A Pure Neoclassical Theory of the Firm XIV: Critique VIII (Microeconomics)

The Absent Entrepreneur

Proceeding from an understanding of the Walrasian/Paretian firm as a competitive/cooperative endeavor, assembling factors of production owned by diverse households in an effort to expand on the meager returns of subsistence/autarkic production, our approach to the firm has consistently been advanced under the shadow of a relentlessly conspicuous absence.  Emphatically, where is the entrepreneur in our story?  I have endeavored to argue that a true Austrian Neoclassical account of capitalism necessarily makes space to recognize that, if risky, uncertain ventures in productive roundaboutness/investment of capital are to take place, there must be some agent willing to shoulder the risk with the prospect that a sudden change in market conditions might render a capital investment wholly worthless.  I will subsequently present the more characteristically Marshallian articulation of entrepreneurial returns to uncertainty advanced by, among others, American economist Frank Knight.  Finally, in the Classical tradition, a substantial legacy of respect for the risk-taking behavior of the entrepreneur exists in Adam Smith's Wealth of Nations, in David Ricardo's Principles of Political Economy and Taxation, in J.S. Mill's writings on political economy, and, even, in Karl Marx's Capital.  And yet, I have here asserted that the entrepreneur falls entirely out of Walrasian/Paretian theorizations of the firm.  In this regard, I am committing this short section to defend my thesis and argue that, notwithstanding any statements from Léon Walras or Vilfredo Pareto to the contrary, the entrepreneur has no discernible role within a general equilibrium economy and that firms within general equilibrium economies are entirely reducible to their production technologies/production functions and the collaborative contexts within which they assemble individual, autonomous household agents, through the dual, complementary workings of competition/cooperation.
              Emphatically, neither Walras nor his theoretic forebears in the development of French political economy, from le Sieur de Boisguilbert in the 1690s to Antoine-Augustin Cournot in the 1830s, was oblivious to the importance of entrepreneurship in the organization of economic activity.  Long before the French Revolution had vigorously applied nails to the coffin of feudal economy, the question of how to generate and sustain the initiative of individuals in undertaking fundamentally risky economic projects arises in the writings of the same French economic thinkers that motivated Walras' efforts to systematize a theoretic approach to general equilibrium economics in the 1870s.  Definitively, a century before Walras, Smith's contemporary and Louis XVI's first contrôleur général des finances Anne-Robert-Jacques Turgot argued that, within an integrated system of market exchange, agricultural proprietors sustained an unassailable role as first-movers of all economic activity and that social progress in the creation and accumulation of landed property transformed land holders into agricultural entrepreneurs, transforming less capable, industrious, frugal, or simply fortunate cultivators into their hired hands.  In this regard, Turgot introduces an unmistakable class dynamic into the relations between land owners and cultivating lessees that both reflected his own influences and shaped the theories of subsequent French economists - the fact that Turgot labeled non-cultivating land owners as a non-productive, "disposable"/disponible class could only have nurtured the negative evaluations on land owners evident a generation later with Walras' father, Auguste, who then passed on his ethical prejudices against land owning to his son (see A-R-J Turgot (1766), Réflexions sur la formation et la distribution des richesses, chapters V, IX-XIII, XV, McMaster University Archive for the History of Economic Thought at:  http://socserv2.socsci.mcmaster.ca/econ/ugcm/3ll3/turgot/reflfr.htm).  The main theme that I mean to emphasize with Turgot, however, concerns the idea that progressive economic development demands the initiative that can be found as land owners consolidate property holdings and demand the highest possible returns on their investments in cultivation.  
                A century later, Walras, writing in the wake a tradition of political economy that conceded of necessity a certain privileged role for initiative and direction/supervision in economic activity, could not entirely avoid the entrepreneurial concept.  In fact, he commits two lessons in his Éléments d’économie politique pure to situate the entrepreneur within his larger model of equilibrium in production.  However, over the course of this treatment, Walras' relegation of a place for the entrepreneur appears wholly superfluous and unnecessary within his larger model.  Rather than conceiving of an independent and autonomous agent of production, in possession of privileged knowledge on the assemblage of production factors into profit maximizing combinations, willing to take the risk of tasking households to provide factors in the production of commodities that may or may not find a market at a desired price, Walras advances the portrait of a largely irrelevant, dependent agent for whom, under theoretically ideal conditions, no rate of return for the services of entrepreneurial activity will obtain.  A crucial differentiation is evident here, as across the larger account presented in this document, between the theoretic ideal and real firms.  Walras appears to acknowledge that, for real firms, entrepreneurship is an absolutely essential component in determining the viability and sustainability of collective production, but, under the particular operative conditions of a theoretic general equilibrium economy, at the level of individual firms, the necessity of the entrepreneur is vacated.  In its place, we get the cooperative/competitive story of tâtonnement, where a set of households with diverse factor endowments come together to produce goods and services, exchange them with other households as needed to maximize their respective utility functions, and distribute the gains from cooperation and exchange in mutually beneficial ways.  At length, Walras makes the point quite explicitly:

                     This state of equilibrium in production is, like equilibrium in exchange, an
                      ideal state and not real ... But it is the normal state in the sense it is the state
                      which activity tends to approximate under free market competition applied to
                      production as to exchange ... We can further, in the state of production
                      equilibrium, abstract from the intervention of the entrepreneur and consider
                      not simply productive services exchanging for finished products or finished
                      products exchanging for productive services, but also consider productive
                      services, ultimately, exchanging between each other.  
                             Thus, in the state of production equilibrium, entrepreneurs neither
                     benefit nor lose.  They therefore subsist not as entrepreneurs, but as land
                     owners, workers, or capitalists, in their own enterprises or others.  I
                     suppose that, to establish his real worth, an entrepreneur who is owner of
                     the land he exploits or occupies, who participates in the direction of his
                     enterprise, and who has capital invested in its operations, should deduct his
                     general costs and credit to himself a share of (land) rent, a salary for his
                     labors in direction, and a share of interest on the capital he has invested,
                     each calculated at market rates, and, to the extent that he subsists, as an
                     entrepreneur per se, he would neither gain nor lose. (Léon Walras (1874),
                     Éléments d’économie politique pure, 231-232 (translation my own).
                     Lausanne, Switzerland: Imprimerie L.Corbaz and Co., accessed online from
                     Google Books (http: //books.google.com/) , 27 Dec. 2015)

