‘Theory of the Firm’
Abstract: A well-known inference of the Neo-classical model of the firm is that in the short-run
there is only one particular level of output where the factors of production are used efficiently,
i.e. compensated proportionally to their contribution, and that is at the break-even point. While
recognizing that inefficiencies will exist when market conditions cause the firm to deviate from
this point, the model also inadvertently produces latent theoretical inconsistencies describing the
behavior of the firm when it deviates from the break-even point. Bruce Larson, in a 1991 article
identified mathematical inconsistencies between the U shaped ATC and AVC curves employed
in introductory courses, and the standard ‘isoquant‘ analysis. Similarly, a 2001 article by X.
Henry Wang and Bill Z. Yang, pointed out another foundational issue in the way principles texts
distort the discussion by merging the concepts of fixed and sunk cost. Combining the insights of
Larson, with those of Wang and Yang reveals how these internal inconsistencies prescribe
efficiency criteria for the firm which induces consistent over payment of capital relative to its
marginal productivity, and thus underpayment of labor, as output fluctuates around the break-
even point. While the theoretical inconsistencies can be resolved, the solution reveals the fact
that profit maximization is not the sole viable criteria for operating an efficient firm: Other ends
such as sustainable employment are equally compatible with the theory. As a consequence,
economists must be prepared to engage in normative debates about the relative social merits of
competing ends that the firm might pursue, and the way in which these alternative goals are
fostered or hindered by other social institutions.
Roger D. Johnson
Professor of Economics
‘Theory of the Firm’
3
A well-known inference of the Neo-classical model of the firm is that in the short-run
there is only one particular level of output where the factors of production are used efficiently,
i.e. compensated proportionally to their contribution, and that is at the break-even point. While
recognizing that inefficiencies will exist when market conditions cause the firm to deviate from
this point, the model also inadvertently produces latent theoretical inconsistencies describing the
behavior of the firm when it deviates from the break-even point. Bruce Larson, in his 1991
article, “A Dilemma in the Theory of Short-Run Production and Costs”, identified mathematical
inconsistencies between the U shaped ATC and AVC curves employed in introductory courses,
and the standard ‘isoquant‘ analysis. Similarly, a 2001 article by X. Henry Wang and Bill Z.
Yang entitled, “Fixed Costs and Sunk Costs Revisited”, pointed out another foundational issue in
the way principles texts distort the discussion by merging the concepts of fixed and sunk cost.
Combining the insights of Larson, with those of Wang and Yang reveals how these internal
inconsistencies prescribe efficiency criteria for the firm that induce consistent overpayment of
capital relative to its marginal productivity, and thus underpayment of labor, as output fluctuates
around the break-even point. While the theoretical inconsistencies can be resolved, the solution
reveals the fact that profit maximization is not the sole viable criteria for operating an efficient
firm: Other ends such as sustainable employment are equally compatible with the theory. As a
consequence, economists must be prepared to engage in normative debates about the relative
social merits of competing ends that the firm might pursue, and the way in which these
alternative goals are fostered or hindered by other social institutions.
4
The nature of models dealing with human behavior is that they serve to both describe
and prescribe behavior, e.g. profit maximization as the goal of the firm (Whitin, 1960, pp. 550-
552). Given the dominant position of Neo-classical pedagogy, and the presence of foundational
errors noted by Larson, Wang and Yang, it would seem to be imperative to address these
concerns at the basic level rather than to construct an elaborate pedagogical edifice on a weak
foundation. This turns out to be a difficult proposition to sell. 1 David Colander, in his response
to Wang and Yang, accepts the validity of their observations, but argues that we can simply
reveal the error later on in the educational process. He takes the position that the appropriate
rubrics for deciding whether to confront and introduce these issues are KISS (Keep it simple
stupid), and CLAP (Change as little as possible) (Colander, 2004, pp. 360-364; Wang and
Yang(B), 2004). My intention is to essentially raise the stakes of the argument by combining the
independent observations of Larson with those of Wang and Yang to reveal latent distributional
biases in the existing framework that are too serious in nature to simply take refuge under
Colander’s criteria. Removing these inconsistencies does not require a complete rejection of the
existing edifice, nor an intensive theoretical reconstruction, but even after these changes have
been made, the distributive issues remain (Lee and Keen, 2004). The difference is that they now
become overt rather than latent. For Neo-classical economists, the downside of clarifying the
analysis and rhetoric is that it then requires them to both overtly recognize and justify the
normative dimension of their presuppositions concerning the nature and motivation of the firm.
1 Khaneman, Daniel. Thinking, Fast and Slow , 2011. Critics of the standard neo-classical methodology often find
themselves fighting an uphill battle to have their ideas taken seriously even when they offer significant and cogent
insights. Part of the difficulty they face is that they have to seemingly re-invent the wheel by designing an
alternative mathematical metaphor that is sufficiently ‘elegant’, i.e. intuitive. The problem is, of course, that the
prevailing metaphors are so well ingrained that they appear to be intuitive, whereas challenges force us to question
our intuition- think slowly - and thus appear ‘inelegant’ and convoluted.(pp. 44-47)
5
The foundational part of this discussion involves an attempt to untangle the rhetoric surrounding
the theory.
