishment and physical location. Vertically integrated firms
often have establishments at different stages in the supply chain producing one component or
aspect of the final product. For example, an automobile manufacturer might own a company that
produces engines or brakes in addition to the company that produces the finished automobile.
Likewise horizontally integrated firms usually have numerous firms scattered throughout the
economic landscape competing in different geographic areas, such as WalMart owning stores
across Southern California and, indeed, the world. Conglomerates are firms that own
establishments in a wide variety of industries, both horizontally and vertically, that are unrelated
to the firm’s primary or original business; thus General Electric owns companies in energy,
home and business solutions, aviation, transportation, healthcare, and media.
The upshot of this is that there are always more establishments than there are firms (since
a significant minority of firms have multiple establishments). If our purpose is to understand the
behavior of firms then this reality must be taken into account. Indeed, if our purpose is to lay out
the key features of a typical core firm and a typical peripheral firm, then we’d have to represent
the core firm as owning numerous establishments carrying out business in numerous locations,
industries, and markets and under differing condition, while the peripheral firm would consist of
only one establishment located in a specific geographic region, industry and market. Clearly, the
multiestablishment firm wields much more power than the single establishment firm, and it has
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the ability to draw on resources (financial and otherwise) from the various industries and parts of
the world in which it does business to subsidize and buttress any one establishment. This has an
enormous effect on the behavior of markets, which we will be seeing later on.
II. Production Functions and Labor Productivity
We’ll start by imagining a single establishment that’s producing a physical product. But
this immediately poses a problem, what kind of product? It turns out, when all is said and done,
production can be classified into two very large categories: products generated directly from
nature (the primary sector), and products generated from manufacturing (the secondary sector).
This classification goes back to the classical economists who tended to break up the economy
into two sectors: the agricultural sector and the manufacturing sector. Now-a-days we have, in
addition to the primary and the secondary sectors, a tertiary (services) sector; but the productive
behavior of the firms in the tertiary sector can usually be seen as a version of firms in one of the
previous two categories, i.e. as primary or secondary.
A common theme of firms (single establishments) in the primary sector (agriculture) is
that they’re dealing with nature and, as such, their production processes are subject to
diminishing returns. In contrast, firms operating in the secondary sector (manufacturing) are
dealing with machine-driven process and, as such, their production processes are subject to fixed
proportions. Given this, we can think of the firm as an institution that transforms raw materials
into a finished product, for a profit of course. Some of these firms will be producing primary
sector goods, in which case they’re subject to diminishing returns, while other firms will be
producing secondary sector goods, in which case they’re subject to fixed proportions
technologies.
In both cases we can think of the production function as system that transforms raw
materials with the aid of labor and capital into a product. The capital consists, of course, of the
physical structure within which production takes place, the building within which the
establishment is located. But it also consists of the tools that are employed by the workers to
generate the product, the hand tools, the assembly line, the compressors, etc. The usual
procedure is to find each worker using a set of tools within a physical structure to transform the
raw material into a finished product. The amount of tools available to the workers is a function of
the capital investment, which the owners of the firm have already made. In the short run, the
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physical structure of the firm as well as the amount and variety of tools it makes available to the
workers is stable or fixed. But the amount of workers, or hours of work, which the firm can use
to generate the product can vary within that physical capacity, assuming, of course, that the
requisite raw materials are also available. The production function would thus focus on the
relationship between the number of workers (or hours of work) and the amount of output
produced by those workers (each worker employing the requisite tools and using the needed raw
materials). This production function would then provide us with information on the two most
common measures of labor productivity: the average product (ap) and the marginal product (mp)
of labor.
The average product of labor is a measure of the amount of output generated by the
existing labor force (or existing hours of labor per time period). For example, if a firm is
currently generating 200 units of the product while employing 10 workers, then the average
product of that labor force (the amount produced by the average worker) is 20 (ap =Q/L = 200/10
= 20).
