Every first or second year microeconomics text book has a chapter on the "theory of the firm" which doesn't make sense since the 'firm' doesn't really exist in neoclassical theory. There is a theory of supply, but no real theory of the firm.
As has been pointed out by Demsetz (1982, 1988 and 1995) before Knight (1921) and Coase (1937) the fundamental preoccupation of economists was with the price system and hence little attention was paid to the firm as a separate, important, economic entity. Firms existed as handmaidens to the price system.
The interest in the price system, culminating in the "perfect competition" model, has its intellectual origins in the eighteenth-century debate between free traders and mercantilists. This debate wasn't about competition, in any meaningful sense, and it wasn't about the existence and organisation of the firm; it was about the proper scope of government in an economy, and the model it gave rise to reflects this. The central question of the debate was, Is central planning necessary to avoid the problems of a chaotic economic system? Adam Smith famously answered no.
For Smith, markets are one very prominent mechanism for solving the problems of coordination and motivation that arise with interdependencies of specialisation and the division of labour. Market institutions leave individuals free to pursue self-interested behaviour, but guide their choices by the prices they pay and receive. The following 200 hundred years amounted to a closer examination of the conditions necessary for the price system to be able to avoid chaos.
The formal model that arose from this examination is one which abstracts completely from any form of centralised control in the economy. It is a model delineated by "perfect decentralisation". Authority, be it in the form of a government or a firm or a household, plays no role in coordinating resources. The only parameters guiding decision making are those given within the model - tastes and technologies - and those determined impersonally on markets -prices. All parameters are outside the control of any of the economic agents and this effectively deprives all forms of authority a role in allocation. This includes, of course, the firm. It doesn't matter whether it is general equilibrium, characterised by Walras's auctioneer, or partial equilibrium, characterised by Marshall's representative firm, there is no serious consideration given to the firm as a problem solving institution.
In neoclassical theory, the firm is a 'black box' there to explain how changes in inputs lead to changes in outputs. The firm is a conceptualisation that represents, formally, the actions of the owners of inputs who place their inputs in the highest value uses, and makes sure that production is separated from consumption. The firm produces only for outsiders, there is no on the job or internal consumption, no self-sufficiency. In fact there are no managers or employees to indulge in on the job consumption and as production is separated from consumption, no self-sufficiency. Production for outsiders is, according to Demsetz (1995), the definition of a firm in the neoclassical model: "[w]hat is needed is a concept of the firm in which production is exclusively for sale to those formally outside the firm. This requirement defines the firm (for neoclassical theory), but it has little to do with the management of some by others. The firm in neoclassical theory is no more or less than a specialized unit of production, but it can be a one-person unit." (Demsetz 1995: 9). As inputs are combined in the optimal fashion by the actions of independent owners of inputs motivated solely by market prices, there is no need for 'management of some by others', there is no role for managers or employees. Also note that as competition assures the absence of profits and losses in equilibrium, there is no need to have a residual claimant. This means that, in one sense at least, there are no owners of the firm. As there are no physical assets controlled by the firm, there are no (residual) control rights over these assets to allocate. This implies there are no owners of the firm in the Grossman/Hart/Moore sense.
Hart (1995) criticises the neoclassical model based on three characteristics of the theory. First, he notes that the theory completely ignores incentive problems within the firm. The firm is a perfectly efficient 'black box'. Second, the theory has nothing to say about the internal organisation of the firm. Nothing is said about the hierarchical structure, how decisions are made, who has authority within a firm. Third, the theory tells us nothing about how to pin down the boundaries of the firm. The theory is as much a theory of plant or division size as firm size. As Hart points out "[t]o put it in stark terms ... neoclassical theory is consistent with there being one huge firm in the world, with every existing firm ... being a division of this firm. It is also consistent with every plant and division of an existing firm becoming a separate and independent firm." (Hart 1995: 17).
Cyert and Hedrick (1972) addressed similar points. They argue that in the neoclassical system the firm doesn't exist, that no real world problems of firms are considered, that there are no organisational problems or any internal decision-making process at all. "In one sense the controversy over the theory of the firm has arisen over a non-existent entity. The crux of microeconomics is the competitive system. Within the competitive model there is a hypothetical construct called the firm. This construct consists of a single decision criterion and an ability to get information from an external world, called the "market" [8, Cyert and March, 1963, pp. 4-16]. The information received from the market enables the firm to apply its decision criterion, and the competitive system then proceeds to allocate resources and produce output. The market information determines the behavior of the so called firm. None of the problems of real firms can find a home within this special construct. There are no organizational problems nor is there any room for analysis of the internal decision-making process." (Cyert and Hedrick 1972: 398). Thus within the neoclassical model of the price system, the firm's only role is to allow input owners to convert inputs into outputs in response to market prices. Firms have no internal organisation since they have no need of one, they have no owners since there is nothing to own. Questions about the existence, definition and boundaries of the firm are to a large degree meaningless within this framework since firms, by any meaningful definition of that term, don't really exist.
As Foss, Lando and Thomsen (1998) summarise it: "The pure analysis of the market institution leaves almost no room for the firm (Debreu 1959). Under the assumption of a perfect set of contingent markets, as well as certain other restrictive assumptions, the model describes how markets may produce efficient outcomes. The question how organizations should be structured does not arise, because market-contracting perfectly solves all incentive and coordination issues. By assumption, firm behaviour (profit maximization) is invariant to institutional form (e.g. ownership structure). The whole economy can operate efficiently as one great system of markets, in which autonomous agents enter into very elaborate contracts with each other. However, by treating the firm itself as a black box, where internal structure, contracts, etc. disappear from the picture, there are many other issues that the theory cannot address. For example, the theory does not tell us why firms exist." (Foss, Lando and Thomsen 1998: 1-2).
Thus we see the dichotomy between theory and practice: in practice the firm is the "dominant feature of the landscape" while in the neoclassical theory, the 'firm' does not exist.
Coase, Ronald Harry (1937). 'The Nature of the Firm', Economica, n.s. 4 no. 16 November: 386-405.
Cyert, Richard M. and Hedrick, Charles L. (1972). 'Theory of the Firm: Past, Present, and Future; An Interpretation', Journal of Economic Literature, 10(2) June: 398-412.
Cyert, Richard M. and March, James G. (1963). A Behavioral Theory of the Firm, Englewood Cliffs, New Jersey: Prentice-Hall, Inc.
Debreu, Gerard (1959). Theory of Value, New York: Wiley.
Demsetz, Harold (1982). Economic, Legal, and Political Dimensions of Competition, Amsterdam: North-Holland Publishing Company.
Demsetz, Harold (1988). 'The Theory of the Firm Revisited', Journal of Law, Economics, and Organization, 4(1) Spring: 141-61.
Demsetz, Harold (1995). The Economics of the Business Firm: Seven Critical Commentaries, Cambridge: Cambridge University Press.
Foss, Nicolai J., Lando, Henrik and Thomsen, Steen (1998). 'The Theory of the Firm', Working Paper, August 24.
Hart, Oliver D. (1995). Firms, Contracts, and Financial Structure, Oxford: Oxford University Press.
Knight, Frank H. (1921). Risk, Uncertainty and Profit, Boston: Houghton Mifflin Company.