Firm, Theory of The

BIBLIOGRAPHY

The theory of the firm is that branch of economic theory which deals with the determination of the most important economic variables associated with the individual business unit, such as price, output, and growth. There are no readily defined boundaries for the theory, although it is usually distinguished from the theory of production, which deals with the selection of inputs and techniques of production by the firm; from programming, which explains how optimal techniques of production may be discovered; and from the study of business enterprise and the corporation, which have a more institutional focus [See CORPORATION; PRODUCTION; PROGRAMMING]. The theory of the firm is closely associated with the concept of the industry; the industry is composed, roughly, of those firms producing similar products. The relationship between the firm and the industry will be described in some detail later in this article.

The theory of the firm has a considerable history in economic thought, going back at least as far as Cournot (1838) and appearing implicitly a good deal earlier. The development of consumer theory and the basing of economics upon a theory of individual choice obviously called for an analogous development in the treatment of units of production, and after 1900 more and more attention was directed to the theory of the firm.

There are many possible approaches to the theory of the firm. These approaches may be categorized in various ways, the most fruitful of which seem to result from the division between: (a) static and dynamic approaches; (b) those theories that derive their results from the assumption of profit maximization and those that do not; and (c) deterministic and probabilistic theories.

Static and dynamic approaches . By a static theory of the firm we mean a theory that describes the characteristics of a firm in a position of equilibrium. We will deal first with the case in which this equilibrium arises when the firm is maximizing its profits.

The first part of the static theory to be well developed was the theory of the price and output policy of a profit-maximizing monopolist. A monopolist is defined as the only supplier of a particular “commodity.” He is therefore confronted by a market demand curve giving a total revenue (R) that varies with output:

where x is the quantity produced and sold. (Inventories are seldom allowed for in the simple theory.) Total costs (C), which include normal profits, are also affected by output. Normal profits are defined as those only just sufficient to keep the entrepreneur and his firm in the given industry:

Profit is maximized when R—C is maximized, when

i.e., output is set at a profit maximizing level when marginal cost equals marginal revenue and marginal cost is rising faster (or falling less quickly) than marginal revenue.

Perhaps one of the most striking things about this solution is that it makes no assertion about the level of profits. In fact, it is often assumed that the monopolist must make in the normal way profits that are in some sense “supernormal.”

It was the achievement of Pigou (1928) and others to see that some of the results obtained above are in fact of wider applicability and hold for the static theory of the firm in perfect competition as well as in monopoly. The chief differences between the two cases arise from the fact that in perfect competition price is treated as fixed, so that marginal revenue equals price. Thus

where P is the price of the product as seen by the firm. It follows that

This is to say that in perfect competition marginal cost equals price and that marginal cost is rising at the point of equilibrium output. Since in perfect competition entry is free and all factors of production are freely available at given prices, it is also deduced that average cost is equal to price in equilibrium and that average cost is at its lowest at the point of equilibrium output.

The above results are very important in welfare economics and form a part of the basis for asserting the optimality of perfectly competitive systems. [See WELFARE ECONOMICS.] But this fact has led to much confusion in the theory of the firm. It has led some writers to the paradoxical view that the theory of the firm is merely a part of welfare economics and that no evidence of the actual behavior of firms is relevant to the theory. Others have been unwilling to accept any evidence that tends to cast doubt on the universality of perfect competition in the real world. Both of these pitfalls should be carefully avoided.

It was pre-eminently Chamberlin’s contribution (1933) to the static theory of the firm to notice that some degree of monopoly power is consistent with free entry and that the equality of average costs and prices is consistent with monopolistic equilibrium. (This point was noted also by Robinson [1933], but she was, on the whole, more concerned with considering certain special aspects of monopoly theory.) Chamberlin centered the bulk of his attention on achieving the marriage of monopoly and competition, and he proceeded in an elaborate diagrammatic exposition to show how it could be accomplished in certain hitherto unexplored situations.