The marginal product of labor is a measure of the amount of extra output generated by
the use of one extra unit, or batch, of labor. For example, if in going from the employment of
labor from 9 to 10 workers, the firm saw its output growing from 190 to 200, then the marginal
product of employing the 10th worker would be 10 (mp = ∆Q/∆L = (200-190)/(10-9) = 10/1 =
10).
The average productivity of labor can be broken down into two components: the
efficiency of work (we) and the intensity of work (wi). The efficiency of work (we) is a measure
of the amount of output that’s generated per hour of work, while the intensity of work (wi) is a
measure of the amount of work done per hour. The average productivity of labor (ap) is thus a
product of the efficiency of work and the intensity of work; that is, ap = we*wi. Thus the average
productivity of labor can increase if either the efficiency of work increase, the intensity of work
increases, or both increase.
In the short run, the efficiency of work is fixed, but the intensity of work, and thus the
productivity of labor, is not. Increasing the intensity of work will increase the productivity of
labor, and decreasing work intensity has the effect of decreasing labor productivity. The
efficiency of work is determined by the technology available to the firm. The kind of machinery,
and thus technology, available to the firm determines the amount of output that laborers can
8
generate through their work. Over the long run the firm can improve the technology it employs
by introducing better machines, thus making it possible for direct laborers to generate a greater
amount of output per unit of work. In the short-run, the firm’s machinery is given, and thus, so
too, is the efficiency of the direct labor force.
In contrast, the intensity of work is determined by the manner in which the firm organizes
the labor process. In fact one of the major functions of the firm is to insure that work be extracted
from labor power. When the firm buys labor power, that is hires workers, all it has really done is
pay for the possible use of labor effort, not its actual use. Thus, whether or not a specific laborer
will work depends among other things, on the extent to which management can motivate, cajole,
or threaten direct laborers into working at the tempo and at the activities deemed necessary.
Other things equal, laborers who work very little during the course of one hour are more costly to
the firm than those who work quite a bit. Thus, management will be forever seeking ways to
increase the amount of work it can extract from the labor force. Increasing the intensity of work
increases the productivity of labor and, consequently, reduces the firm’s unit cost.
There is, of course, an upper limit to the degree to which management can extract labor
from workers. The most obvious, and ultimate, limit is determined by the physical capacities of
the human body. Short of that extreme, the limit is determined by the technology available to the
firm, the extent of competition within the labor market, and the legal and political relations
implicit in society at large. While the broad legal and political context will set a boundary to the
amount of work that management can extract from its labor force, the extent of competition
within the labor market tends to be more immediate. After all, the extent to which the
management of any one firm can extract labor from its work force depends in part on the
treatment that workers receive in other firms. Finally, the kind of machinery available to the
firm, that is its technology, will also set a limit to the amount of work that can be extracted from
the laborers. Since the tempo at which machinery can operate depends on technology, the
maximum level of work intensity, given the other boundaries, will be fixed by technology.
The following two graphs show two production functions, one is subject to diminishing
returns (the one on the left) and the other one is subject to fixed proportions (the one on the
right). Note that in both cases we’re focusing exclusively on the relationship between the usage
of labor on the one hand and the generation of output on the other. In both cases we’re assuming
that each worker (or hour of work) is using a specific combination of tools and equipment along
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with a specific combination of raw materials. We’re also assuming that the intensity of work
remains the same as the usage of labor increases. The neoclassicals generally assume that the
intensity of work is as high as it can possibly be and that it remains at that level regardless of the
amount of labor employed. This assumption is common in neoclassical literature since the focus
tends to be on very competitive markets; and in such a context, the incentive would be to have
the labor force work as hard as possible.
Corresponding to these two production functions there exist a set of labor productivity
functions that show the behavior of the average product and marginal product of labor under
these two technologies (diminishing returns and fixed proportions).