The Inconsistent Rhetoric of Cost Analysis
In setting forth the problem I start with the pedagogical approach recommended by
Colander, and the one that seems to be implicit in most principles texts, i.e. to treat all fixed costs
as if they are sunk costs. There seems to be a general agreement that the concept of ‘sunk’ costs
is an easily defined and useful analytic concept. This is not to infer a lack of controversy
surrounding the concept, however, as numerous empirical and ‘behavioral’ economic studies
suggest that individual decision makers may not respond to the presence of ‘sunk’ costs in the
simplistic ‘rational’ manner prescribed by theory, i.e. to ignore them (Baumol and Willig, 1981;
Bucheit and Feltovich, 2011; Roberto, 2009: McAfee, Mailon and Mailon, 2010, p323-325).
Putting these issues aside, the convention is to define sunk costs as costs that have been
irretrievably committed ( they are in the past), and cannot be recovered(undone). Un-
recoverability does not mean that the firm will be incapable of generating sufficient returns to
enable them to recoup this sunk cost: This after all is the agenda driving the discussion of the
short-run model of the profit maximizing firm. Identifying the presence of ‘sunk’ costs,
moreover, is in part a simple recognition of the real risk involved in beginning any business
venture. It is important to point out that the rhetoric used to describe these ‘costs’ does not
necessarily connect them to actual payments.
The presence of sunk cost is inferentially tied to the existence of a fixed factor of
production, the physical/technical characteristics of which generate the ‘law of variable
proportions’ and its corollary, ‘the law of diminishing returns to the variable factor’ i.e.
diminishing marginal productivity (MP). These ‘laws’ serve as the logical foundation for the
6
Neo-classical model of the firm, yet inexplicably the ‘law’ is modified by adding the assumption
that marginal productivity of the ‘variable’ factor initially rises as more units are employed, and
then at some undetermined point begins to obey the ‘law’ and falls. (Maxwell, 1969, p. 216;
Miller (B) 2001, pp.185). While anecdotal evidence, arguments by analogy and theoretical
explanations abound for the presence of diminishing MP, there is a paucity of similar support
offered for inserting the added assumption that the MP of the ‘variable’ factor initially increases
before it decreases. In their 2006 article, “The Origins of the U-Shaped Average Cost Curve”,
Jan H. Keppler and Jérôme Lallement, have provided us with a well-researched discussion of the
origins of this idea and an explanation of how it came to be a ubiquitous presence in modern
Neo-classical theory, despite the absence of connections to real world behavior ( Miller (A),
p.120).
The combined effect of initially increasing and then decreasing marginal productivity
with the presence of sunk costs is used to generate the familiar U-shaped average variable
cost(AVC), downward sloping average fixed costs curve(AFC), and U-shaped average total costs
curve(ATC) used to analyze the short-run ‘profit maximizing’ behavior of the firm. If AFC
merely represent sunk costs, then their presence in the discussion is that of an implicit cost that
involves no actual payment, and according to the standard logic ought to have no influence on
the short-run decision making process of the firm. The sometime careless conflating of the terms
‘cost’ and ‘payment’ is another one of those important rhetorical issues that plagues the analysis.
Given the implicit nature of the sunk costs, the ATC curve then merely reveals the ex post results
of the firm as it attempts to match market demand with its short- run MC constraints. Payments
to K appear then as residual payments. As we follow the logic of the model, however, we find
that this is not what the model actually assumes.
7
As Keppler and Lallement observe, it turns out that the U-shaped AVC curve emerged
as a component of an early 20 th
century argument that attempted to finish the Marshallian long-
vs. short-run analysis by blending comparative statics with long–run dynamics in order to
produce a model that would yield a long-run ‘efficient’ equilibrium in a perfectly competitive
model, i.e. P=MC=ATC (Keppler and Lallement, 738-9, 742, 764-766) Falling AVC, however,
is not a necessary condition for explaining the short-run decision making process of the profit
maximizing firm. Here we face one of the major conundrums of the Neo-classical
methodology: In order to begin discussing the ‘real’ world it must first construct a minimalist
model of the ‘ideal’ world.
All economic model building, whether it is Neo-classical or heterodox, intrinsically
struggles with this since some form of equilibrium condition must be presumed in order to make
the model deterministic. The Neo-classical approach, however, seems to go beyond this to
require conditions sufficient to both allow for the existence of perfectly competitive markets and
also produce perfectly efficient long-run, general equilibrium outcomes (Whitin, pp. 549, 551).
A common criticism is that too often Neo- classical economists insert such agendas into the
analysis surreptitiously rather than explicitly stating the agenda (Miller(A), p. 127). If we
assume that the agenda for constructing the model is not to create a theoretical proof for the
existence and/or viability of ‘perfect’ competition, the “KISS’ principle and the more venerable
‘Occam’s Razor, would then seem to lead us to adopt the minimalist assumption of strictly
diminishing MP. Problems arise, however, when we assert that the actual and necessary goal of
the firm is to profit maximize, and we begin to connect this goal with the apparent short-run and
long-run ‘need’ to recover sunk costs.
8
As Wang and Yang point out, and as Colander concedes, the standard Neo-classical
rhetoric and logic concerning the short-run behavior of the firm essentially merges the term
‘sunk’ costs with ‘fixed’ costs. It does so, moreover, without noting the fact, or recognizing the
importance of the distinction in explaining the decision making of the firm. Wang and Yang, in
an effort to bring coherence to the Neo-classical argument, attempt to delineate the difference
between fixed and sunk cost as follows.
