The account in this document has sought to achieve two ends: to present a theory of the firm in an integrated general equilibrium economy, abstracted from a broader theory incorporating household choice in factor supply and output demand; and to critique the various component parts and assumptions of such a theory. The title of the document presupposes the idea that such an account constitutes a "pure" Neoclassical theory. My application of the label meant to emphasize that the theory seeks to be firmly grounded in utility maximization, subordinating considerations on production costs and entrepreneurial direction central to the Classical (Ricardian or Marxian) tradition. Along these lines, I further differentiated the theory from Marshallian approaches to the firms, which I will approach in the next document, because the concerns of the latter with space/geography, time frames, entrepreneurial strategizing, and the role of production cost in long run commodity pricing conflict with the assumptions of the theory presented here. By contrast, I offered the initial position that the theory could be labeled Walrasian/Paretian (in regard to the usually conjoined schools of Neoclassical theory associated most closely with general equilibrium theory) and, potentially, Austrian (in regard to its rigorous foundations in utility maximization by autonomous household agents, the theoretically transitory character of the firm as an agent of production, and the reliance of free market mechanisms as the sole regulatory institution for the operation of firms).
Over the course of our critique, however, we gradually undermined the conditions enabling us to apply the Austrian characterization, most critically because our theory of the firm lacks, for all intents and purposes, a capitalist entrepreneurial agent, imperative to any rigorous Austrian account of free market economies. The Walrasian/Paretian firm, as we have conceptualized it here, is a transitory and cooperative enterprise, undertaken by household agents in possession of diverse production factors with the motive of enjoying gains from their cooperation, either through direct consumption of collectively produced goods and services or through exchange with other households producing alternative sets of goods and services. In this manner, the notion of a proprietary return payable to an entrepreneur for the service of acting as an instigator for the production process disappears. Consequently, it might be fair to label the Walrasian/Paretian firm, as we have here characterized it, as (quixotically) both market-oriented and non-capitalist/cooperative. In a larger sense, the concept of capitalism, per se, appears largely absent in our account, except in those rare moments of our critique where the influence of Austrian theory creeps into view (e.g. our theorization of capital, influenced by the Austrian idea of "roundaboutness").
Our theorization established a set of theoretic tools. Most notably, it developed an understanding of the forms and significance of production and cost functions in the mathematical determination of profit maximizing/cost minimizing factor combinations. Production functions, in this manner, represent the embodiment of feasible technological combinations of production factors, producing determinate quantities of outputs. Every possible combination of production factors, defined in accordance with varying degrees of factor heterogeneity, produces determinate quantities of a particular good or service under examination. On the other hand, cost functions map the quantities of production factors available for rental by the firm under given factor market prices for each factor, again, in accordance with varying degrees of factor heterogeneity. Approaching output markets through the insular window of a firm, under conditions of perfect competition across all output and factor markets, we established that the intersection of household utility maximization in consumption decisions and the technological constraints on production faced by all firms in a given market determines the output market price for an equilibrium quantity of a given good or service. Pivoting off to the opposite side of production, we concluded that the intersection of household utility maximization in factor supply and technologically-driven demands for factors by firms determines the price for each factor of production utilized in particular production processes.
To the extent that the firm continuously faces its output and factor markets as a pure price-taker, incapable by itself to impact the decisions of diverse, heterogeneous households to supply factors or demand goods and services (both as products of given internal, psychological predispositions in the household), its decisions on factor demand and output supply are strictly grounded on the technological contours of the production function. On the other hand, we simplified matters by assuming a given functional form for our production function: our Walrasian/Paretian firm operates with a continuously differentiable linearly homogeneous production function, in which every set of positive factor market prices generates a unique factor market combination that will maximize profits/minimize costs for every scale of output. At every profit maximizing factor combination, each production factor rented from households, moreover, will be compensated at a rate proportional to its productivity at the margin of employment, under a condition of diminishing marginal productivity for all production factors. Under the particular conditions of our production function, such a compensatory rate will realize a condition of product exhaustion, where the sum of all factor payments will exactly exhaust the incomes generated by the firm. Such a result is both mathematically necessary, under the particular functional forms utilized to describe production technology, and ethically expedient, to the extent that we firms do not generate incomes for non-productive agents. Under the principle that each rented factor must strictly be paid its productivity at the margin of employment, the distribution of payments between factors, moreover, can be characterized as both efficient and fair, relative to the marginal productivity of each factor.
