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.