A fixed cost ( c ) is a cost associated with a fixed input: when in use, its use does not vary
with the output level (y) produced, that is c(y) = k ( a constant) for all y>0.( Wang and
Yang(B), p. 366)
Like sunk costs, a fixed cost does not change with the level of output, but unlike sunk
costs they do not exist when output is zero. Wang and Yang, moreover, seem to further
differentiate ‘fixed’ cost in that there is an actual payment made to these resources ‘when they
are in use’, and in that senses they share a characteristic of variable costs. To differentiate these
costs from both sunk and variable costs, Wang and Yang choose to adopt the label ‘avoidable
fixed cost’((B), pp.366, 367 ) An illustration of such ‘avoidable fixed costs’ would be a
salaried sales force. Even this, however, does not adequately address all the rhetorical and
behavioral issues involved in defining the cost curves of the firm.
It makes considerable difference, for example, whether the term ‘sunk costs’ refers
strictly to past expenditures, or to contractual obligations to make payments to cover the sunk
costs, even if y =0. To help clarify the discussion, I will refer to the latter as ‘sunk fixed costs’:
This is the concept that Colander seems to accept as being the norm for current pedagogy,
although he doesn’t supply this specific label. The difference between these concepts does play
an important role in explaining the behavior of the firm. Historical ‘sunk costs’ constitute
purely short-run implicit costs which, according to basic level analysis, can and should be
9
ignored in the short-run; They only have relevance to the forward, long-run decision making of
the firm as it makes the initial choice to purchase certain assets. There is an extensive discussion
regarding the role of such costs in acting as barriers to entry, but that is an issue separate from
the purpose of this paper and more directly related to long-run behavioral issues (Arvan, 1986;
Cabral and Ross, 2008; MacAfee, Mailon and Mailion, 2010). If on the other hand, they
constitute ‘sunk fixed costs’, then they have some impact on the short-run decision making of the
firm.
If we were to accept strictly diminishing MP as a legitimate starting pre-supposition, the
marginal cost curve(MC) of the firm would begin at the origin: Rational businesses, who ignore
sunk costs, will find the competitive market pressure could drive output and price for each
individual firm down to zero before it shuts down. If the firm also has ‘sunk fixed costs’,
however, it will be forced in the short-run to cover not only its MC but also the payment of its
‘sunk fixed costs’ in order to avoid shutting down. The financing of capital acquisition by the
issuance of stock seems to correspond most closely to the concept of ‘sunk’ cost, whereas the
financing of capital acquisition through bond financing fits the idea of ‘sunk fixed costs.’
Similarly, the short-run decisions of the firm will be different if the firm looks at the cost of its
capital in a forward looking sense, i.e. its replacement cost. If the physical depreciation of
capital, for example, is a function of its rate of usage rather than merely passage of time, one
might treat the cost of capital as a variable, rather than either a fixed or a sunk cost. What is
significant in the above discussion, and what is omitted in the normal introduction to the theory,
is the rationale behind how and why the firm chooses to structure its costs in any given manner.
Perhaps this is merely the result of the effort to simplify, but the question remains as to
why ‘sunk fixed costs’ has become the default option. This specific interpretation appears to
10
have evolved along with the emergence of the iso-quant analysis. The Neo-classical approach
implicitly treats the question of the cost structure as if it is determined by the physical/technical
characteristics of the inputs rather than as a choice. This becomes a key point in the following
analysis regarding the distributional issues which are latent in the Neo-classical model of the
firm, and also a seeming lightning rod for criticisms of the Neo-classical paradigm.
The Physical Laws of Production and Cost
One standard critique of the Neo-classical production theory involves the perceived lack
of realism regarding the presumed ability to measure the separate marginal productivities of the
various factors of production. For Neo-classical economists the possibility of such calculations
may be partly founded upon confidence in the ability of the evolving fields of accounting and
production management to generate such information (Flesichman and Tyson, 1993). A
common line of defense for this approach is that the math is merely a form of analogy: e.g. the
billiard player who acts ’as if’ she/he actually did the geometry and physics. The measurability
critique, however, is simply one more potential loose end in the Neo-classical argument and
following it will distract rather than add to the insights offered in this paper. For that reason
alone, we will grant the measurability assumption as merely an ‘as if’ simplifying assumption.
Here we turn our attention to the Neo-classical use of production functions and iso-quants to
analyze the assumptions necessary to make this analysis of the physical use of resources conform
to cost curve analysis. This turns out to be a somewhat intractable problem, and one which
bring the distribution issues to the forefront.
In his 1991 article, Larson shows that the isoquant approach to explaining the cost curves
of the firm, while not mathematically inconsistent with increasing MP, fails to automatically
produce the increasing MP and unique shut-down point inferred in the basic model of the firm.
11
The conventional approach, for example, is to employ a generalized linear homogeneous
production function of degree one, with the Cobb- Douglas and CES type functions being two of
the most common forms (Miller (B), pp.184). The ‘degree one’ assumption is essential in order
to eliminate the possibility of economies of scale, which would then obviate the possibility of
‘perfect’ competition. Granting the assumption, however, does not guarantee the presence of
‘perfect competition’, but can be treated as merely a simplifying assumption employed in order
to avoid complicating the analysis of MP which would occur with the presence of either
economies or dis-economies of scale.(Ramenofsky and Shepherd, 2001). Linear homogeneity,
similarly, can be granted as a simplification introduced to allow us to think in terms of specific
and unique types of embodied production techniques, broadly specified in terms of the ratio of
capital to labor (Miller (A), pp. 123-5). They are generalized models in the sense that there is
some room for variation even with a given production technique: The use of the rhetoric of
marginal rate of technical substitution (MRTS) in place of relative marginal productivities
(MPL/MPK) to describe the choice of production techniques captures the intended spirit of the
theory, but the tie to the ‘doctrine’ of compensation based upon marginal productivity obviously
remains intact . For these standard models the 2 nd
partial of any factor of production is
continuously negative rather than initially positive and then becoming negative. Larson goes on
to provide an illustration of one type of production function that could in fact generate increasing
and then decreasing MP.