Note that in the presence of diminishing returns the productivity of labor is declining,
with the marginal product of labor falling faster than the average product of labor. In the case of
fixed proportions, the productivity of labor remains constant and, what’s more, the marginal
product of labor is equal to the average product of labor. It should also be remembered that the
above curves, both the production functions and the derived productivity functions, are assuming
a constant level of work intensity. A change in the intensity of work, say due to a labor
Labor
Q ua nt it y
Labor
M ar
gi na
l P ro
d uc
t &
A ve
ra ge
P ro
d uc
t
ap
mp
Labor
A ve
ra ge
P ro
d uc
t &
M ar
gi na
l P ro
d uc
t of
L ab
or
ap = mp
10
slowdown or an increase in intensity due to an owner imposed speed up, would have the effect of
moving the above curves. In the case of a slowdown the production functions would rotate
downward and the productivity of labor curves would shift down. In the case of a work speed up,
the productivity functions would rotate upward and the productivity of labor curves would shift
up.
It should be obvious that the above relationship between labor and output is focused
exclusively on direct labor, that is the labor that is directly needed to produce the product. Yet,
firms always have two forms of labor; in addition to the direct labor force that’s generating the
product, there is also the indirect, or overhead, labor force that isn’t directly producing the good
but is nevertheless used by the firm for purposes of management, marketing, lobbying, research,
safety, etc. In short, the labor force of any firm can be divided into an overhead (indirect)
component (with management being the most obvious example of overhear labor) and a direct
component (the workers directly working with the raw materials to produce the product).
The overhead labor force also relies on machines and tools to carry out it’s activities, but
their work is not directly relevant to changing the amount produced. That is, increasing the usage
of overhead labor and/or increasing the usage of machines associated with overhead labor will
not change the volume of output produced in the short run. Of course, over the long run, it’s
reasonable to imagine that a change in the nature of overhead labor can bring about a change in
the productivity of the direct labor force which in turn will affect the volume of production, but
that’s a long run phenomenon, not a short run issue.
III. Cost
Every firm experiences two very broad categories of cost. First, there are those types of
cost that do not vary with the level of output; they are referred to as fixed, or overhead cost.
These are the forms of cost associated with the upkeep of the firm’s productive capacity, the
maintenance or supervision of its productive processes, and the defense or aggrandizement of the
firm as an institution. Common examples of this category of cost would be the rental or
mortgage payments of the firm, the interest payments on loans, the amortization fund, and the
salary of the firm’s overhead labor force. This last entry would include, in addition to the
managerial and secretarial staff, the accountants and economists hired by the firm, the
researchers in the R & D division, the marketing department, the sales force, the legal staff, the
11
public relations division, the security force, and so on. In short, the firm’s fixed, or overhead,
costs include all of those expenditures that are not directly related to the production and delivery
of the firm’s output. As long as the firm’s productive capacity and institutional structure remains
unchanged, its usage of fixed or overhead inputs will not vary with the level of production.
The second type of cost refers to those that vary with the level of output. This category of
costs is referred to as variable, or direct, because they increase as the level of production
increases, and decrease as the level of production decreases. The most obvious examples of this
category of costs are the expenditures associated with the use of the materials and labor effort
directly applied to the production and delivery of the good. A manufacturer, for example, will
clearly require more labor effort and material inputs when producing a greater volume of output
per month than when producing a smaller volume of output per month. As a result, its variable or
direct costs will be greater at the higher level of production than at the lower level.
The distinction between fixed (or overhead) cost and variable (or direct) cost is based on
the idea that in the short-run the productive capacity and institutional structure of any firm is
stable. In fact, the short-run is defined as a period of time during which the productive capacity
of a firm is fixed. Thus, the expenditures associated with the maintenance of that capacity and
structure are thought of as fixed. The expenditures associated with the production of changing
levels of output, within the context of a fixed capacity and structure, are thought of as variable.4
But, over the long run, the productive capacity and institutional structure of the firm changes. In
the context of economic growth, the firm’s productive capacity increases, causing the inputs
needed to maintain that capacity to also grow. The inputs that in the short-run were thought of as
fixed, would now be thought of as variable. The long run is thus defined as a period of time
during which the firm’s productive capacity is altered.