The Chamberlinian relationship which is best known is summarized in Figure 1. Here all firms are assumed to have identical cost curves and identical demand curves. CC’ is the average cost curve of any one of the firms. DD’ is the demand curve confronting any one of the firms, after allowance is made for exit and entry of firms and for the assumption that all firms charge identical prices: dd is the demand curve that would face the firm if it could alter its prices without action or reaction by its competitors. In equilibrium the number of firms must adjust until all firms make only normal profits, and each firm still remaining in the industry believes that it is making maximum profits. This will occur at point T in Figure 1 if each firm believes its rivals will ignore its price policy.

Chamberlin’s argument for the universal applicability of his models seems, in retrospect, somewhat unconvincing. Even if the economic world is in the main some blend of monopolistic and competitive elements, there is no reason to think that it is the very simplified blend that Chamberlin has assumed. If the world is more complex than Chamberlin has surmised, it is at least possible that other models, and perhaps simpler models, may be more useful predictors of economic behavior. The merits of any consistent model are not to be determined so much by argument as by performance.

An alternative to Chamberlin’s approach has emerged from the development of the theory of oligopoly. Indeed, some writers seem to claim that oligopoly is in fact the norm in nonperfectly competitive markets. Unfortunately there are many competing oligopoly theories; they are not always presented in testable form; those that are testable in principle would often be difficult to distinguish empirically; and little testing has so far been attempted.

The dynamic theory of the firm has, on the other hand, received only limited treatment. The outstanding

contribution to the subject is probably contained in Hicks (1939). Hicks’s treatment is, however, confined to a discussion of intertemporal equilibrium. The question of the path of adjustment to a new equilibrium position, or the extent to which the costs of the firm depend upon the production experience of the firm, has been largely ignored until recent years (Clower 1959; Arrow 1962).

Profit maximization . Next we turn to the controversy over the role of profit maximization in the theory of the firm. The assumption of profit maximization has proved a very useful starting point for investigations in many areas closely connected with the theory of the firm, particularly in the theory of investment and replacement. But some economists have been suspicious of the profit maximization assumption and have preferred to substitute something else. This substitute has usually taken one of two forms: utility maximization or behavioral relations. The former is generally used in static equilibrium systems, the latter are usually not. An example of utility maximization is provided by the work of Scitovsky (1943). He shows in effect that if entrepreneurs maximize utility rather than profit, if utility is influenced by effort, and if effort is related to the size of output, then the traditional deductions of minimum average costs, in equilibrium, of perfect competition will be falsified.

An alternative utility maximization hypothesis asserts that utility is affected by the level of expected profits and by the variance of these profits. If variance decreases with output, the entrepreneur might, for example, decide to operate at outputs above minimum cost output, even under conditions of perfect competition.

One group of writers, of whom the best known is Papandreou (1952), has tended to argue that a large number of considerations will enter the utility function of the entrepreneur, so that propositions derived from profit maximizing assumptions are bound to be misleading. This approach is no doubt highly plausible, but the advantage of plausibility is purchased at the expense of any meaningful hypothesis. Putting it another way, while we increase the immediate acceptability of the theory of the firm by increasing the number of variables that the firm is said to consider in maximizing utility, we achieve this by reducing the number of testable results of the theory.

Some writers have felt that the deduction of the behavior of the firm from static equilibrium models is beyond the present powers of the economist and have instead directed their attention to the formulation of behavioral hypotheses about the firm. Such hypotheses may or may not be consistent with the profit maximization hypothesis. One of the leading species of this genus is the so-called “full-cost pricing principle.” Roughly, this asserts that prices of manufactured products will be set at a level that will yield a “normal” profit to a firm operating with modern equipment at a high level of capacity utilization. A great deal of effort has been expended in trying to show that such behavior is consistent with profit maximization. However, the behavioral hypothesis itself, which was first suggested by interviews with businessmen, cannot be said to have been subjected to rigorous statistical testing.

Somewhat similar remarks can be made about many of the alternative behavior hypotheses that have been offered for consideration. It has, for example, been suggested that firms aim at maximizing their share of the market rather than their profits. It has also been suggested that firms “satisfice”-that is, that they only seek to increase profits if profits fall below a certain “acceptable” level. In both these cases it can be said that discussion has been aimed more at finding justifications for these hypotheses than at testing their validity by observation. A similar difficulty has plagued efforts to develop a behavioral theory of the growth of the firm.