In these terms, I consider myself justified, at least in relation to Walras' core theory of general equilibrium, in expunging the entrepreneur from my theorization of a Walrasian/Paretian firm.  As an integrated, multi-level market structure, a general equilibrium economy, in a pure Walrasian mold, is always just a cooperative/competitive project between households with no necessary functional place for an instigator.
             In regard to Pareto, as Walras' most prodigious and influential student and colleague, the relevance of entrepreneurship appears at least somewhat more complicated.  Roberto Marchionatti and Enrico Gambino argue persuasively that Pareto's insistence on variable factor coefficients in the profit maximization/cost minimization, as a means of closing the gap between theoretic abstraction and real economic practice through successive approximation, opens a space for entrepreneurial practice beyond strict reliance on technological constraints (see Marchinonatti and Gambino (1997), "The Contributions of Vilfredo Pareto to the New Theories of Economics in the Years of the 'Cours d'Économie Politique'," in History of Economic Ideas, Vol. 5, No. 3, 49-64, downloaded from JSTOR (27 Dec 2015), at: http://www.jstor.org/stable/23722575).  That is to say, Pareto's more consistent desire to link general equilibrium theory to real economic practice forces him to acknowledge, in ways alien to the pure logic of Walras' Éléments, that real firms were directed by real entrepreneurs who possessed a functional role in determining, among other things, the mix of production factors to be rented from households in order to maximize profits.
           If we have to acknowledge that, in certain ways, Pareto's departure from strict reliance on linearly homogeneous production functions with fixed coefficient values makes the operation of production equilibrium more complicated and more conducive to overall direction/supervision, I am nonetheless reluctant to introduce an entrepreneur into my account of the Walrasian/Paretian firm, because, generally, it would introduce a degree of epistemic empiricism that I have sought to downplay in my overall treatment of general equilibrium economics as a rationalist theoretic construct and, on a more detailed level, it would unnecessarily complicate the process of production equilibrium without necessarily adding anything to a system rigorously grounded in tâtonnement.  In the end, if production coefficients readjust with dynamic technological transformations, then autonomous household agents on the production side could instantaneously adjust to such changes to arrive at new equilibria without the benefit of entrepreneurial direction.  At stake here is not a set of formal specifications on function roles but a larger way of thinking about how integrated economic systems are organized and for whose benefit they operate.  For my purposes, the autonomy and capacity for cooperation/competition of utility maximizing household agents remains at the heart of general equilibrium economics regardless of Pareto's attempts to generate theories of general equilibrium that could benefit from a deeper empirical connection to real economies.
            Moreover, as Marchionatti and Gambino further argue, the Paretian legacy in general equilibrium theory introduces a strong degree of ambiguity on the role of markets as distributive institutions, not otherwise evident with Walras, subsequently exploited by Paretian theorists like Oskar Lange to defend socialist institutions of centralized planning of production and consumption.  Debates arising over the course of the 1920s and 1930s between Paretian defenders of socialist planning (Lange and the American Paretian Abba Lerner) and Austrian defenders of free market mechanisms (Ludwig von Mises and Friedrich Hayek), ultimately grounded on the problems of obtaining, consolidating, and integrating information into the organization of production and consumption, demonstrate the systemic substitutability of the entrepreneur, both for Pareto and for his students.  In market systems, characterized by recurring uncertainties in the demand for goods and services along extensive supply chains with divergent temporal horizons in investment and production, entrepreneurial agents embody a substantially different functional role relative to state bureaucrats, in centrally managed distributive systems where, on the basis of information collection, bureaucrats determine a priori what goods and services will be supplied to households.  Ultimately, the Paretian conflation of market-oriented entrepreneurs and state planning bureaucrats demonstrates a fundamental devaluation of the entrepreneur in relation certain other Neoclassical approaches and, even more clearly, in relation to the Classical treatment of entrepreneurship.
            Concluding, the various perspectives on the entrepreneur arising in the writings of Walras and Pareto raise questions regarding certain assumptions of general equilibrium economics.  Most notably, Walras' virtual elimination of a functional role for the entrepreneur becomes conceivable, on an abstract level, if we accept the idea that household agents continuously embody perfect information, not only about production technologies but, equally important, about their own needs and desires in consumption.  As such, we will, at the appropriate time, need to consider the problems of need and desire in the context of household consumer choice, if only to critique the Walrasian/Paretian perspective that resides at the heart of general equilibrium economics.  For now, the problem we face relates specifically to the primacy of the entrepreneur as an intermediary agent linking diverse households that lack complete information on how to produce the goods and services they want and/or simply how to determine what it is that they really want.  If household agents continuously know precisely what they want to consume and have detailed knowledge on the availability of consumption articles across a larger integrated economic system, then we do not need entrepreneurs to collect information on these needs in order to translate them into consumable inventories - households will achieve these tasks on their own.  They will, likewise, know precisely how to combine household factors of production to most efficiently produce goods and services, taking full advantage of heterogeneous factor endowments across discrete households.  To the extent that perfect information remains a critical problem to Walrasian/Paretian general equilibrium theory, the functional role of the entrepreneur appears as the unexploited source of a potential, if imperfect, resolution.  To the extent that we remove the entrepreneur from consideration, we, thus, leave the Walrasian/Paretian theory of the firm with an unrealistic and unpersuasive perspective on the capacities of household agents to assemble and utilize information on both production and consumption.

Elasticity in Output Supply and Factor Demand, the Financing Constraint, and Monetary Neutrality