This so- called Sato production function takes the following form:
Q = L 2 K
Where a, b > 0.(p. 469)
12
Other than the fact that it matches up with the standard presumed pattern of increasing and then
decreasing MP, however, there is no rationale supplied as to why one ought to adopt this more
restrictive type of production function. In the process of this discussion, moreover, Larson
independently anticipates the observations of Wang and Yang as he reveals some additional
insights into how the standard model shifts its rhetoric and terminology in order to explain the
internal decision making of the firm in regards to the efficient physical use of resources.
The standard isoquant model takes as its starting point the long-run choice framework
where the firm is free to choose the optimal combination of resources based purely on their
relative prices and physical productivities. These optimal points, identified by the expansion
path in the Figure 1, serve as a simplifying metaphor to illustrate the way in which firms choose
a particular production technique. The choice of a particular technique depends upon the present
and anticipated relative prices of the inputs, while the amount of K purchased is determined by
the initial start-up budget constraint of the firm (Miller (B), p. 195). The anticipated level of
demand is irrelevant as we have a priori assumed away the presence of economies or dis-
economies which would affect the choice of scale of production.
The slope of the iso-cost lines is the ratio of the price of L to the price of K- (PL/PK),
which at the point of tangency with an iso-quant(MRTS), also corresponds to ratio of the
marginal products (MPL/MPK). In a simple two input model, one of the inputs is then identified
as the ‘fixed’ input, the quantity of which determines the capacity and marginal productivity of
the remaining variable factor. If we merely identified the inputs as inputs X and Y there would
be no particular reason to choose one or the other as the ‘fixed’ input, but in keeping with
tradition it is capital (K) which is treated as the fixed or limiting factor, and labor (L) is defined
as the variable factor. If we think of payments for K as strictly a sunk cost, then PK might be
13
interpreted as the implicit payments needed to meet the amortized value of the existing stock of
capital, and the question is then what is the basis for deciding the life of the capital investment.
Alternatively, one could conceive of it in terms of payments to cover the replacement of the
existing stock of capital as it is used up over time, and thus more like a ‘sunk fixed cost’
(Trowell 1981, pp. 8, 9). 2 When the firm is operating at point ‘a’ the cost attributed to each
factor is proportional to its relative marginal productivity, and it is this point that corresponds to
the breakeven point in the standard cost curve analysis. The question then is how to interpret
the response of the firm when it is led by market forces to deviate from this point.
Figure 1
2 Assuming depreciation is a function of time rather than usage implies that depreciation continues even if output is
zero. Depreciation nevertheless appears as an implicit cost rather than an actual payment.
a*
b
c
d
4
MPL/MPK
MPL/MPK
PL/PK
(K/L)*
K
K*
L
e
L*
14
One common approach is to describe movements to the left or right of point ‘a’, in terms
of movements along the horizontal line defined by the fixed amount of K*, so that the firm is
forced to use the inputs in a less than efficient ratio: The obvious implication is that neither
factor is paid or used proportionately to its relative productivity.(Sexton, Grove and Lee, 1993,
pp. 35,36) 3 To the right of ‘a’ the limiting effect of K comes to bear, as the firm would prefer
to move to point ‘b’ in order to expand output to isoquant 6 , but is constrained to move to point
‘c’. At ‘c’ the slope of the iso-quant, is less than the slope of iso-cost line tangent to that curve,
indicating that, given the existing rates of compensation(PL/PK) the labor input would be
relatively overpaid, while capital is underpaid. What is of course missing from the graph is
some type of revenue curve to indicate the size of the revenue to be distributed (Mishan, pp.
1273-1275). We know, however, based upon our prior discussion of the Neo-classical costs
curves, that points to the right of ‘a’, also represents points above the breakeven level of output
where the firm is earning ‘pure’ profits, i.e. profits above the rate implied by Pk. Presumably
these ‘pure’ profits/rents would then more than effectively compensate owners of K, thus raising
the actual compensation above the level indicated by PK. 4 One would then expect a symmetrical
treatment of the factors to the left of ‘a’, but this turns out to not be the case.
To the left of ‘a’, the standard iso-quant analysis effectively treats K as a ‘sunk fixed
cost’, in that the firm cannot reduce the cost and payments of using that input. Colander, as
noted at the beginning of the paper accepts this as the norm. As a result, the firm’s least cost
choice in allocating resources is to move along the horizontal line given by K*. In terms of
3 Larson illustrates the possibility of moving past the ridge line(e) as we move to the left so that MPL becomes
negative. By implication, once in the region where MPL,is negative, movement to the right along K* results in
increasing MPL(pp. 467-470). 4 Since PL/PK is greater than MPL/MPK the surplus profits must be large enough to overcome the excess rate of
payment to labor.