The firm’s costs can thus be expressed in the following terms,
3.1
where tc represents total cost, vc represents variable, or direct, costs, and fc represents fixed, or
overhead, cost. Because firms need to know their unit costs before setting a price for their
product, we will generally work with the per unit counterparts to the above measures of cost.
4 There are some forms of expenditures that can be thought of as semi-variable. Examples of these would be the
set-up costs associated with the production of a particular good. While this is a significant type of cost, particularly for firms in the service sector, this complication does not destroy the basic distinction being introduced here.
€
tc = vc + fc
12
Dividing the above expression by the quantity produced, q, would provide us with the following
equation, representing the firm’s unit costs,
3.2
where, ac, referred to as average cost or unit cost, represents the firm’s total cost per unit of
output (tc/q); afc, referred to as average fixed cost or unit overhead cost, represents the firm’s
fixed costs per unit of output (fc/q), and; avc, referred to as average variable cost or unit direct
cost, represents the firm’s variable costs per unit of output (vc/q).
The behavior of the firm’s unit cost will depend on the volume of output being generated
by the firm. In the case of overhead it will always be true that, with a given short-run capacity,
average fixed cost will decrease as production levels increase. Since afc is equal to fc/q,
increasing q, with a constant fc, will cause afc to fall. What happens to direct costs depends on
whether the firm’s productive processes exhibit diminishing returns or fixed proportions. Firms
that experience diminishing returns require increasingly greater amounts of direct labor and
material inputs per unit of output as output increases. That is, as q increases, vc increases at an
increasing rate. As a result, the unit direct cost of such firms increases as output levels increase.
However, firms that experience fixed proportions use a fixed amount of direct labor and material
inputs per unit of output, regardless of output levels. That is, as q increases vc increases at the
same rate. For these firms unit direct costs remain stable as output levels increase.
A measure of unit cost that is not shown in the above equation is marginal cost (mc); it’s
a notion of cost that is used primarily by economist to explain economic behavior but seldom
used by firms in their estimation of cost and pricing. The marginal cost of production refers to
the extra cost that’s incurred from producing one more unit of the product, i.e. mc = ∆TC/∆Q. In
the case of firms experiencing diminishing returns, the marginal cost of production is always
growing faster than average variable cost. In the case of firms experiencing fixed proportions, the
marginal cost of production is always equal to the average variable cost of production.
Firms that interact directly with nature, such as those in the primary sector of the
economy, tend to experience diminishing returns, whereas firms in the secondary sector, and
most of those in the tertiary sector, experience fixed proportions.
The following two graphs show the behavior of total cost (and its components) for firms
experiencing diminishing returns and firms experiencing fixed proportions. The graph on the left
afcavcac +=
13
is for a firm experiencing diminishing returns, the graph on the right is for a firm experiencing a
fixed proportions productive technology.
The unit counterparts to the above cost curves are shown below; they display the
behavior of average variable cost, marginal cost and average cost for firms experiencing
diminishing returns (on the left) and firms experiencing fixed proportions (on the right). Note
that the behavior of these measures of unit cost assume a stable intensity of work and a given
wage rate and rental rate of capital; a change in the intensity of work, the wage rate or the rental
rate would shift these curves up or down.
Quantity
C o st
VC
TC
Quantity C o st
VC
TC
Quantity
U ni
t C
os t
avc
ac
mc
Quantity
U ni
t C
os t
avc= mc
ac
14
IV. Direct inputs and labor extraction
Let us now consider the effect that changes in the price of direct inputs or their usage
might have on the firm’s average variable cost and thus its unit cost. To keep the discussion
focused, we will start by defining the firm’s unit direct costs, that is average variable cost, in the
following terms,
3.3
or
= % &’ + *+ ∙
*+ -.
&’ 3.4
where w represents the wage rate of direct workers, l represents the hours of direct labor power,
pmt the price of material inputs, mt the amount of material inputs, and q the quantity produced per
time period. The ratio (l/q), represents the hours of direct labor power used per unit of output or,
as in 3.4, the inverse of the average productivity of labor. mt/q represents the amount of material
inputs used per unit of output or, as in 3.4, the ratio of material inputs per unit of labor divided
by the productivity of labor. Note that average variable cost depends on the productivity of labor,
given the wage per unit of labor and the price of material inputs per unit of labor.