This concluding section of my critique represents an attempt to tie up a handful of related, residual very loose ends in the theoretic account presented in this document.  Specifically, following from our restriction of production functions to linearly homogeneous forms characterized by constant returns/constant costs and our assumptions of perfect competition between all firms in all industries and perfect information, I draw market supply schedules in output markets and market demand schedules in factor markets that are universally perfectly elastic.
           A number of separate considerations enter into my defense of this practice.  First, if production functions for all firms are continuously differentiable and linearly homogeneous, then firms will always be able to arrive at a unique profit maximizing/cost minimizing factor combination where marginal productivity factor pricing results in product exhaustion.  Under these conditions, production costs will be invariant to differences in scale.  Thus, every individual firm will operate with a perfectly elastic (flat) supply schedule at its profit maximizing/cost minimizing cost per unit of output.  Second, if all households and all firms operate with perfect information on production technologies and all firms operate in perfect competition, through which every firm must strictly minimize its costs per unit of output, then all firms in a given industry/production process will operate with an identical production function and will realize an identical cost minimizing/profit maximizing ratio of production factors.  In this respect, the only difference between firms may arise from differences in scale, resulting from differences in the financial constraints faced by individual firms.  As a result, market supply schedules for individual output markets are simply additive combinations of the supply schedules from individual firms, a result buttressed by the timeless and spaceless character of a general equilibrium economy (that is, any differences in transportation costs between firms operating at diverse distances from common market sites must face a countervailing locational rental adjustment or simply be abstracted away).
           Moving over to factor demand, in which multiple industries compete for factors characterized by various degrees of homogeneity/heterogeneity, the demand schedules for each factor must be an additive combination of the factor demand schedule for individual industries and, in turn, each industrial factor demand schedule must be an additive combination of factor demand from individual firms, characterized by diverse individual scales of production.  If all firms in all industries operate with continuously differentiable linearly homogeneous production functions, then, at a given vector of equilibrium prices, the schedule of demand for each factor must be flat, even if certain industries utilize a given factor more intensively than others contained within the aggregate factor market.  In a certain sense, the factor market demand schedule, thus, conveys a relationship between the quantities of a factor supplied by households and the quantities demanded by all industries under the improbable (if not impossible) circumstance that changes in the macroeconomic scale of output production maintain a perfect balance of proportional factor demand across all industries, reflected in a static vector of equilibrium prices.
            Under such circumstances, the factor market demand schedule itself lacks virtually any meaning - the only thing that interests us is the point at which the quantities supplied by households equal the quantities demanded by all industries for a given factor price (expressed in relation to all other prices in a given equilibrium price vector).  The same might be said for factor demand and output supply schedules for individual industries and individual firms.  In a world where constant costs are operative at every level and at every conceivable context of production and, more importantly, any deviation from a given equilibrium price vector will simply lead to an instantaneous readjustment to arrive at a new equilibrium price vector, information on short run rigidities conveyed by output supply schedules demonstrating increasing marginal costs per unit of output, where firms possess some freedom to adjust to short run changes in household demand, simply have no relevance.  In fact, it would be fair to argue that my drawing of output supply and factor demand schedules is merely a rhetorical device, intended to express a kind of continuity between a theory of the firm in a Walrasian/Paretian general equilibrium economy and a theory of the firm under Marshallian partial equilibrium dynamics, where firms are more than transitory, captive intermediaries between households.        
            Having conceded the point that our perfectly elastic output market supply schedules and factor market demand schedules are virtually meaningless in relation to the single, determinate points of equilibration arising from the realization (through tâtonnement) of each discrete equilibrium price vector, a question of dynamism remains open.  That is to say, how do we account, in simple terms, for changes in the demand for factors and changes in the supply of outputs if our conceptual/graphical tools are meaningless?  Our development of the theory proposes that we shift our perfectly elastic schedules up or down to account for changes in equilibrium prices.  Insofar as we remain interested only in the points at which household factor supply and output demand schedules coincide with quantities of factor demanded and outputs supplied, I continue to accept the idea of shifting perfectly elastic curves up or down as equilibrium prices change, if only because it enables us to deploy a relatively simple graphical tool to explain how a change in household utility maximizing choices, on the factor supply or output demand side, impacts our technologically determinate intermediary institution.
              Continuing beyond the problem of output supply and factor demand schedules, two related residual problems remain in the theoretic mechanics of profit maximization/cost minimization for individual firms.  Specifically, we define the cost function of individual firms in terms of individual, given factor market prices and an overall total cost level.  This function, in turn, graphically configures the isocost schedules faced by the firm.  At various points, I apply the terminology of a financing constraint to specify the particular total cost level that is binding to a firm at any given context.  To the extent that firms in a given industry, engaged in perfect competition but otherwise in possession of perfect information, vary in scale, they do so because they have different financing constraints.  In view of the larger contributions that I have advanced in the two previous sections, concerning the operation of tâtonnement and the absence of an entrepreneur in the Walrasian/Paretian firm, it is worth questioning the meaning of this financing constraint and its relevance to our conception of dynamism within a general equilibrium economy.
             Conventionally, finance for real firms constitutes a subset of capital understood as a mass of specifically monetary resources capable of being deployed to invest in various production factors.  Ideally, the financial resources of the firm must be characterized by a substantial degree of liquidity in order to readily transform available funds into usable resources for production.  At first blush, this monetary image of finance might be adequate, particularly if we were developing a theory of the firm from a financial accounting perspective or, even more so, within a roughly Keynesian approach, where the relative liquidity of diverse financial instruments remains a central theme.  However, for Walrasian/Paretian theory, as with most other theoretic approaches in both the Classical and Neoclassical traditions, any explanatory reliance on monetary variables raises significant problems.
            As I noted in my initial discussion of cost functions, Neoclassical economic theories reject the notion that money can be regarded as an object conferring utility on its possessor.  Rather, the utility of money to household consumers arises strictly from its capacity to be converted into a mass of final goods and services.  As such, households diminish their total utility by holding positive money balances rather than spending these balances on desired goods and services.  Alternatively, for household investors, money does not truly exist as capital, per se.  It does not make the production process more "roundabout" if it is not invested in tools, machinery, or the acquisition of knowledge that can enhance the production of goods and services.  When household investors of retained money incomes hold positive cash balances rather than investing in new capital assets, they diminish the utility that they might enjoy from contemporaneous consumption without any potential for offsetting such losses by enhancing future consumption possibilities.  In these terms, money is continuously neuter with respect to utility.
           The utilization of monetary prices in the development of our theory to account for pricing in output and factor markets is, thus, undertaken merely as an explanatory convenience.  To the extent that this is the case, however, our account on dynamic change, in response to a transformation of household preferences in factor supply or output demand or technological changes in production, remains complicated because such changes may involve expansions or contractions of the financial constraints of individual firms.  How do we account for such changes if our conception of the financial constraint is monetary in nature?  We need a real, non-monetary explanatory pathway to express how, say, an increase in the quantities of a given output demanded at all prices (i.e. an outward shift of an output market demand schedule) translates into an expansion of the financial constraints of individual firms in the output market, facilitating an increase in the scale of production, holding factor market prices constant.  Emphatically, we need to articulate the workings of tâtonnement as if households enter into the cooperative project of the firm and conduct exchange with other households within a strict framework of pure barter.
         If monetary assets never enter into market exchange, then the notion of a financial/scale constraint on firms refers jointly to the available quantities usable production factors within reach of each individual firm and to the realizable mass of goods and services available to compensate households for use of their production factors.  The first component is a register of the potential scale of the cooperative endeavor between households if all production factors could be employed.  It is a function of the geographic reach of a given firm in relation to available household factor resources and the larger scale of household demand for the goods and services produced and exchanged by the firm.  We can further specify the dynamics of such a constraint based on the preponderant rate of expansion of available labor services, investment in new machinery, accumulation of skills/training and technological knowledge, and progressive utilization of natural resources.  Again, approaching these issues within an otherwise timeless and spaceless theoretic structure, our financial/scale constraint becomes, in some measure, abstract and arbitrary as it applies to individual firms.  At the level of a given industry, no precise reason exists for why certain firms, all of which operate with identical production functions, would operate at different scales if we do not simultaneously articulate, for example, a spatial structure relating certain firms more closely to given available factor resources with a particular geographic distribution.  
         The second component in our conception of the financial/scale constraint of the firm is, in certain respects, purely technological.  The quantities of output that a given economy, as a whole, can generate and distribute as compensation to household factor owners is a function of the production technologies available to firms, embodied in their production functions.  In the articulation of financial/scale constraints, applicable to individual firms, however, the technological limits on the availability of goods and services for compensation become internalized for all household owners of production factors as expectations for compensation in exchange for the provision of their factors for the production process.  Such expectations return us to the subject of our discussion on tâtonnement as the process through which individual households assess the potential gains from cooperation, tempered by the potential for certain household agents to exercise short-side power and/or first-mover advantages, in order to resolve their own two-sided (factor supply and output demand) utility maximization problems in conjunction with all other households.  Ultimately, the expectations of households for compensation in exchange for cooperation in collective production provide the foundation for the determination of factor market prices, in relation to the determination of output prices.  Thus, the real price of an hour of human labor services, considered in some abstractly pure sense, equals the mass of goods and services that households expect to receive for the inconvenience of providing their labor services in order to balance the utility gained from consumption against the disutility incurred from working.  This relative price of labor services constitutes one argument in the firms financial/scale constraint through its cost function.
          If we, thus, regard all factor prices as real quantities (masses of exchanged or exchangable goods and services destined to be consumed as compensation for the provision of a factor by the household to the firm), then we need a more convenient form to account for such a quantity that does not necessarily degenerate into some nominal, monetary register.  That is to say, we have to reduce all quantities of goods and services to a universal register that reflects the comparative utility of a good or service to some universal baseline of utility.  Effectively, we need to define a numeraire against which the utilitarian value of all other goods and services can be measured, and such a numeraire must, itself, have a utilitarian value (by virtue of monetary neutrality, we have determined that money lacks such a value).
          It is not the purpose of this section to elaborate the properties of such a numeraire or even to ask whether, on the basis of such properties, it might even be possible to identify a good or service as numeraire.  Rather, the sole purpose in specifying this role in relation to the financial/scale constraint of firms is to argue that the financial/scale constraint is a real, not nominal/monetary quantity.  When we talk about increase or decrease in a firm's financial/scale constraint, perhaps arising from a change in the relative prices of the factors it employs intensively or from a change in household demand for its outputs, we are continuously arguing that a larger or smaller mass of real goods and services is now destined to be consumed by the households that rent their production factors to the firm.  Whether we articulate such a change in nominal/monetary terms or not, we are explicitly not talking about a nominal/monetary phenomenon.
         Pressing home, moreover, the consequences of a transformation in our discussion from nominal to real financing, we can pursue a redefinition of the cost function.  If M represents some nominal/monetary total cost/financial/scale constraint for a firm utilizing diverse quantities of labor l, capital k, and land n, then we can express the firm's nominal cost function as:

M = Pll+ Pkk+ Pnn

Where Pl is the nominal price of labor, Pk is the nominal price of capital, and Pn is the nominal price of land.  If we now identify select some commodity r with price Pr to be numeraire, then we redefine:

M/Pr = R
Pl/Pr = pl
Pk/Pr = pk
Pn/Pr = pn

And, thus, our real cost function becomes:

 R = pll + pkk + pnn

Expressed in these terms, the firm's capacity to rent and deploy a certain quantity of production factors in the production of goods and services faces a constraint measured strictly in terms of r, as a particular substance commanding a certain level of subjective utility for consuming households and commanding quantities of other goods and services in exchange.
             The imagery of a barter economy conveyed by the transformation of the firm's cost function in terms of a real commodity/numeraire reinforces the basic conclusion, emphasized continuously over the course of this document, that the ultimate rationale of the firm is to consolidate household factor resources for the purposes of augmenting household consumption.  The existence of markets, operating with monetary means of exchange, is ancillary to this broader conclusion.  Effectively, households should be understood to act as if we continuously operated within a pure exchange economy, where the firm itself is a transitory cooperative endeavor to meet temporary ends without a permanent existence or an instigating entrepreneurial agent, and the market simply facilitates barter of real goods and services without any residual consolidations of monetary wealth and without any accumulations of profit.  In this manner, figure 33 pursues the definitive consolidation of our insights on firms in a Walrasian/Paretian general equilibrium economy by graphically encapsulating the firm as a pure captive, price-taking intermediary in panels A and B into a consolidated panel C, where, for commodity 1, the firm itself is expunged from the broader exchange of household agents supplying production factors and other household agents supplying commodities in exchange.