Extending beyond the limits of our firm, we argued that the interaction of perfect competition and perfect information, as assumptions in Walrasian/Paretian general equilibrium theory, ensured that all firms within a given market would operate with the most efficient available technologies and that, as such, each firm would exist as a representative firm within a given market, with a production function equivalent to that of every other firm. Differences in scale between firms might exist, as a result of differences in the financial constraints faced by individual firms, but such differences would not be reflected in costs per unit of output because linearly homogeneous production functions are characterized by constant returns to scale at profit maximizing combinations. If all industries within a general equilibrium economy, moreover, are characterized by firms facing constant returns to scale, then every industry, as a combination of individual firms, would approach factor and output markets with perfectly elastic demand and supply schedules, respectively, because, the profit maximizing factor ratios of all firms would be proportional for all scales of output. We argued, in this manner, that, in a general equilibrium economy, firms exist as pure technological intermediaries, translating factor inputs into finished goods and services, ultimately exchanged between the autonomous household agents constituting firms and engaging in the exchange of their collectively produced outputs.
In our critique, we argued that argumentation on the nature of firms within a general equilibrium economy ultimately reinforces the partisan preferences/prejudices of Walrasian/Paretian theories. Emphatically, the reduction of the firm to a place as pure, captive intermediary between autonomous household agents reinforces a broader image of a general equilibrium economy as cooperative/competitive endeavor between households, each in possession of production factors and each possessing a set of preferences for consumption of goods and services. In this manner, the firm represents a practical institution, through which free, autonomous household agents combine their production factors to undertaken cooperative production with the expectation that such processes enlarge the consumption possibilities for each household beyond what each is able to gain from individual/autarkic production of consumption goods and services. Our reasoning here attempts to articulate one dimension of the larger negotiation of gains from exchange which Walras encapsulates in the French term tâtonnement meaning to jostle or grope one's way tentatively forward. We argued that the concept of tâtonnement is pivotal to any understanding of general equilibrium economics - beyond any articulation of mathematical functions and assumptions on functional forms, we are left with the portrait of individual household agents coming together to bargain, auction, or otherwise negotiate the terms of mutually beneficial exchanges. Our theory of the firm is entirely grounded on this imagery, even to the extent that it diverges from other theories of the firm in a Neo-Walrasian frame and, perhaps, constitutes a caricature of the very assumptions latent within Walrasian/Paretian general equilibrium thought.
Pursuing, as relentlessly as possible, the consequences of Walrasian/Paretian theories of production on the structural role of the firm, we concluded that assumptions about the homogeneity of production factors, while simplifying to our overall presentation of the theory, create certain problems in translation of the theory into the contexts of real factor markets. It remains difficult if not impossible to rigorously define abstract, homogeneous factor resources called labor, land, and capital, even if our capacity to calculate marginal productivities is absolutely predicated on our capacity to add discrete quantities of such homogeneous substances to the production processes of firms. Our individual examinations of land, labor, and capital ultimately led to the conclusion that the real production factors rented out by households and utilized by firms are likely to be highly heterogeneous in nature (and may involve complex combinations of production factors, like basic labor and human capital, that exchange as a combined unit) and that our calculation of compensatory payments to such factors may more readily rely on imputation from given output market prices. To the extent that we rely on output price imputation of factor prices, however, we may imperil the ethical corollaries of product exhaustion through marginal productivity factor pricing - our factor compensation rates become wholly disconnected from the mathematical determination of factor prices through differentiation of the production function, enabling market forces to skew compensatory rates as a result of, say, short-side market power, not evident if we relied strictly on the technological contours of our production function to determine the relative contribution of each production factor at its margin of employment. Again, however, to the degree that we ground our theory of the firm on tâtonnement and we grant the possibility of some role for exogenous (governmental) mediation of market outcomes to ensure basic fairness between participating household agents, the potential for divergence from strict marginal productivity factor pricing may be mitigated.