The theories discussed above have been concerned with explaining only the main features of the behavior of firms. Recently, however, effort has been devoted to the development of models that could predict the detailed conduct of business units in particular aspects of their work. Thus the detailed pricing policy of a particular department of a department store may be studied and a formula found that will enable us to predict this behavior. Much of this work has been stimulated by the suggestions of H. A. Simon (1959), and it remains until now largely descriptive in character. Little effort has been directed toward rationalizing the observed behavior in terms of profit maximization or utility maximization. It may indeed be surmised that simple explanations of detailed behavior patterns would be difficult in models excluding uncertainty and decision costs.

Probabilistic theories . Another line of development in the theory of the firm involves a twofold departure from the neoclassical formulation. First, the notion of static equilibrium of the individual firm is abandoned. Second, the focus changes from deterministic theories of the behavior of a single firm to probabilistic rules about the behavior of large groups of firms. This approach is also behavioral in orientation. While there may be a recognition of the desire for profit maximization, its effect is in many individual cases swamped by a myriad of other forces. As a result, the impact of any change in parameters at best changes the probabilities that govern the conduct of the firm.

The originator of this approach to the theory of the firm appears to have been Alfred Marshall. In the second edition of his Principles of Economics (1890) Marshall introduced the notion of the “representative firm” to explain the determination of long run supply price. The representative firm is not any particular firm; rather it is a descriptive fiction by means of which Marshall attempted to amalgamate a dynamic probabilistic theory of the firm with an essentially static and deterministic theory of price determination for the industry.

Marshall’s attempt to harness the static with the dynamic approaches was vigorously rejected by most of his successors. Foremost among the critics was Robbins (1928), who objected correctly but irrelevantly that Marshall’s implied theory of the firm was inconsistent with static equilibrium assumptions.

Marshall’s approach fell into disuse for nearly 25 years but was re-established by P. K. Newman and J. N. Wolfe (1961). They showed that the Marshallian doctrine could be interpreted in terms of the stationary state of a probabilistic (Markov) process. [See MARKOV CHAINS.] It was shown that if the probabilistic laws governing the rise and decline of firms were affected by the price of the product, then a particular size distribution of firms and consequently a particular output would emerge from each price. It will be seen that this formulation allows by means of a single process the simultaneous determination of price, output, and the size distribution of firms.

More concretely, we may imagine the probability that a firm will change its size in any period as being governed by a “transition matrix,” or matrix of transition probabilities, A . This takes the following form:

where a₁₂, for example, is the probability that a firm in the first size-class at a particular period will be in the second size-class one period later. (The figures on the left-hand margin and across the top of the matrix are of course the various size-classes.)

If the matrix A obeys certain so-called Markovian assumptions, its continued application to a large group of firms will ultimately produce a definite size distribution that is independent of their initial distribution. And if the entries in the transition matrix are not fixed but are different for each price prevailing, there will be a different size distribution of firms for each particular equilibrium price. [See MARKOV CHAINS.]

This sketch of the probabilistic theory of the firm is necessarily incomplete. It will, however, be seen that this theory has the merit of dealing with the firm more nearly in the context in which it appears in real life than does a static theory. Nevertheless, the theory remains highly abstract, and its practical usefulness has yet to be demonstrated.

It will be apparent that the theory of the firm is moving increasingly in the direction of empirical science—that is, toward the formulation and testing of hypotheses about how firms actually behave. This is true whether the hypothesis being put forward is cast in deterministic or probabilistic form. It is at the same time less tied to the assumption of profit maximization. But profit maximization has not lost its usefulness, however frequently it may seem to be contradicted as a descriptive hypothesis. Profit maximization will always be the aim of at least some firms during at least some portion of their history. And so we would expect that profit maximization would continue to play an important role in the normative aspect of the theory of the firm.