15
allocative efficiency, it means that to the left of ‘a’ the slope of the isoquant(MPL/MPK) is
steeper than the slope of the iso-cost line (PL/PK) at all the points along the horizontal lines, so
that L is now underpaid relative to K. The distributional inequity is amplified by the fact that
payments to K are a ‘sunk fixed cost’ so that the entire burden of falling revenue effectively falls
upon labor cost. Movement along the horizontal line-K*implies, moreover, that all the units of
K are being fully utilized. This seems to contradict our intuition, and empirical evidence which
shows that firms faced with falling demand operate with idle plant capacity (Miller (A), p.120).
Within the logical and rhetorical constructs of the Neo-classical model ‘labor cost minimization
is nevertheless consistent with what one would expect from a firm whose explicit goal has been
framed in terms of maximizing returns to the owners of capital. At the risk of using rather
inflammatory terminology, we can call this the ’profit maximizing/worker exploiting’ model of
the firm.
In order to rationalize this type of movement along the horizontal K* line, we have had
to implicitly abandon the idea that the firm, having chosen ‘a’ as the starting point, has to rigidly
limit itself to a production technique that it must work with. The fact that it chose ‘a’ is
relevant only in the fact that it limits the amount of K available, but it can nevertheless
effectively choose to deviate from the existing optimal production technique. Richard Miller
attempts to clarify this by noting the crucial distinction between the capital stock and the flow of
services from that stock. From a cost perspective , however, once the payment to capital is
defined as a ‘sunk fixed cost’ it is not the flow of services of the capital stock that is at issue, but
rather payments (Miller (A), pp. 120-122;(B) pp. 185-187). In this ‘profit maximizing/labor
exploiting’ model the relative prices of L and K become irrelevant to the firm, as optimization is
defined purely in terms of minimizing the labor payments for any given level of output. The
16
problem reduces itself to a Leontief type of production function decision (Miller (A) p. 123-125).
Here we come across one of those unexpectedly provocative, insights of the Neo-classical
model. Firms guided by the principles of maximizing returns/payments to owners of capital
will be led to cut their labor force to the absolute minimum, and compel workers to maintain
levels of productivity(flow of services) which are unsustainable, i.e. not consistent with the
optimal production technique currently in place. 5 Moreover, these decision makers would also
tend to over invest in physical capital if they anticipate that market demand will enable them to
sustain these high and seemingly ‘fixed’ returns/payments to capital. This narrative, however, is
out of sync with the cost curve analysis discussed earlier.
According to the cost curve analysis, when the firm is operating below the breakeven
point, i.e. to the left of ‘a’, the firm meets the requisite payments to the units of the variable
factor(L) being used, but is not generating sufficient revenue to cover its fixed costs: I.e., it is
not paying, nor is capable of paying the price indicated by PK. Larson effectively anticipates
the arguments of Wang and Yang, noting that if we are to make the iso–quant analysis fit the
Neo-classical cost curve analysis we need to modify out treatment of the cost of K so that it is
not a sunk cost, or ‘sunk fixed cost, but rather something like the ‘variable fixed costs’ described
later by Wang and Yang. The implication of this shift in terminology and logic is that the
efficient firm can and should both effectively lay-off /not use every unit of K that is available,
and not fully compensate the entire existing stock of K.(Larson, pp. 467-469 : Miller(B), pp. 185.
186)
Instead of operating at point ‘d’, the firm moves along the same iso-quant to the
expansion path(K/L)*, and as a result appears to operates at a lower cost level. This creates a
5 The inherent real world danger in such a short-run strategy is that once general labor market conditions improve,
workers will seek employment elsewhere, with typically the best workers being the most successful emigrants.
17
problem, however, in that we no longer have a clear basis for determining the payment to capital.
One possibility is to change rationales and argue that because the ‘efficient’ payment is
proportional to the amount of capital being used, we can treat it ‘as if’ it represents ‘real’
physical depreciation based upon the intensity of use of a given capital stock. It would exist
then as a sort of implicit variable cost.(Trowell, pp. 9, 10) 6 Once we abandon the assumption
that all units of K are fully utilized and compensated as a ‘sunk fixed costs’, we will be forced,
as Larson notes, to adjust our analysis of the cost structure of the firm. The firm could then
operate on a lower iso-cost line than if it attempted to maximize profits/minimize labor costs, but
it does so only by consciously not attempting to recover the full amortized cost of all the units of
K initially purchased. 7 What then emerges is a far different model of the cost structure of the
firm than the simple ‘sunk fixed cost’ of capital and variable cost of labor model.
As Richard Miller observes, the firm is free to choose any point on a given isoquant that
lies between the ‘ridge line’. The determination of which point constitute the least cost solution
will depend upon how the firm perceives/chooses to treat the implicit and explicit cost associated
with each factor. (Maxwell, pp.217, 218; Miller(B)). If, for example, it focuses upon operating
in a technically efficiently manner by on the expansion path, it can choose to treat any of the
factors as a sunk, fixed, variable fixed, or variable cost. Some of these decisions might have
been made when point ‘a’ was chose, but there is no reason to assume that these prior choices
cannot be altered. The firm might, for example, choose initially to rent capital rather than
purchase it and thus avoid incurring a sunk cost, and then later choose to purchase the
equipment. It might treat labor as a variable fixed cost and compensate it on a salary basis.
6 One could reduce payments to capital even further and attempt to maintain full employment of the existing stock of
labor along the vertical L* line. Just as labor is underpaid and used too intensively along the K* line, capital would
be used too intensively and not compensated sufficiently to replace K that is being used up. 7 The inherent problem with all such models of production is the assumption concerning the ability of decision
makers to measure marginal productivities, quantities of inputs or real rate of depreciation.