More critically, the Walrasian/Paretian theory of the firm suffers, in its engagement with the economic reality of firms that it means to theoretically simplify and explicate, from the absence of an entrepreneurial agent. In this respect, we argued that neither Léon Walras nor Vilfredo Pareto, as the foundational theorists in general equilibrium economics, seriously grasped the potential necessity of entrepreneurial action, decision-making, and risk-taking in the face of uncertain outcomes to production or investment decisions. Ultimately, the rationale for this absence of an entrepreneurial agent resides in the timeless and spaceless character of general equilibrium theory. I have attempted to convey these deficiencies in the ontological construction of general equilibrium economics by asserting, among other things, the instantaneous character of adjustments to changes in individual preferences and/or production technologies as an outcome of continuous tâtonnement between households in continuous possession of perfect information. In subsequent theories of the firm, we must further engage in the problem of information and the consequences of differential distributions of key information concerning production technologies, household preferences, and market opportunities on the organization of an economy. Insofar as we have here collapsed every species of information problem and their respective consequences by imposing an assumption of perfect information, we likewise have no need for an active, autonomous, and entrepreneur/risk-taking production agent to negotiate contemporaneous information deficiencies and uncertain future outcomes, particular with respect to capital investments that take time to come to fruition. In a Walrasian/Paretian economy, we can replace such an agent with a continuously differentiable, linearly homogeneous production function as the wholly captive, technologically-driven signature of the firm.
Notwithstanding the obvious short-comings of Walrasian/Paretian thinking on the organization of production in a general equilibrium economy in relation to the institutions of real economies, I want to conclude this summary by pressing home the fundamental, partisan arguments that, at least in my view, underlie this theory of the firm. By virtue of its single-minded, rationalist reduction of economics to exchange between autonomous, utility-maximizing agents across an integrated ensemble of output and factor markets, Walrasian/Paretian constructs, if inadvertently, an image of the firm in which the cooperative impulse of human agents overcomes the impulse for exploitation arising from differentials in market power. The firm, as an outcome of the rigorous elaboration of general equilibrium thinking, ensures fairness for all cooperating households, expressed as a distribution of the gains from cooperation in rigorous conformity with marginal productivity factor pricing. Moreover, it constitutes a single element in a broader economic structure, driven by tâtonnement, in which the balanced effects of cooperation and competition aim to achieve the greatest augmentation of social welfare by means of individual, self-interested, utility-maximizing behavior. Such a structure not only exemplifies its rationalistic epistemological grounding, as an effort to arrive at the fundamental truth of market economics by means of abstract speculation and introspective deduction, but it unabashedly approximates a utopia in human interaction.
In positing Walrasian/Paretian theory as a species of utopian thinking, we can obviously advance the criticism that it represents an unrealistic analysis and appraisal of the workings of a market economy and that, consequently, theories of the firm emerging from such a construction are of no value. Conversely, to the extent that we view utopian projects as discursive interventions intended to transform the realities that they describe, the image of market economies grounded in cooperation/competition as a dual regulatory mechanism and the imagery of firms as pure, transitory cooperative projects, functioning to enhance the utility of participating households, presents one hopeful starting place in a broader project of enhancing economic democracy in place of exploitation. Evaluating such a theory from a Marxian standpoint, it seems at least as possible to me to extract from Walrasian/Paretian theory a cooperatist/communistic project, articulating progressively participatory, real manifestations of tâtonnement in order to generate a fair, democratic, and, still, efficient distribution of incomes from the assemblage of production factors in collective production. The key point, in this respect, remains epistemological. Insofar as we view Walrasian/Paretian theory as an epistemologically realist, rationalist body of ideas about the workings of a market economy, we foreclose against the possibility of utilizing the theory and its conceptual elements as transformative/performative tools, shaping new efforts to validate non-capitalist, non-exploitative organizational forms.
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