The firm and the industry . The notion of the industry goes far back in economic thought; it probably derived intact from the market place. By the time of Marshall’s Principles of Economics (1890) it had come to occupy an important place in economic theory. The industry was there defined as a group of firms producing an identical product. This definition is highly ambiguous, but to some it seemed to imply a homogeneity of output that was most easily related to a state of perfect competition. Chamberlin’s assumption of identical cost and demand curves for all firms enabled him to work with “groups” that behaved rather like Marshallian industries. But the abandonment of perfect competition created difficulties for the concept of the industry, once differences in cost and demand conditions between firms were admitted. In the first place, firms might be selling apparently identical products at different prices. Moreover, as Robinson (1933) pointed out, a shift of demand in a perfectly competitive industry would (in the absence of external economies at any rate) have an unambiguous effect upon price and output, while in an imperfectly competitive “industry” it might not. The latter seemed a particularly damaging point, since one of the main motives for the development of the theory of the firm seems to have been to obtain greater certainty about the shape of the industry supply curve. Finally, Triffin (1940) argued that general equilibrium under conditions of nonperfect competition admitted no clear conceptual division between industries. Perhaps partly as a result of these arguments there has been a tendency for theoretically oriented economists to avoid using the concept of the industry and to some extent to neglect the study of the determinants of supply.

From a pragmatic point of view these developments seem ill judged. Ever since Plato and Aristotle, philosophers have been vexed by the problems of finding useful categories under which the large numbers of slightly differing objects we see about us can be grouped. Any such grouping is almost always an abstraction, and the important question is not whether it is a truly homogeneous grouping but whether it is a useful grouping. On the basis of the experience of students of economic institutions, the concept of the industry appears a highly useful abstraction for many purposes, although not for all. The spread of quantitative techniques seems likely to reinforce that conclusion, since statistics are usually available only on an industry basis. Indeed, from the statistical point of view the problem of defining the industry appears to arise from asking the wrong questions. The question should be whether some characteristics of a group of firms (e.g., the mean output of the firms or the mean price charged by them for their products) change in a statistically significant way as the result of changes in some specified variable. It would be difficult in an uncontrolled situation to test for the effects of a very large number of variables. The preponderating influence of a small number of strategic variables is an assumption that must be satisfied if testing is to give useful results. These strategic variables may be those predicted by standard theory or they may not, but this question is one of fact and not of theory.

The conclusion seems to be that the concept of the industry may well remain of great practical use whatever theory of the firm is adopted. This was one of the essential messages of Marshall’s “representative firm.” In that construct the “industry” is preserved, although firms are neither in equilibrium nor perhaps even operating under conditions of perfect competition. In this respect at least, Marshallian notions appear to have had a more “modern” empirical flavor than most of the later work on the theory of firm and industry. [See MARKETS AND INDUSTRIES.]

External economies. A good deal of attention has been given to the effect of changes in the total output of the industry upon the costs of the individual firms in the industry. These effects are termed “external economies” when the costs of production of the firms in the industry are lowered by an increase in the output of the industry. Since it is commonly argued that all firms have identical minimum costs in the long run equilibrium of perfect competition, all firms will in this case be affected equally.

It is usual to distinguish between pecuniary external economies, which arise through reduced factor prices, and technological external economies, which arise through improved organization of industry. The latter are most significant from the welfare point of view, but much doubt has been expressed about the frequency of their occurrence in a perfectly competitive milieu. However, for political or other reasons it may be impossible to enforce perfect competition, and the external economies associated with monopoly may be of great practical importance in some lines.

Scitovsky (1954) has suggested that a further source of external economies would arise if different stages of production were expanded (or contracted) in an uncoordinated way. Such external economies are essentially temporary in character. However, where monopolistic conditions are present, this type of external economy may lead to the permanent neglect of otherwise profitable investment opportunities.

It would appear that the estimation of the actual size of external economies in particular industries would be extremely useful. The task is made difficult, however, by the absence of data, by the uneven pace of technical advance, and by the great variation among the production processes performed by firms that are perforce lumped together in the same “industries.” [See EXTERNAL ECONOMIES AND DISECONOMIES.]

J. N. WOLFE

[See alsoCOMPETITION; MONOPOLY; OLIGOPOLY. Other relevant material may be found inDECISION MAKING, article onECONOMIC ASPECTS.]

BIBLIOGRAPHY

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