18
What efficiency simply requires is that firms generate and allocate sufficient revenue to hire and
replace the services of factors of production as they are used. We can call this the ‘profit
satisficing’ model, or a ‘labor satisficing’ without distorting the implications. An example of
this type of behavior or analysis would be the way in which the Mondragon Cooperatives
contractually determine the compensation of capital and labor (Mikami and Tanaka, 2010;
Miyazaki and Neary, 1983, pp. 260, 270). 8 This is significant in that it suggests that the ‘profit
maximizing/labor exploiting’ model generated when we treat capital as a ‘sunk fixed cost’ is not
a necessary interpretation of the optimization goal of the firm. It also frees the model of the
artificial confines of the U-shaped AVC curve.
Abandoning the U- Shaped AVC Curve
Sticking with a simplified linear homogenous production function of degree one, a
‘profit satisficing’ firm with labor treated as a variable cost would move along an expansion path
in the region below ‘a’, and as a result MPL remains constant. This in turn means that the MC
curve is horizontal up to point ‘a’, and MC equals AVC within this region. To the right of ‘a’
inefficiencies arise due to the inability of labor inputs to fully overcome the limitations imposed
by the fixed stock of K. The existing stock of K will essentially be pushed to operate in a
manner that is not sustainable in the long-run. 9 As Larson notes, we end up with the typical J-
shaped-Engineering Rated Capacity (ERC) type of cost curves for the firm where ‘a’ in Figure 1.
coincides with the ERC(pp.471-473; Miller(B), pp. 188-190; Maxwell, pp. 221-223). ERC cost
curves don’t seem to be intrinsically in conflict with standard, observable business behaviors, but
they do pose some particular problems for the Neo-classical agenda. Although the ERC model is
8 This is in contrast with the earlier Illyrean model of worker owned firms which cast the model in terms of ’wage’
maximization. That model parallels the discussion in this paper regarding inconsistencies that occur in the neo-
classical ‘profit’ maximizing model, and concluded that maximizing wages’ is an untenable strategy. 9 More L is being used, but not necessarily with greater intensity. One could infer to the contrary that L is used
with less intensity as MPL falls relative to MPK.
19
not inconsistent with the existence of ‘perfect competition’, it does not yield the desirable long-
run efficiency conditions which are attributed to ‘perfect competition’.
If we assume perfect competition in the product market so that each firm faces a
horizontal demand at the market equilibrium price, it is not possible for the firm to equate MC
with price at unique level of output below the ERC when P= MC= AVC. Arbitrarily assuming
some minimal disutility associated with managing the firm would, however, allow us to define
the ERC point as the shut-down point for the firm. For any P > greater than this shut-down
price, however, the typical firm will operate above the ERC, and thus combine resources in an
inefficient manner, i.e. the firm could move to a lower iso-cost line if it had a larger stock of K .
Thus even firms driven by competitive forces to operate at the minimum point on the ATC
curves would continuously operate with a sense of having insufficient capacity. 10
Perfect
competition could exist in a scenario where firms are characterized by ERC types of cost curves,
but they simply would never achieve the type of long-run equilibrium efficiency touted by the
standard model. As Miller notes, the ERC model has an advantage over the traditional perfectly
competitive-profit maximizing model in that it is consistent with the mounting empirical
evidence suggesting that MC and AVC are constant up to some capacity limit. (Miller (A), 121-
3) The implication of this is that real world firms operating in less than perfect competition, will
typically and comfortably operate at less than the ‘ideal’ full capacity.
This does not seem entirely illogical in markets characterized by random variations in
demand and less than perfect competition. Unlike the standard cost curve analysis, however, the
ERC approach suggests that there is no innate, long-run tendency for the firm to operate at the
10
The ERC model also seems to be more amenable to describing choices regarding the level of output. Since MP =
AP, the firm can normally rely upon a much more accessible piece of information- AP. MP only becomes relevant
when operating above the firm’s ERC. This doesn’t, however, cause us to abnegate the usefulness of marginal
analysis in analyzing the relative internal allocation or resources where the marginal costs can be approximated.
20
lowest point on its ATC. We are thus forced to accept the reality of a less than perfectly efficient
outcome of ‘perfect’ competition defined by operating at the minimum possible ATC. Unless
we are fixated upon modeling or justifying ‘perfect’ competition this incompatibility seems to be
a moot point. We would perhaps have to accept a more pragmatic, stochastic approach wherein
market dynamics merely suggest that even in the long-run there will always be a random mix of
outcomes for individual firms, some of which earn pure profits and some that are operating at a
loss.
Using the graph in Figure 2, a firm operating under conditions of less than perfect
competition will operate where its MR curve intersects its MC curve. Unlike the traditional U-
shaped cost model which identifies the ‘shut-down’ and ‘break-even’ point in terms of some
minimal level of output, the existence of profits or losses will not depend strictly upon the level
of output but rather upon the slope of the demand curve.
Figure 2
MC ATC
21
There doesn’t seem to be any obvious explanation as to why normal market dynamics will
necessarily drive demand and market prices to a unique break-even price level for each
individual firm. In Figure 2, for example, with the given demand (D) and corresponding MR
curve the firm will price its product a P* and earn pure profits. The persistence of pure profits
in the ‘long-run’ is both possible in this less than perfect world, and consistent with what we
normally think of as a successful business venture. On the other hand, the model does not
guarantee profits. Both possibilities pose a problem, however, as the Neo-classical model lacks
‘a’ mechanism for determining how these quasi-rents. i.e. ‘profits’ or ‘losses’, will be
distributed.