              Figure 33: Reconceptualization of the Market as Pure Exchange Between Households.

From the framework represented by panel C, the production of additional quantities of good 1 clearly manifests increasing marginal costs per unit of output as we increase the amount of 1 demanded by households.  Such increasing costs reflect both the increasing disutility to households providing production factors for firms producing good 1 (or, alternatively, the higher disutility of households previously outside the margin of employment by firms in the industry) and the additional social cost from diverting factor resources away from the production of other goods and services, registered in turn by the inclusion of all other prices as arguments in the calculation of the market supply schedule.  Having arrived at this crucial juncture in which we can draw a proper Marshallian cross with the appropriate explanations for an upward sloping supply schedule and a downward sloping demand schedule, we must dispense, in the Walrasian/Paretian world that we have constructed, with the conception of the firm - this is a market equilibrium between autonomous household agents on the supply and demand side where our captive intermediaries have disappeared entirely.

A Pure Neoclassical Theory of the Firm XIII: Critique VII (Microeconomics)

 Tâtonnement: Assessing the Cooperative Groundings of the Firm in a Market Economy

This section will attempt to briefly introduce a larger theme to which I will return in considering the household as a utility maximizing agent in factor supply and output demand.  The particular portrait of the firm advanced in this document has effectively reduced production to a simple mathematical problem of profit maximization/cost minimization, undertaken where firms in all industries operate with given vectors of output and factor market prices under given, universally known, and universally available technologies.  The conceptual glue holding together this structure of autonomous household utility maximization problems and captive profit maximizing/cost minimizing solutions is Walras' tâtonnement/"jostling."  Given its importance to our larger story of a general equilibrium economy, it is time to interrogate this concept in order to situate in relation to the Neoclassical tradition and economic theory writ large.  
            Without giving away too many of the details in our general equilibrium theory of household agents, an economy operating with firms in accordance with our description must have households in possession of one or more factors of production, demanding heterogeneous portfolios of consumer goods and services.  In some way, shape, or form, it may be possible for at least some of the households to obtain a limited share of their consumption portfolios through independent production processes.  That is to say, in the absence of firms, individual households may be able to combine quantities of land, labor, and capital in their own possession to generate a basket of goods and services for their own consumption.  We can label such a basket a subsistence consumption set.  The concept of subsistence that I introduce here does not necessarily mean biological subsistence, implying a state at which any relative deprivation of consumption might endanger the biological survival of household members.  Rather, I am simply using the term subsistence to describe a state at which a given household consumes a minimum expected quantitative and qualitative ensemble of goods and services to maintain its desired standard of living.  We would have to assume that most subsistence consumption sets would be labor and/or land intensive.  Capital investments require sacrifices of household consumption possibilities in which, below a certain threshold level in the definition of subsistence, we would not expect most households to engage.  On the other hand, the decision of a household to restrict its level of consumption in order to invest in capital must reshape the set of minimum expectations held by a household regarding its consumption possibilities, framed around the contemporaneous decision that consumption can be curtailed in the name of greater future consumption.      
             At some level where minimum expectations on consumption possibilities across a collective ensemble of multiple households has risen significantly, the strictly limited endowments of production factors available to each individual household agent must preclude prolonged reliance by most households on individual/autarkic production and subsistence consumption.  If households can generally obtain a basket of goods and services preferable to their subsistence set through cooperation with other households, bringing together a wider set of production factors to expand the range or quantity of goods and services that can be generated in isolation, then all cooperating households might be made at least as well off in cooperating as they would be by producing goods and services in isolation and at least some households might be made better off.  In the latter circumstance, a cooperative strategy of goods and services production would be Pareto superior to individual/autarkic production.  That is, by definition of Pareto superiority, as a central principle in Walrasian/Paretian welfare analysis, all individual members to the strategy would be at least as well off and some would enjoy utility gains.  The concept encapsulating this cooperative strategy between households, assembling factor endowments into a collective agency in production, is the firm.
           Before moving on to a rudimentary welfare analysis of the distribution of gains from cooperation, I want to briefly consider the sources of productivity gains from cooperation.  First, it is likely to be the case that the initial distribution of household factor endowments of land and labor are both quantitatively and, acknowledging factor heterogeneities, qualitatively uneven.  Such unevenness both shapes differences in initial conceptions of subsistence and generates an elementary source for gains from consolidation of household factor resources.  The quantity and qualitative range of factor endowments available to a given household must determine the household's minimum expectations for consumption.  Ready access to arable land, conducive to cultivation of a limited range of food crops, will, thus, configure a subsistence basket heavily laden with such agricultural produce.  If we integrate other households into the agricultural production process, adding additional labor services to those undertaken by the household with access to the land, then a potential exists for the production of a larger mass of consumable produce, even if the returns to adding labor services diminish as we add additional labor time.  Conversely, as we add other households, we may add additional land of differential quality, bearing heterogeneous factor resources.  The consolidation of diverse factor resources from multiple households into a consolidated unit of production, which then shares its consolidated outputs based on some mutually beneficial and mutually consented formula, may involve the articulation, by trial and error or by conscious construction, of an efficient production model, where the unit of production pieces together available heterogeneous factors in order to derive the maximum quantity of outputs given each available set of factor inputs.  
             Pure quantitative augmentation of factor resources across multiple households, even under diminishing returns to individual variable factors, thus, constitutes one source for gains from factor consolidation/cooperation across households.  Secondarily, accounting for factor heterogeneity and the possibilities for capital accumulation (i.e. productive roundaboutness) with factor consolidation, the production unit may traverse some initial range of increasing returns to scale through which it achieves a threshold in the integration of all production factors that manifests a global cost minimizing combination of factors.  Postulating that such a threshold might exist for the firm takes us beyond the conceptual boundaries of our Walrasian/Paretian theory of the firm.  Rather, as with the Austrian theory of capital and interest, such a conceptual transition point in cost minimization/profit maximization represents an element in the implicit backstory of the Walrasian/Paretian firm, where the accidental or conscious piecing together of complementary heterogeneous factor resources culminates in units that might be fully capable of realizing factor combinations that objectively maximize efficiency such that no reorganization of factors between production processes can increase outputs in one production process without diminishing outputs in at least one other production process (i.e. Pareto optimality in the organization of production factors).  That is to say, our Walrasian/Paretian general equilibrium economy is organized in order to exhaust all possibilities for increasing returns to scale from a reorganization of production factors.  Assuming, again, that households possess perfect information on the technological possibilities for efficient maximization of outputs, such an objective maximum is at least theoretically conceivable. 
               If cooperation yields increases in outputs relative to individual/autarkic production, then it remains for us to consider how the gains from cooperation are to be distributed among cooperating households, under the initial assumption that the households constituting the firm will distribute the outputs they collectively produce among themselves rather than undertaking exchange with other households outside the firm's boundaries.  Assuming all households have access to technological information concerning the additional returns as each factor is added to the production process, then, heterogeneities between individual factors aside, each household should be fully cognizant of the marginal productivity contributed by their factors.  If this is true, if each household is strictly compensated in accordance with the marginal productivities of their factors, and if the firm operates with a production function characterized by linear homogeneity, then there is no question that the total product of the firm will be wholly exhausted paying each household for its contributions to production.  Such is the logical culmination of the Walrasian/Paretian theory of the firm.  We need to interrogate this conclusion further, however, because, quite simply, Walrasian/Paretian theory does not conclude or even centrally pertain to production.  General equilibrium economics most critically pertains to the operation of markets and the negotiation of equilibrating price vectors.  If the sterile conclusion that each household would be compensated for each factor that it contributes in accordance with its marginal productivity is to be believed, then this conclusion must be situated within the larger structure of the determination of equilibrium factor market prices and, in turn, the simultaneous determination of all equilibrium prices.  How, in this manner, do we get from individual/autarkic production to cooperative production by means of tâtonnement/auctioneering/bargaining between households to arrive at product exhaustion under marginal productivity factor pricing?  
