1

Resolving Foundational Conflicts and Distributional Issues in the

‘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

Messiah College

Grantham, PA 17027

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Resolving Foundational Conflicts and Distributional Issues in the

‘Theory of the Firm’

By

Roger D. Johnson

Professor of Economics

Messiah College

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.

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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)

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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

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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.

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As Keppler and Lallement observe, it turns out that the U-shaped AVC curve emerged

as a component of an early 20th

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.

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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

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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

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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.

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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 2nd

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 = L2K

2/(aL

3 + bK

3) if L,K > 0

Q = 0 if L = 0, or K = 0

Where a, b > 0.(p. 469)

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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

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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

6 5

4

MPL/MPK

MPL/MPK

PL/PK

(K/L)*

K

K*

L

e

L*

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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.

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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

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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.

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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.

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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

8This 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

AVC

MC = AVC

P*

ERC BE

D MR

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 3rd

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:

The assumption of increasing and subsequently decreasing marginal productivity appears as an

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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