In the discussion leading up to this point I have noted the inconsistencies in the existing
Neo-classical framework regarding treatment of returns to capital. The standard Neo-classical
operative assumption is that capital is a ‘sunk fixed cost’, i.e. always paid at or above the rate
needed to compensate it appropriately and always fully utilized. Even if the U shaped ATC
curve is arbitrarily inserted into this framework, the continuous overpayment of capital means
that the Neo-classical agenda of explaining the transition from the short-run to long-run
efficiency in resource allocation collapses. Adopting the ERC approach allows us to retain the
insights of the Neo-classical production function analysis regarding the technically efficient use
of resources, but resolves the short-run resource allocation question by treating capital as a
‘variable fixed cost’, and recognizing that capital does not have to be fully utilized. This still
leaves the question unanswered, however, as to the distribution of potential profits and losses
since payments to both labor and capital can be adjusted. One possible venue for dealing with
the issues is to arbitrarily introduce a 3 rd
factor of production - the risk taking entrepreneur or
manager - into the model in order to absorb the quasi-rents from the shifting surpluses and
22
losses. This is a little like introducing the errors and omissions entry into the Balance of
Payments Accounts, in that it merely admits the error rather than explaining it. Moreover, in
terms of foundational principles, there seems to be little gain from this addition. In reviewing
the prior discussion, it appears that much of the debate in fact arises because writers are offering
their own unique interpretation of the possible nature of the real world costs and contracts which
fully caricaturize the firm (Mishan 1968, p. 1279). It may be that the Neo-classical mathematical
metaphors regarding production functions are inadequate tools for either grounding the
discussion regarding the theory of the firm or for carrying it forward. What is significant to note
about the prior discussion in this paper, therefore, is the subtle and recurring references to the
critical role that the type of ‘contract’ plays in determining relative factor compensation. Mishan
and Maxwell, among other major writers have noted the central role of contracts, yet it is totally
absent in the principles texts (Mishan, p. 1279; Maxwell, p. 211). It turns out that questions
regarding how these contracts emerge and function is part of the very foundation of Classical
economics, but one which lost its salient position with the emerging Neo-classical preoccupation
with spontaneous market exchanges.
The Central Role of Contract Theory
Adam Smith, in his pseudo – historical analysis of the development of market systems,
observes that in the early stages of economic development the distinction between wages and
profits was largely irrelevant as the same individual who supplied the labor also owned the
capital. The distributive problem arises once a separation occurs between the suppliers of labor
and owners of capital (WN, I.viii.2-5). 11
He describe the problem as one of establishing a
‘contractual’ relationship between these two groups of participants, thus clearly seeing this as an
11
WN is used to reference An Inquiry Into the Nature and Causes of the Wealth of Nations. The notation indicates
respectively , book, chapter, section and paragraph.
23
activity that is different in character than the spontaneous exchange of goods in the market. He
further notes that the appropriate basis for and nature of these contracts hinges much more upon
growing interdependencies that exist between the parties than upon simple market efficiency
criteria. The term ‘interdependencies, is obviously out of place in a methodology which focuses
upon individual, autonomous rational choices (Posner, 2005, p. 1582). Smith, in what would
have been a rather radical view for his time, seems to have come down on the side of workers in
this debate.
He clearly articulates the point that labor is, in principle, much more dependent upon the
continuation of employment than the owner of the firm is dependent upon the continued
employment of his stock of capital, and therefore at a disadvantage in determining the conditions
of the employment contract. He bases this in part on the idea that the ‘sunk’ costs of the owners
of capital can at least be partially recovered by liquidating the capital stock. Owners of labor, in
contrast, were observed to typically lack such surplus value /wealth to fall back upon.
Secondly, he notes that labor above all other factors is the least mobile (WN, I.viii.11-15,31,
I.x.c.27-37, 43-45, I.xi.9; LJ(B) 264) 12
. The observed result of this is that the owners of capital
will normally have an advantage in negotiating contracts to determine the relative distribution of
the income stream (Dow, 1993). Thirdly, he notes that property rights, contrary to the view of
Locke, are not a natural right in the same sense as the right to control one’s person. Instead they
are ‘derivative’ rights that require the acceptance of society.(LJ(B) 9-11, 154, 175, 176)
Moreover, these property rights must evolve over time in order to take into account the growing
interdependencies that exist in an increasingly market based society.
12
LJ(B) is used to reference Smith’s second set of lectures delivered in 1763-64, and found in Lectures on
Jurisprudence. The notation refers to paragraph number.
24
The problem he notes, is that from a socio- political perspective, the growth of market
based societies lead individuals to have a greater sense of personal autonomy and independence,
while in reality they are increasingly more dependent upon others.(Johnson 1990, 253-57;
LJ(B), 149-150) . John S. Mill continues these theme, noting that while physical production may
be constrained by the laws of physics, the distribution of that output is determined by the laws
and institutions chosen by society (Mill, 2, II.1.1-3) 13
. Writing in a time period in which the
Neo-classical methodology seems to have clearly won the day, John M. Clark attempts to revive
these Classical foundations with his advocacy of institutional rules which treat labor rather than
capital as the ‘social over-head cost’ (Clark 1923, pp. 361-370, 377-383, 485; 1978 rprt.,pp.