Equation 3.4 points out that the firm’s unit direct cost depends on the usage of labor
power and material inputs per unit of output, as well as the wage rate and the price of material
inputs. As long as the wage rate, the price of material inputs, and the hours of labor and materials
per unit of output remain fixed, the firm’s average variable cost will also remain fixed. A change
in any one of these factors will have the effect of changing avc and, given that ac = avc + afc,
average cost as well.
If the wage rate or the price of material inputs were to increase, then the firm’s avc would
also increase. In terms of the above unit cost figures, an increase in the wage rate or the price of
material inputs would cause the avc curve (or line) to shift up, while a decrease in the wage rate
or the price of material inputs would cause avc to shift down; likewise, with the usage of direct
labor and material inputs. If more labor or material inputs are needed per unit of output, then avc
would shift up. And if less labor or material inputs are needed per unit of output, then avc would
shift down. However, it should be noted that even in the context of fixed proportions the
÷÷ ø
ö çç è
æ ×+÷÷
ø
ö çç è
æ ×=
q mtp
q lwavc mt
15
productivity of labor can change as a result of a change in the intensity of labor, and this, in turn
will affect avc. Increasing the intensity of labor (and consequently the productivity of labor) will
have the effect of reducing avc even if technology, and thus material inputs per unit of labor,
remain unchanged. Decreasing the intensity of labor will cause avc to increase.
In the short-run, with a given technology and a stable set of wage rates and material input
prices, the only method by which the firm can lower its average variable cost, lower avc, is to
increase the intensity of work. However, the extent to which management can do this depends on
the manner in which the labor process is organized within the firm, the conditions of work in
other firms, and the broad legal and political environment within which the firm operates.
The average variable cost information displayed in the above unit cost figures was built
on the assumption that the intensity of work was stable. But, as might be expected, this is not
always true. Workers may go on strike or management may institute a work speed up. These
types of changes have the effect of altering the intensity of work and thus the firm’s average
variable cost, causing the avc curve (or line) to shift up or down. In fact, it is common to find the
productivity of labor falling as a business expansion reaches its peak and increasing as the
economy moves out of a recession. Many theorists have attributed this behavior to the fact that
the intensity of work changes during the course of the business cycle.5
What happens is that, as the business expansion proceeds the level of unemployment
falls, making it easier for workers to quit their jobs and find alternative employment. At the same
time, workers begin to demand better working conditions and become more willing to strike and
engage in work stoppages. As a result, the intensity of work begins to fall as management’s
ability to extract labor from workers declines. This has the effect, other things equal, of
decreasing the productivity of labor and increasing unit direct cost. The opposite set of
circumstances tends to occur in the context of a recession.
V. Machines and overhead labor
In this section we will examine how changes in the productive capacity and institutional
structure of the firm alter its cost. In particular, we will examine how overhead expenditures are
5 See Howard J. Sherman, “Cyclical Behavior of the Labor Share,” Review of Radical Political Economics, vol.
22 (2-3), Summer/Fall 1990, pp. 92-112.
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altered though an increase in the productive capacity of the firm. After that, we will outline the
effect of, and possible reasons for, a larger institutional structure.
Obviously, changes in physical capacity have the effect of changing the expenditures
associated with the maintenance of that capacity. In the case of growing firms, the expense
associated with the maintenance and replacement of physical capital increases with the creation
of new capacity. These increased costs are willingly accepted if they allow the firm to generate a
greater flow of profit.
To keep our attention focused on the key ideas we’ll start by representing the firm’s
overhead expenditures, that is its fixed cost, in the following terms
= ∙ 3.5
where v represents the cost or price of capital per unit of time and K represents the monetary
value of the firm’s physical capital. It’s common in neoclassical literature to refer to v as the
“rental rate” even though they realize it is not, strictly speaking, a flow of rental income. The
term “rental rate” is used to underscore the idea that capitalists could always rent out their plant
and equipment to other capitalists who might be willing to borrow it for their own purposes.