              At this point I want to make an argument reflecting the partisan prejudices of Walrasian/Paretian general equilibrium theory.  Specifically, we will assume that the gains from cooperation evident in the assemblage of the firm must be shared strictly in accordance with the technologically-determined marginal productivity of each factor of production, and that otherwise cooperative production will not take place.  Such an assumption goes beyond merely stating that, under a linearly homogeneous production function, product exhaustion will obtain if all of the factors are paid their marginal products.  As an ethical and political statement, strict compensation in accordance with marginal productivity means that compensatory distributions from the total product of the firm will be rigorously fair, in the sense that each factor will be strictly paid its contribution to the total product at the margin of employment.  Strict marginal productivity factor pricing requires, in my view, two things: first, that the inception of the cooperative endeavor of production by cooperating households is strictly simultaneous, and, second, that, heterogeneities notwithstanding, none of the households are capable of exercising market power in conferring access to its factors of production.  
           Elaborating on the first of these conditionalities, simultaneity is important for two reasons.  First, considering the potential for diminishing marginal productivity as additional units of variable factors are added in relation to other factors (fixed or variable), sequential contracting of factors would result in higher compensatory rates for infra-marginal units of each factor.  That is to say, if the marginal productivity of one of the factors, say labor, falls as we add more labor to the land and capital provided by other households, but we compensate labor units according to the sequence in which they were hired, then the factor payments due to labor units hired first would be higher than the factor payments due to the last labor units.  The point is that all units of all factors of production must be compensated at their marginal productivities only when all units have been assembled for production.  Again, under a linearly homogeneous production function, this condition would mandate that each of the factors would receive a factor payment proportional to its average productivity, precisely realizing product exhaustion.  Second, simultaneity precludes the possibility of a strategic first-mover advantage.  That is to say, if the assemblage of production factors is orchestrated by some first-mover household agent, capable of commanding some infra-marginal return for assembling the factors into a final profit maximizing/cost minimizing combination, then, maintaining the conditional requirement of product exhaustion, all other household agents would have to receive a compensatory payment less than the productivity of their factors at the margin of employment.  Consistent with a wide array of economic theory, we might label this household first-mover the entrepreneur.  The requirement of rigorous simultaneity in the assemblage of production factors for the Walrasian/Paretian firm is equivalent to strictly precluding the possibility of an entrepreneur.  
           Regarding the second of our conditionalities, if any of the household owners of production factors is able to command access to a relatively or absolutely scarce resource, without which production cannot take place, then any such household will be able to command a return in excess of their marginal contribution to the production process, a monopoly return.  Again, the presence of large numbers of households in possession of generally or strictly homogeneous production factors, generating competition in the determination of compensatory rates, is absolutely critical to Walrasian/Paretian theory.  If employment confers an ethical right to consume a share of the total product of a firm and participation in the project of cooperative production only emerges from a competitive struggle among households to offer their production factors to the collective project, then the more households in competition the more likely it will be that compensatory rates will settle to some minimum acceptable rate (i.e. a reservation price) beyond which no households in possession of a common or readily substitutable factor will offer their services to the firm.  On the other side, households with relatively or absolutely scarce resources command strategic short-side power.  The relatively short supply of their factor resource in relation to other factor resources translates into a capacity to command rates of return in excess of their minimum acceptable rates (i.e. rent-seeking).    
            Notwithstanding its ubiquity within economic theory, price competition among households in factor markets does not constitute a sufficient condition for strict marginal productivity factor pricing.  No matter how many households command access to certain, relatively common factor resources, contextual or institutional (e.g. organization of households offering a given factor resource, like a labor union) mechanisms can always generate some measure of short-side power in order to command rates of return in excess of minimum acceptable rates.  Moreover, the notion of a minimum acceptable compensatory rate that I offer here is not strictly equivalent to marginal productivity factor pricing.  Returning to the conception of a subsistence consumption set introduced earlier in this section, we could reasonably argue that any augmentation of consumption possibilities through cooperation relative to individual/autarkic production might prompt a household to offer their production factors to a cooperative endeavor.  This proposition does not in any way account for the marginal productivity of factors added by the household to a cooperative project, which, in any case, demands the full complement of Walrasian/Paretian theoretic instruments and assumptions (e.g. linearly homogeneous production functions).  
            In an unqualified market regime of strategic rent-seeking, contextual or institutional maneuvering by household agents, in the absence of some overarching market regulatory agent (e.g. government regulators), can always cause compensatory rates to diverge from some technologically-determined "fair" or "efficient" rate.  As such, the basic existence of relative differences in factor scarcity/abundance, however mitigated by competition and substitutability of factor resources, is sufficient to enable rent-seeking by households in possession of factor endowments that confer short-side power, however minimal in scale or scope.  Market activity might, thus, be reducible to a zero-sum game between agents with differential market power.  If this is true, then what more is needed to redeem the conclusions of general equilibrium theory concerning the welfare maximizing potential of market systems?  How can Walrasian/Paretian theory advance a portrait of the firm that privileges mutually beneficial exchange in the place of market-driven exploitation?  
             The partisan prejudices of Walrasian/Paretian theory emerge when we consider the basic conception of the market as a cooperative environment rather than one of self-centered profiteering by first-movers or households with short-side power.  And, critically, the firm exists simply as a product of mutually beneficial collaboration between households extending from the factor market context.  If there is no precise reason why the market and, by extension, the firm should be contexts of mutually beneficial collaboration rather than the exercise of short-side power or first-mover advantages, then Walrasian/Paretian theory appears, on the one hand, to simply deduce the necessity of such an environment from the presumption that deviations from a rigorous mutually beneficial cooperative environment would tend to violate norms of basic human sociability.  Along these lines, contemporary evolutionary game theoretic approaches might contribute insights from multi-stage simulations of market interaction between individuals reinforcing reciprocity in interpersonal behavior, either as an ingrained psychological norm of human social interaction or as a pattern arising stochastically and replicated as a strategy supporting mutual gain in multiple iterations of an interaction in which participants might otherwise reap excess returns from defecting against a cooperative strategy in the interest of personal gain.  The difference here between sources reinforcing cooperative behavior in evolutionary game theoretic contexts seems key in evaluating the partisan position of Walrasian/Paretian theory relative to the gains from cooperation.  To the extent that market interaction results in cooperative production between autonomous household producers that stand to gain from such cooperation, the explanation why such interaction would result in a "fair" distribution of gains must arise, again in the absence of an exogenous market regulator, either from a psychological predisposition favoring equality as a principle of interpersonal justice or from some utterly random institutional pattern, without any explicable rationale other than "that is simply the way things have always been done."  Without the conceptual weaponry and mathematical sophistication of contemporary evolutionary game theory, neither of these explanations is entirely satisfying as a means of evaluating the Walrasian/Paretian view on the inception of cooperative production/the firm as an outcome of tâtonnement. 