206,207). Fortunately these threads of thoughts have not been entirely lost. Here we can turn to
another more recent intellectual branch of the Neo-classical tradition, i.e. Ronald Coase’s
transaction costs analysis, and its application to business structures analysis by O.E.
Williamson(Coase, 1937, p. 400; Williamson,1979, 1985). A closely related alternative is the
bargaining approach advocated by Gregory Dow (Dow, 1993).
Coase and Williamson present us with a cogent explanation which draws upon the
presence of transaction costs and the specificity of resources. How the transaction costs and
specificity of resources are defined will of course depend upon the perspective of the decision
maker. Coase’s foundational argument notes the impact of transaction costs on both the
suppliers of capital and of labor inputs. Williamson describes optimal choice making from the
perspective of the owners of capital and their management agents to offer an explanation as to
why the profit maximizing ‘firm’ is an optimal structure for meeting their goals (Williamson
1985, p. 242, n. 5). Dow characterizes these approaches as emphasizing “the economization of
total production and transaction cost” at the, “social rather than individual level.” His
13
Notation refers to volume, book, chapter and paragraph from Mill’s Principles of Political Economy.
25
‘bargaining’ theory approach, in contrast, maintains a closer tie to the Neo-classical focus on
spontaneous exchange by emphasizing the impact of individual rationality and strategic behavior
(Dow, 1993, p. 120). Michael Jensen and William Meckling take an even different approach to
argue that a better approach is to explicitly define the production function in terms of the
structure of property and contracting rights within which the firm exists.( Jensen and Meckling,
1979). What become obvious from surveying the literature of this genre is that there exist a
multiplicity of possible models of ‘efficient’ firms based upon varying forms of contractual
agreements between the owners of labor and capital.
One might assume that the collective weight of these arguments would be sufficient to
convince Neo-classical economists that the profit maximizing model is not the only efficient
form of organization for the business firm. Furthermore, recognizing the significance of these
insights does not require abandonment of the Neo-classical production function models, but
merely clarification of the rhetoric and terms employed. It seems however, that pedagogical
convenience(CLAP) combined with intellectual inertia rule the day, and the principles texts
continue to prescribe ‘the’ profit maximizing model of the firm as the ideal. Drawing an analogy
from engineering, it is as if engineers trained in the 1960’s persisted in designing motors which
maximized horsepower, without noting that in the context of today’s gas prices an alternative
design should have been developed which use miles per gallon as the measure of efficiency. To
both the non-engineer and engineer, it is obvious that the appropriate definition of efficiency will
depend upon the defined end or goal of the process. Neo-classically trained economists,
however, appear to be engineers who both lack and consciously avoid a social, historical and
political context for their analysis.
26
Conclusions:
artifice for constructing a long-run perfectly competitive market, but is otherwise superfluous.
Maintaining the conventional approach of treating capital cost as ‘sunk fixed costs’, however,
leads to a set of egregious errors. It implies that capital inputs are, and must be both fully
utilized, and fully compensated even when demand falls below the level needed for the firm to
break-even. The full utilization of capital certainly conflicts with real world behavior of firms,
while full compensation contradicts the proposition that capital, as a residual claimant, is
underpaid in this loss minimizing range of output. What is not noted, however, is that the logic
of the ‘sunk fixed cost‘ approach to profit maximization implies that labor will be used in an
unsustainable manner and under compensated when the firm operates below the break-even
level of output. When the same analytical approach is applied to evaluating the impact of wage
maximizing strategies, however, the primary criticism is that, capital will be used in an
unsustainable manner and under compensated when the firm operates below the break-even
level of output. Abandoning the use of the ‘sunk fixed costs’ rubric to describe the treatment of
capital inputs restores internal consistency to the Neo-classical model, placing greater emphasis
upon the technical choices firms face. 14
Once this venue is pursued another problem arises, as
it becomes obvious that other goals/ends, such as creating sustainable employment, are equally
compatible with the principles of technical efficiency. It would appear, however, that there is
something about the Neo-classical choice of rhetoric and methodology that make its practitioners
incapable of recognizing or engaging in a conversation about the presumed ends of the process
14
The ability of the Neo-classical paradigm to maintain a fixation upon profit maximization is analogous to the
power of the magician’s trick of misdirection. By constantly switching between various equally credible definitions
of cost and forms of compensation to capital, we are never able to focus on the central question of the nature of the
contract which determines labor’s relative share of the income generated by the firm.
27
and the contractual nature of these relationships, other than as a tool for meeting efficiency
criteria (Posner, 1987, pp. 5, 6).
Here we enter the realm of value based analysis where economists must be prepared to
comprehend the ‘social’ merits of alternative compensation plans that firms might choose or that
the legal system might validate ( Demsetz(A), Demsetz(B; Jensen & Meckling, pp. 469-471;
Offe, 2008, pp. 4-6). If they can make this philosophical/methodological jump, Neo-classical
economist can offer significant insights into the constraints and trade-offs that societies face in
obtaining these goals. Robert Heilbroner and other prominent economists have persistently
noted that these issues of value and distribution are foundational, yet these are the very issues
which economists, by virtue of their positivist training and methodology, are unfortunately least
trained to evaluate or even discuss (Heilbroner 1983, p. 253). It is perhaps no accident that
these foundational issues never surfaces in our principles texts.
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