Competition as a Specific Market Structure
Smith considered free competition as a synonym of the “obvious and simple system of natural liberty” IV.ix.51), an ideal benchmark against which various sociopolitical arrangements may be compared and assessed (Aspromourgos 2009: ch.
5). Therefore, his notion of competition is far removed from the contemporary notion of competition as a specific market structure, alongside pure monopoly, monopolistic competition, duopoly a la Cournot, a la Bertrand, a la Stackelberg, and so on. In this latter context, the various market structures are defined in terms of well-defined assumptions concerning the characteristics of the goods produced, the technology of production, the elasticity of demand, the number and size of existing firms, the nature and significance of entry/exit barriers, the type of firms’ conjectures on rivals’ reactions etc. In particular, a perfectly competitive market is characterized by the assumption that each competitor faces a perfectly horizontal demand curve, that is, she takes market price as a parametric datum when she chooses the profit-maximizing quantity to produce. (As noted by Arrow 1959 and now acknowledged by some contemporary advanced textbooks, the price-taking assumption drastically reduces the theoretical domain of the perfect competition model just to Walrasian equilibrium states. In fact, consumers and producers have no incentive to quote a price different from the ruling market price if and only if the ruling market price is the Walrasian market-clearing price: see Mas-Colell et al. 1995: 314, fn. 1, and 315.) The price-taking behaviour by each competitor is usually justified by the further assumptions that (1) competitors are so many as to make a collusive agreement unfeasible and (2) each competitor is “small” in relation to the extent of the market. (Formally, the market is inhabited by a continuum of traders: see Aumann 1964.) As is well-known, the “negligibility” assumption was first introduced into the economic literature by Antoine-Augustin Cournot in chapter 8, “Of unlimited competition”, of his Recherches sur les Principes Mathematiques de la Theorie des Richesses:The effects of competition have reached their limit, when each of the partial productions Dk is inappreciable, not only with reference to the total production D = F(p), but also with reference to the derivative F,(p), so that the partial production Dk could be subtracted from D without any appreciable variation resulting in the price of the commodity.
(Cournot 1838 [1897]: 90, original emphasis)Cournot justifies his “negligibility” assumption on the basis of two different arguments, one empirical and one formal: he claims that the assumption holds true for “a multitude of products, and, among them, for the most important products” and “[i]t introduces a great simplification into the calculations” (ibid.). Cournot does not further elaborate the empirical argument; while he investigates at length the formal argument. In fact, Cournot writes down the profit-maximizing equation for the k-th firm as:
where Dk is the quantity produced by the k-th firm, p the market price (goods are homogeneous to the effect that there is just one market price), D = D1 +... + Dn = F(p) the market demand function and Φk(Dk) the marginal cost function of the k-th firm, respectively. The above equation, with some manipulation, turns out to be the now familiar marginal revenue-marginal cost equality. (As noted by Magnan de Bornier (1992), with the single notable exception of section 43 where the famous duopoly model is introduced, Cournot consciously uses p and not D as the independent variable in the maximization problem.) Thanks to the negligibility assumption the above equation boils down to:
which is the price-marginal cost equality of any textbook model of perfect competition.
It may be worth stressing that Leon Walras too endorses an empirical argument similar to Cournot’s but he defends it at length. Walras is ready to admit that markets best organized from the point of view of competition are auction markets, where there are “stockbrokers, commercial brokers or criers acting as agents who centralize transactions in such a way that the terms of every exchange are openly announced and an opportunity is given to sellers to lower their prices and to buyers to raise their bids” (Walras, 1874 [2003]: 84); but he insists that his view of competition is not in the least confined to auction markets and he goes on enumerating a series of real world markets where competition works quite adequately, notwithstanding the absence of centralized transactions.
And he concludes by saying that: “the whole world may be looked upon as a vast general market made up of diverse special markets where social wealth is bought and sold” (ibid.).Some decades after Cournot’s path-breaking but long-neglected contribution, the notion of competition as a specific market structure has been refined and enriched by the analyses of the Law of Indifference (Jevons 1871), the recontracting (Edgeworth 1881) and tatonnement (Walras 1874) processes, the role of returns to scale and the optimal dimension of competitive firms (Wicksell 1901-06 [1934]), the stationary state (J.B. Clark 1902) and the relationship between (extra)profits and uncertainty (Knight 1921). Finally, the market structure notion of competition has been codified in the course of the imper- fect/monopolistic competition revolution of the early 1930s launched by Joan Robinson (1933) and Edward Chamberlin (1933). (Stigler 1957, Backhouse 1990 and High 2001 provide excellent historical reconstructions of the notion of perfect competition, while Tsoulfidis 2009 explores the issue of monopolistic competition as a failed revolution in the field of value theory. For a stimulating reformulation of the perfect competition model without the price-taking assumption see Makowski and Ostroy 2001.)