              On the other hand, the Walrasian conception of tâtonnement contains another, more "hands on" interpretation of the processes through which we arrive at market equilibria, and this interpretation is particularly fecund in addressing the problem of gains from cooperation in production.  That is to say, we can read tâtonnement to mean "auction behavior," meaning that the determination of market prices across a general equilibrium system arises from some variation of auctioneering in order to assemble a vector of prices that will simultaneously bring all markets into equilibrium.  In this sense, tâtonnement can be understood to embody a range of variations on the practice of determining prices through an auction.  Certain variations on auctioning practices may incorporate minimal organizational structuring.  A silent variation of an English style auction in which sealed bids are assembled and a winning bidder selected based on the highest (among competing buyers) or lowest (among competing sellers) obtained bid might be suitably conducted solely by the participants to the auction without any formal incorporation of an exogenous and impartial auctioneer.  Other variations in auctioning practices demand the presence of an auctioneer to direct the process, assemble competing bids, and declare a winning bid.  This is the case for both open English (highest ascending bids for buyers and lowest descending bids for sellers) and all Dutch (single descending bid for buyers and single ascending bid for sellers) style auctions.  
            If we interpret tâtonnement strictly in reference to the psychologically ingrained and ostensibly balanced self-interested utilitarian and reciprocally cooperative tendencies of entrants to market contexts, then we need not further speculate on organizational structuration.  Human nature will take care to make markets fair for all participants, where fairness in factor markets implies strict marginal productivity factor pricing.  Interpreting tâtonnement in relation to auction behavior, by contrast, offers us the possibility for incorporation of a metaphorical auctioneer, in order to ensure that the process remains fair for all participating households.  Moreover, considering the overall complexity of a system in which all factor and output markets must equilibrate simultaneously, across all participating households, the inclusion of an auctioneer, at least in a metaphorical sense, appears indispensable.  Theory and real world market practices represent divergent fields, however.  If we concede, on a theoretic level, that general equilibrium requires the institutional structure of an auctioneer to ensure fairness for all parties, then we should simultaneously recognize that real market contexts manifest a need for regulation to ensure fairness.  At this point, Walrasian/Paretian theory diverges from other approaches in the Neoclassical tradition, most notably the Austrians, by seriously recognizing the necessity of an exogenous regulator of market activity, at least at a step removed from everyday price determination in localized market contexts, and acknowledging, at least in certain circumstances, that the identity of such a regulator may be located in the institution of civil government.
            The most basic historical grounding for Walrasian/Paretian reliance on government to provide a fundamentally fair context for tâtonnement emanates from Walras' own writings.  As argued in the previous section, Walras favored the wholesale nationalization of land in order to definitively eliminate the exercise of short-side market power by land owners in the extraction of rents from capitalists and laborers.  He apparently also held that the accumulation of revenues from marketing of natural resources to downstream users, in accordance with marginal productivity pricing in resource utilization, would be sufficient to finance the fiscal obligations of the state in lieu of taxation from income sources or personal property valuations.  
            More generally, Walrasian/Paretian welfare economics maintains, as one of its axioms (i.e. the Second Fundamental Theorem of Welfare Economics), that any initial distribution of factor endowments can generate a Pareto optimal general equilibrium if tâtonnement is enabled to take place free from interference with competitive/cooperative mechanisms for the determination of market prices.  Thus, any wholesale redistribution of factor endowments or of rights to earn incomes from their use in production across households might also realize a Pareto optimal general equilibrium, perhaps under more materially egalitarian, "fair," or otherwise "better" conditions than those that would have obtained in lieu of such a redistribution.  The sorts of redistributions contemplated here, as described in the literature of contemporary welfare economics, concern transfers (i.e. taxes or subsidies) of wealth that can be effected in ways that are invariant toward the behavior of individual households (i.e. lump sum transfers).  That is to say, redistribution would have to affect the asset holdings/factor endowments with which individual households approach markets prior to exchange.  Any redistribution of incomes derived from production would impact the decision of households to contribute factors to the production process (e.g. reducing the quantity of labor services contributed by a household if taxes are extracted from labor incomes).      
           Presumably, such redistributions would have to be effected by some exogenous and impartial agent, capable of balancing the desires of individual households to maximize their utility using the factor endowments at their disposal against the social welfare enhancing potentialities evident in a redistribution of factor endowments.  It would be highly presumptuous to confer on the institutions of government, under any variation of representative or participatory democratic practices, rigorous characterizations of exogeneity and impartiality.  In principle, the more representative a government relative to the majority of a population, the more likely it will subordinate the interests of minorities.  Moreover, we need to separate two distinct motivations for the possible intervention of government, as I have introduced them so far.  First, we have the differential capacity of households with access to certain relatively or absolutely scarce factors to exercise short-side power or first-mover advantages in order to extract rent from other households.  Second, assuming that a market economy already operates at a competitive market general equilibrium characterized by Pareto optimality and strict marginal productivity factor pricing, other competitive equilibria exist under different distributions of factor endowments that would result in enhanced consumption possibilities across all households than those that obtain under the present equilibrium.  Only the first of these motivations is really pertinent to our considerations on the maintenance of competitive/cooperative conditions in factor markets.  However, assuming that governmental intervention always emanates from a complex interplay of partisan political and technical/economic (i.e. efficiency-driven) influences in an environment where the presence or absence of rent-seeking behavior by particular household agents may be ambiguous, it may be difficult to draw a fine line between the correction of a market failure and the selection of a subjectively "better" equilibrium outcome by means of politically contested policy mechanisms.                
       To posit an example that might evoke the complexities involved in governmental intervention, if household owners of capital, as a minority within a population dominated by owners of labor services, are capable of exercising short-side power in their relationships with the latter, then a democratically elected government, acting in the majoritarian interests of the owners of labor services, might redistribute claims to capital income, say, by extracting and distributing shares of equity in capital implements.  Theoretically, such a redistribution could undermine the capacity of capital owning households to extract rents from the owners of labor services by enhancing competition in capital markets.  In more practical terms, it might achieve a redistribution of claims to rents generated through short-side power by forcing capital owning households to part with a share of their incomes.  In either case, the government's decision to intervene reflects a conscious determination that a redistribution of factor endowments or claims to capital income might restore a Pareto optimal competitive equilibrium, shaped both by the perception that existing market outcomes demonstrate a failure of competition and by the relative political clout of a democratic majority of households owning labor services.  In any case, a broader evaluation of the potential welfare enhancing features of such policy would force us to develop tools in Walrasian/Paretian welfare analysis that I do not intend to introduce at this time.  Therefore, it will suffice to argue that, if, on the one hand, the virtues of governmental intervention to enhance the competitive/cooperative character of factor markets are contestable, then, on the other hand, it is noteworthy that Walrasian/Paretian theory is at least willing to countenance the introduction of exogenous (governmental) intervention in order to redress potential failures in competition/cooperation between households.  
              In concluding this section, I want to argue that the divergent possible interpretations of tâtonnement apparent within Walrasian/Paretian theory suggest that we need not rely on a single regulatory principle to ensure that factor market processes can promise a "fair" distribution of total product under cooperative production/the firm.  If theoretic approaches within the Neoclassical tradition as a whole have prioritized the workings of competition between large numbers of buying and/or selling agents in order to ensure that factor market outcomes are both efficient (in the sense that no redistribution of factors across production processes can augment certain outputs without decreasing others) and fair (in our terms, strict marginal productivity factor pricing), then Walrasian/Paretian theory seems to, at least implicitly, buttress its claims about the salutary effects of competition with an assumption that household agents approach markets with a fundamental sense of reciprocal fairness.  Conversely, Walrasian/Paretian theory can be faulted for not adequately developing the sort of conceptual apparatus through which to substantiate possible claims regarding reciprocity as a motivation for households in market exchange.  Rather, it holds in reserve the idea that intervention by exogenous and impartial agents might guard against short-side power and first mover advantages by particular household agents and promote subjectively "better" equilibrium outcomes by redistributing factor endowments across households.  Proceeding, therefore, from a standpoint that cannot singularly posit competition as the sole regulatory principle underlying the bargaining/auctioneering processes through which individual households assemble themselves in order to augment the meager promises of subsistence production by cooperating to constitute firms, I feel adequately justified to offer the dual regulatory principle of competition/cooperation as the definitive signature of Walrasian/Paretian tâtonnement.        
             

