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.
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