While such scenarios do occur and there are markets in the renting of tools and equipment, it is
not a widespread feature of capitalist production. That is, the overwhelming proportion of
capitalist production is carried out by firms that own their own plant and equipment.
Nevertheless, neoclassicals like the term because it draws attention to the fact that the owner of
the physical capital could always sell the use of their capital, that is lend it, to other capitalists.
The minimum price the owner of physical capital would demand for lending her/his
physical capital would have to be, at a minimum, the depreciation charges that must be made to
maintain that physical capital in good repair, plus the interest forgone on the value of that capital.
That is,
= ( + ) 3.6
where d represents the rate of depreciation and i represents the opportunity cost capital, i.e. the
rate of return on safe long-term bonds, such as 10-year U.S. Treasury bonds.
But note that these charges are actually nothing more than the minimum needed to keep
the capital in good repair while providing its owner with a flow of income equal to the interest
foregone (or, in the case of a capitalist who took out a loan to purchase that physical capital, the
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interest charges on that loan). Rent, as normally thought of by economists – including
neoclassical economists, represents a flow of income that would exceed the minimal amount
needed to draw that resource into use. Since that’s not what’s happening here, the use of the term
“rental rate” is confusing. The only way in which we could think of this as a form of rental
income is if the flow of income were in excess of v. For this reason, I prefer to think of v as the
cost or price of capital per time period.
If we now divide equation 3.5 by the quantity of output, and remembering the definitions
for labor productivity and the capital-labor ratio, the firm’s average fixed cost can be represented
as
= ∙ 5 6 &’ 7 3.7
where k represents the capital-labor ratio and ap represents the productivity of labor.
We can now see that increasing a firm’s physical capacity, that is increasing its stock of
physical capital, can impact average fixed cost through the impact it has on the capital-labor
ratio, k, and/or the productivity of labor, ap. Note, furthermore, that an increase in a firm’s stock
of physical capital can impact the productivity of its labor force and this, in turn, will affect not
only average fixed cost (as seen in equation 3.7) but average variable cost as well (since ap is a
component of average variable cost as seen in equation 3.4).
Let’s now examine these possibilities. Productive capacity can be increased through the
installation of greater amounts of the same type of machinery or the installation of better, more
efficient, machinery. In the first case, the firm buys machinery embodying the same technology
as the machinery currently being used. This allows the firm to generate a larger volume of
output. Since the technology is the same, the efficiency of direct workers remains unaffected and
so too does the firm’s average variable cost (assuming other things equal). In terms of equation
3.7 this would mean that both the capital-labor ratio, k, remains unchanged and the productivity
of labor, ap, also remains unchanged (since the technology of production remains the same). In
the long run, both avc and afc would remain the same as the capital stock is increased. Since the
capital-labor ratio remains unchanged, then the labor needed to operate capital would grow at the
same rate as capital.
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Figure 3.5 illustrates the average cost and average variable cost of a firm that has
increased its productive capacity by purchasing greater amounts of the same type of machinery.
Notice that since the technology, work intensity, and input prices have remained unchanged, the
firm’s average variable cost remains constant regardless of the firm’s productive capacity. Notice
also that while the firm’s average cost is higher over the range of output compatible with the
smaller capacity, it ends up being the same over the larger ranges of output made possible by the
greater capacity. That is, when producing at capacity, unit cost is the same, regardless of whether
the firm has the capacity to produce 200 or 400 units per time period. This is an example of what
economists refer to as constant returns to scale – a situation in which the firm’s average costs,
when producing at capacity (or some constant fraction of capacity), remains the same as its
capacity is increased.
In the second case, the firm buys machinery embodying a more advanced, more
efficient, technology. This too will allow the firm to generate a larger volume of output. Unlike
the first case, however, the newer technology increases the efficiency, and thus productivity, of
direct workers, causing average variable cost to decrease. In this case, as in the previous one, the
firm’s overhead expenditures are increased. However, while fixed costs will now be greater, the
firm’s average variable costs, and thus average costs, will be smaller as a result of the more
efficient technology.