A Pure Neoclassical Theory of the Firm XII: Critique VI (Microeconomics)

Land: The Conceptual Problem with Strictly Finite Resources

The consideration of land, as a factor of production existing in strictly finite quantities relative to the possible expansion of demand for its products, constitutes a clear problem in the development of modern economic theory, encompassing the English and French pre-Classicals, the Classical economists, and the Neoclassical tradition.  Certain pre-Classicals, like the French Physiocratic school, were noteworthy for elevating land to a foundational role in the creation of wealth.  Conversely, by the early Nineteenth century, David Ricardo had labeled the ownership of land, imposition and extraction of differential rent, and inherent restraints on agricultural productivity at the margins of fertility the critical constraints on industrial capitalist development.  By the closing decades of the Nineteenth century, Léon Walras was reiterating, to a significant extent, the arguments of the American reformer Henry George, calling for the confiscation of land rents by the state, either by means of a single tax on landed property (George) or outright nationalization of land holdings (Walras).  In view of Walras' central place as a key inspiration for the sort of general equilibrium economics that we have elaborated here and the unmistakably radical overtones in his approach to land ownership, it stands to reason that we need to stop and interrogate the extent to which land is different from labor or capital.
         In certain ways each of the factors of production is a catch-all, consolidating divergent ranges of heterogeneous substances into homogenized categories for the purposes of deriving compensatory rates that bear some reflection to physical productivity at the margin of employment.  The previous two sections have provided ample evidence for why abstract homogenization of the production factors, however theoretically possible, may not yield any practical relationship to compensatory rates.  Rather, if we can get to product exhaustion by means of output price imputation of factor prices through linear optimization, then we can afford to downplay the necessity of having abstractly homogeneous production factors - vectors of heterogeneous factors will work fine to construct a more nuanced portrait of production and the distribution of incomes by firms.  Like labor and capital, land can be approached in this heterogeneous manner, recognizing the unique productive characteristics of different forms of land.
         Acknowledging that each of the production factors can be treated in a way that respects the heterogeneity of individual forms, the problems with land emerge most clearly when we posit the characteristics that make each of the production factors unique as a consolidated category.  Labor subsumes all manifestations of basic human exertion, physical or mental, distinct from the accumulation of learning/training and/or experiential improvements on productivity.  Capital, whether mechanical or human, subsumes all sources of productivity enhancing roundaboutness in production processes.  As unifying wholes, both of these categories work and, in their own ways, each advances arguments in economic theory for why their respective contributions to the production process should command a rate of compensation for their household owners.  As such, the owners of labor and capital exert ethical claims to compensation based, respectively, on the inconvenience/disutility of human exertion and the disutility of deferring consumption until some point in the future in the expectation of increased consumption possibilities.
           Land, in this respect, has traditionally been considered differently.  The owners of land might invest resources into the enhanced value productivity of their factor of production, but to the extent that they do so, their land becomes intermingled with capital.  By definition, in multiple distinct approaches to economic theory, both Classical and Neoclassical, land encompasses factors of production with innate productive qualities, incapable of being augmented without transforming the character of an asset.  In this sense, land shares a basic, natural quality with labor - any addition to the productive power of labor transforms it into a composite of labor and (human) capital.  But land differs still more in its relation to labor.  If to some degree, labor and land can both be expended progressively through successive iterations of production processes, natural processes exist for the reproduction of labor (both in relation to its static productivity and in relation to human life, per se!).  Land lacks such reproductive processes.  As such, land is distinguishable among all of the factors of production as a factor that cannot be reproduced - land, by definition, is absolutely scarce.  Any effort to produce land or to replicate its unique productive qualities constitutes not land but capital.  Reclamations of land/natural resources demand investments of capital to generate usable assets.  Such investments transform a natural asset/land into produced capital, arising from the deferred consumption of an investor rather than the bequest of a common natural endowment.
           Before moving forward, I want to develop this distinction between land/natural resources and capital at a margin where the two factors quite readily become blurred by inescapable complementarities - that is, we need to situate land and capital as factors of production in agriculture.  It is one thing to talk about the uniquely fertile capacity of sediment-rich soils in an alluvial flood plain, like that of the Connecticut Valley in Western Massachusetts once occupied by glacial Lake Hitchcock, or the natural reproductive cycles of bovines prior to domestication of dairy and beef cattle.  Such resources and processes are parts of a common natural endowment from which agriculture has derived raw materials for the development of an industry providing elements of sustenance to human society.  It is another thing to talk about the accumulation of knowledge on diverse biochemical compositions of soil, the use of nitrogen enhancing fertilizers to augment the naturally occurring fertility of the soil, research into regulation of reproductive cycles of dairy cattle, and use of particular antibiotic medications to reduce harmful micro-organisms and enhance muscle growth in beef cattle, swine, or poultry.  By any definition, the latter processes and bodies of knowledge incorporate the work of human beings to, directly or indirectly, expand the productive capacity of naturally occurring processes by investing capital.
         This distinction immediately raises questions about how we interpret the existence of domesticated work animals or newly developed varieties of fruits, vegetables, and grains, arising either from cross-breeding or genetic manipulation at a cellular level.  In some measure, the domestication of Holstein dairy cattle reflects a longer process of capital investment in the breeding of more efficient milk-producing bovines.  Likewise, the evolution of durum wheat (triticum durum), from other domesticated and/or wild diploid and tetraploid grasses in Mesopotamia sometime around 7000 BCE, resulted from intentional or inadvertent cross-breeding of diverse species by human cultivators and/or harvesters of wild grass seeds.  If, in this regard, durum wheat manifests certain regular patterns of reproduction/fertility in relation to particular varieties of soil (e.g. nutrient poor sandy soils), in particular climatological (e.g. frequent drought) conditions, and susceptibility to particular micro-organisms, it is possible that in many circumstances such natural characteristics were at least initially lost on the first cultivators of the crop.  Again, to the extent that capital represents a continuum in the development of production process, where the rudimentary becomes steadily more roundabout if only by virtue of the accumulation of knowledge, the project of differentiating between naturally occurring objects and products of capital accumulation in agriculture might be somewhat ill-founded.  The world in which we live truly exists as second nature, in which we, as a species, continually reshape and reinvent the natural endowment from which we draw and to which we return.  Notwithstanding the obvious difficulties involved in sorting out land/natural resources from capital in agriculture, we might at least concede, as a pragmatic gesture, that recent (e.g. within 200 years?) or contemporaneous efforts to augment or otherwise transform natural endowments in agriculture constitute capital rather than land.        
           The idea that land, as such, arises from a common natural endowment (that is, the "commons") is central in constituting the critique of rent as the compensatory return to land ownership in economic theory, writ large.  If wages constitute a compensatory return to the contribution of basic human exertion and interest constitutes a compensatory return to deferred consumption/savings, rent, by contrast, compensates the mere ownership of a productive asset isolated from the commons by private ownership.  As we will see in our considerations of Walrasian/Paretian welfare economics, there may be salutary consequences to the privatization of land holdings with respect to the maintenance of natural endowments over time and prevention of spoilage/overuse (i.e. the "tragedy of the commons"), but land is, again, unique among production factors for commanding a rate of return from mere ownership.  In effect, land rent, and rental payments, per se, (of which wages and interest are special cases where the use of an asset features a palpable inconvenience/disutility for its owner) constitute returns to the owner of an asset in return for transitory use rights by an entrepreneur or, in our Walrasian/Paretian case, by a firm minus an entrepreneur.  If rental payments conferred on the owners of land holdings/natural resources compensate the mere isolation of an asset from the commons and the monopolization of its use rights, then we not only lack a basis for compensation of land in the inconveniences incurred by owners for its supply to a production process, but we have an asset in which the determination of a compensatory rate emanates both from absolute scarcity and the capacity of an owner to exclude competition over use rights vis-à-vis entrepreneurs/firms.
             Summarizing the problem of land and its consequences in relation to our Walrasian/Paretian theory of the firm, certain natural resources, otherwise available for free use by entrepreneurs/firms, are extracted from the commons by certain households, who exert an ownership claim on the assets.  The nature of such claims resides outside of the structure of Walrasian/Paretian theory, wherein land, as a factor of production, is largely ignored for precisely the reason that ownership claims on land are not justified in accordance with the same ethical principles as claims concerning ownership of labor and capital - the production of land is not attributable to its owners and, thus, it would be impossible to deduce an appropriate rate to compensate land owners for the inconvenience of producing their assets.
            Land ownership is an institutional problem, related to the broader development of property rights in diverse cultural contexts.  In Western Europe, such institutions go back to the gradual and uneven breakdown of feudal institutions in rural/agrarian geographies, where local manorial lords, increasingly divested of rights to consume goods and services generated by local agrarian producers, parceled out their manorial lands into lease holdings at rents commensurate with the value productivity of the land for production of marketable goods and services.  This process, accompanied by the sometimes forcible expulsion of small, subsistence-level agrarian producers (freeholders) in the name of pursuing market-driven consolidations of land (in Britain, the "Enclosure" movement), constitutes the beginnings of commercial agriculture in Western Europe.  The broader question of how such a movement of institutional transformation could have occurred, however, demands an explanation incorporating a wide range of cultural processes, including the reconfiguration of theological principles governing commercial/entrepreneurial ethics and the reorganization/centralization of political power between local feudal lords and overarching monarchical authorities.  However the transformation from generally communal land holding to the creation of private property in land actually occurred and for whatever reason, it fundamentally resulted in the creation of durable institutional claims to a share of commercial agricultural and/or extractive incomes as a condition of mere ownership of land, the very claims that so bothered Ricardo, George, and Walras!
           Beyond the development of commercial agriculture and other productive sectors generating or otherwise utilizing natural resources intensively, private land ownership commands incomes as a function of the spatial distribution of economic activities.  That is to say, to the extent that the location of economic activity in relation to sites of market exchange is an important consideration for entrepreneurs/firms, especially with regard to the minimization of transportation costs, the distribution of land ownership and use rights to land in close proximity to relevant sites of economic activity becomes an important issue.  Having briefly considered this problem in relation to the spaceless character of our Walrasian/Paretian theory of the firm, it bears repeating that differential land rent may serve a useful economic purpose of regulating the dispersal of economic activities across space.  On the other hand, from a Georgist perspective, the same ends could be achieved through differential taxation of land holdings relative to their advantageous or disadvantageous locations.  In either case, to the extent that differential extractions of income from other activities are expressly related to spatial relations distinct from the mere ownership of land, the title of ownership solely functions to designate the recipient of incomes generated from the competitive distribution of economic space in accordance with the willingness of entrepreneurs/firms to pay for relatively advantageous locations.
           So far, we have discussed the concept of marginal productivity factor pricing with regard to labor and capital, noting that obstacles to homogenization of these factors might compel us to dispense with marginal productivity pricing in favor of imputation from output market prices.  With regard to compensatory payments for land ownership, recourse to imputed prices may not even provide us with a satisfactory explanation.  Again, the overriding problem here resides in the nature of land as an absolutely scarce, monopolized factor.  On the other hand, the particular circumstances of production processes may at least partly undermine the capacity of land owners to extract rent from firms.  Precisely, the nature of competition between land owners and the substitutability of divergent natural resources, on the one hand, and competition between firms, on the other hand, is at stake.
           The point that Walrasian/Paretian theory and most other Classical and Neoclassical approaches have made about the determination of rent has centered on the residual character of rent.  That is to say, ownership of land/absolutely scarce natural resources commands all excess income over and above compensatory payments to the owners of labor and capital, a definition which appears to negate any basis for the determination of rent as a return to the productivity of natural resources at the margin of employment.  Insofar as we accept this argument, any excess over incomes designated to pay wages and interest on capital that we might otherwise designate as profit would immediately be paid out to compensate land owners.  Such a formula for the compensation of land would not only enforce a zero-profit condition on the firm by the peculiar mechanism of conferring on one production factor all residual income beyond factor payments strictly determined by the marginal productivity, but, to the extent that excess income over factor payments is transitory or otherwise quantitatively indeterminate, we would be unable to calculate any ex ante distribution for the productivity of natural resources in some way related to the mathematical formula of a production function.  If a firm's income was wholly exhausted in compensatory distributions to the owners of labor and capital, then the owners of land would receive nothing, no matter how productive their assets were to a production process.  On the contrary, the particular concerns voiced separately by Ricardo and George, that the unproductive monopoly power of land owners, exercised to extract incomes from the productive owners of labor and capital, would tend to depress both wages and profits/interest, imply that some alternative methodology, strictly related to market forces, must establish the upper and lower bounds for compensatory payments to land owning.
           Emphatically, the character of rent as a residual remains, especially for Walrasian/Paretian theory, if only because the ethical predispositions underlying Walrasian production analysis preclude the possibility of including mere ownership of a natural resource as a service in the arguments of a production function.  However, this character must be mitigated by the capacity of firms to substitute between multiple owners of land/natural resources.  As such, the owners of land bearing extractive resources (e.g. crude oil) might enjoy a monopoly on access to an absolutely scarce resource, but their capacity to extract rents is mitigated by the capacity of firms to select between land owners supplying access to the same or comparable resources.  In the end, the relative scarcity of natural resources in each particular market context is more relevant to the determination of compensatory payments to the owners of land than the absolute scarcity of the resources.  The capacity of firms to draw on a large number of alternative suppliers of natural resources must undermine the aggregate effect of absolute scarcity, in exactly the same way that firms engaging with much wider labor and capital markets will suffer less from relative scarcity of these production factors.  In the near term, the fact that a particular natural resource cannot be reproduced need not constitute a hard constraint on compensation to the other factors.
          Again, with respect to land, firms must face a vector of discrete heterogeneous factors, with varying degrees of complementarity and substitutability considered in relation to other discrete factors.  That is to say, the production of particular goods, like abrasive sands utilized in a range of downstream industrial operations, may demand access to a range of discrete extractive sites/mines.  The rate of return to the household owners of such sites constitutes land rent.  Variations in the quality of materials derived from certain mines will generate variations in rental rates.  Further, the location of mines in relation to downstream production sites may additionally impact rental rates if transportation costs vary substantially, especially due to variations in accessible transportation infrastructures.  The more remote a mine is, the less its household owners may be capable of extracting rent from firms seeking to utilize its materials.  Under all such circumstances, the return to land owning households remains, at least in part, a pure return to land ownership.  Conversely, household investment in infrastructures to improve the capacity of firms to extract materials demands an additional return in the form of interest on capital.  The inclusion of such improvements for natural resources must technically constitute a combination of discrete land and capital factors demonstrating high levels of complementarity in the firm's production function.
           Acknowledging, in these respects, that firms confront heterogeneous forms of land, we cannot simultaneously dismiss the idea of abstractly homogenizing land in order to define a quantitative registry of inputs commanding rates of return on the basis of marginal productivity.  Again, as with labor and capital, the point behind homogenization is to relate the compensation rates for a given factor to the physical and/or value productivity of the factor at the margin of employment.  Expanding our two-factor analysis, we should be able to determine profit maximizing/cost minimizing combinations of labor, capital, and land under the assumption that we have a production function consistent with Walrasian/Paretian assumptions about continuous factor substitutability at discrete scale of output and constant returns to scale.  We would simply be adding an additional dimension to our analysis.  The problem here is less mathematical than it is ethical/rhetorical.  Simply stated, Walrasian theory proper has a lineage in seeing the landowner as, for all intents and purposes, an unproductive social parasite, profiting at the expense of productive workers and productive capital investors on the basis of mere ownership of absolutely scarce assets.
          The Walrasian prejudice against land ownership, reflected, again, in Walras' support for the complete nationalization of land, as a reassertion of the natural collective ownership of land, through the state, may further explain why land is often excluded as a factor of production in general equilibrium theorizations.  Why complicate analyses unnecessarily with a factor for which compensatory payments have historically been regarded as illegitimate?  As such, we again encounter the basic consideration that all theories are partial and partisan in their efforts to reshape the reality that they analyze.  The truths that a Walrasian/Paretian theory of the firm might advance with regard to land ownership must reflect, in certain respects, partisan prejudices against the extraction of rents in exchange for access to absolutely scarce assets.  In turn, they conform to a larger theoretic ideal about industry and competition.  If all of the factors could be readily reproduced, even or especially at the inconvenience of their household owners, then the compensatory rates charged for use of the factors should, in some way, reflect the inconvenience incurred by households in producing the factors in form usable by firms, mitigated in turn by competition between household suppliers of substitute factors.  With land, one of these two dimensions on the supply side is missing - there may be competition between suppliers but land owning households never incur an inconvenience in supplying their factors because they are not produced and cannot be reproduced.  The inclusion of an absolutely scarce factor of production within the larger structure of a general equilibrium economy would, thus, on the whole, enshrine monopoly claims to a share of aggregate incomes not otherwise backed by any productive activity.  For Walrasian/Paretian theory, such an outcome is anathema to the operation of a free market economy in which the productive self-interested behavior of households maximizes social well being.