Figure 3.5
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Figure 3.6 provides a visual representation of this idea. It displays the average variable
cost and average cost of a firm with two different productive technologies. Notice that when the
firm introduces more efficient machinery both its average variable cost and average cost are
decreased. This is an example of what economists refer to as economies of scale or increasing
returns to scale, a situation in which the firm’s average cost (when measured at some constant
fraction of capacity) decrease as the firm’s productive capacity is increased. In terms of equation
3.7 this would mean that the productivity of labor, ap, is falling as a result of the increased
capital stock, causing both avc and afc to fall with the growth of the firm.
But, in addition, the improved technology embodied in the increased physical capital
usually means that the capital-labor ratio, k, will increase. Economists commonly assume that the
improvements in technology brought on by increases in the capital stock, i.e. investment, will be
reflected in rising capital-labor ratios. In terms of equation 3.7 this would mean that long run afc
could only decrease if the rising capital-labor ratio, k, is outweighed by the growth in labor
productivity, ap, brought about by the improved technology. However, it’s possible for the
capital-labor ratio to remain unchanged in response to improvements in technology. In this case,
the capital-labor ratio, k, would remain unchanged but the productivity of labor, ap, would still
increase. In either case however, the net effect of capital accumulation (a growing capital stock)
Figure 3.6
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would be to cause the productivity of labor to rise and the firm’s average cost of production to
fall.
The above two cases assumed that the firm was consciously increasing its productive
capacity, and as a result, consciously incurring a greater overhead expenditure so as to generate a
larger volume of output. However, it is quite possible for a firm to introduce new technologies
without intending to increase production levels or the overhead expenditures associated with the
existing capacity. This can happen through the normal process of capital maintenance and
replacement. As a firm goes to replace obsolete machinery it can find itself being able to
purchase more sophisticated versions of the same machine. These more efficient machines allow
the firm to produce the same volume of output at a lower average variable cost, and thus lower
average cost.
Of course, the introduction of more efficient machinery, in the absence of an increase in
production levels, can, but need not, lead to a reduction in the employment of direct workers.
Two kinds of efficiency are possible. First, some improvements in technology may simply affect
the usage of material inputs without affecting the efficiency of labor. That is, efficiency is
achieved through the usage of new machines requiring less material inputs per unit of output.
Under these circumstances, average variable cost is reduced without a reduction in the level of
direct labor employment. In the second case, the new technology improves the efficiency of
labor, thus reducing the hours of direct labor time needed in the production of any one level of
output. Clearly, and other things equal, this will eventually induce the firm to cut back on the
employment of direct labor. And, of course, it’s possible for new machines to induce efficiency
in the use of both materials and labor.
It should also be noted that the purchase of new machinery is often intended to introduce
efficiency in overhead activities. This kind of capital investment does not affect the productivity
of the direct labor force, the usage of direct material inputs, or the productive capacity of the
firm; instead, it either reduces the usage of overhead material inputs or the usage of overhead
labor. The new machine allows the firm to reduce its average fixed cost by reducing the usage of
overhead material inputs or overhead labor per unit of output. In either case, unit costs are
reduced through a reduction in average fixed costs and not through a reduction in average
variable cost. Obviously, this kind of capital investment can also be labor saving, that is generate
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unemployment. But in this case it would be the overhead labor force that would be affected, not
the direct labor force.
Beyond changes in productive capacity or technology, the firm can also affect its
overhead expenditures by changing the amount of overhead workers it employs. In general, the
number of overhead workers employed by the firm will vary as the productive capacity of the
firm changes. In the two cases introduced above, constant returns to scale and economies of
scale, it was assumed that the size of the overhead labor force, as well as the direct labor force
and direct material inputs, would grow in some constant proportion to the size of the firm’s
capacity. For example, if 2 overhead workers were needed when capacity was at 40, the firm
would need 4 overhead workers at a capacity of 80.
However, this need not always be the case. Take the example of a firm that is adding on a
new plant or factory. Even if the new plant employs the same technology as the existing plants,
so that productive capacity is increased without a change in technology, the firm may be able to
economize on many of the overhead functions associated with the new plant by consolidating
them with the overhead functions of the existing plants. In fact it is not unusual to find core
sector firms creating a central division that oversees the overhead activities common to all the
plants of the firm, thus cutting back on the need to have those same activities duplicated in every
plant. To the extent the firm can do this, it will be able to cut back on the number of overhead
laborers needed per plant. This will lower the firm’s average fixed costs, and thus average costs,
at the greater levels of capacity.
Yet, while economies can be achieved through the consolidation of some overhead
function, there are other pressures motivating growing firms to increase the size of their
overhead. As the firm’s productive capacity is increased the need to insure that the greater output
be sold is also increased. Marketing and sales become an increasingly more important function
as the firm’s capacity, or number of plants, is increased. After all, the capital investment must be
made to pay off, and one of the ways firms try to achieve this is by pushing the product, by
getting the public to believe that it is in their best interest to consume the good. Given this
motivation, it is not unusual to find firm’s increasing the size of their sales force and/or the
marketing budget as the firm’s capacity is increased. The purpose of these expenditures is to
increase the demand for the product and to increase the share of the market controlled by the
firm.
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A closely related form of overhead expenditure is associated with research and
development, or R & D. Core sector firms frequently allocate a portion of their total revenue to
the continued refinement of their existing product lines and/or to the creation of new products.
This activity is similar to the sales effort in that, in both cases, the objective is to increase the
firm’s market share. If the firm’s R & D expenditures result in the creation of a new commodity,
for which there are no close substitutes, the firm will have achieved a monopoly in the sale of
that commodity. And if, in addition, there is a great demand for the commodity, the firm will be
capable of bringing in a considerable flow of monopoly profits.
Another type of overhead expenditure that firms generally incur are those associated with
the legal and political representation of the firm. These involve such obvious things as litigation,
as well the expenses associated with the firm’s lobbying efforts and contributions to political
campaigns. They also include the expenses associated with, and the legal battles over,
government regulations as well as the expenses associated with the payment of taxes. Notice
that, like the sales effort and R & D, these expenditures are outward looking in the sense that
their primary purpose is to alter the environment within which the firm operates. The sales effort,
for example, is undertaken in the hope that it will increase the economic power of the firm by
increasing its market share, whereas the expense associated with the legal and political
representation of the firm is undertaken in the hope that it will create a legal and political context
that favors the firm.
Finally, management needs to insure that there be a steady flow of money to cover the
various expenditures. While sales revenue is the primary medium through which this is achieved,
firms also finance their activities by borrowing money and selling shares of stock. Additionally,
they purchase financial assets for the purpose of earning interest on any money that exceeds the
amount normally required to meet on-going expenditures. The cost associated with insuring that
the incoming flows of money exceed the outgoing flows, that obligations be paid, and that the
value of the firm’s liabilities not exceed its assets, are all a form of overhead expenditures.
Many of the expenditures outlined above are undertaken for the primary purpose of
defending or aggrandizing the firm as an institution. That is, rather than being directly associated
with the maintenance of the productive capacity of the firm, they are instead concerned with the
defense, or expansion, of the firm as a political economic institution. Given that the return from
such expenditures is much more difficult to measure, it is also much easier to overindulge in this
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type of cost without intending to. Of course, its easy to find examples of obvious extravagance,
such as highly ornate space-wasting company headquarters, lavish company sponsored
festivities, or the seldom-used company jet. But, beyond such obvious cases, it is possible for the
expenditures associated with the firm’s institutional structure to expand faster than its productive
base, even though that was not the intention. The firm may have unintentionally hired too many
managers, salespeople, public relations propagandists, lawyers, financiers, and economists.
Under these circumstances, unit overhead costs could very well end up outweighing the
reductions in unit direct cost made possible by improved productive efficiencies. This would, of
course, have the effect of causing unit costs to rise.
