A THEORY OF OLIGOPOLY GEORGE J. STIGLER' University of Chicago N O ONE has the right, and few the ability, to lure economists into reading another article on oli- gopoly theory without some advance in- dication of its alleged contribution. The present paper accepts the hypothesis that oligopolists wish to collude to maximize joint profits. It seeks to reconcile this wish with facts, such as that collusion is impossible for many firms and collusion is much more effective in some circum- stances than in others. The reconciliation is found in the problem of policing a col- lusive agreement, which proves to be a problem in the theory of information. A considerable number of implications of the theory are discussed, and a modest amount of empirical evidence is pre- sented. I. THE TASK OF COLLUSION A satisfactory theory of oligopoly can- not begin with assumptions concerning the way in which each firm views its interdependence with its rivals. If we ad- here to the traditional theory of profit- maximizing enterprises, then behavior is no longer something to be assumed but rather something to be deduced. The firms in an industry will behave in such a way, given the demand-and-supply functions (including those of rivals), that their profits will be maximized. The combined profits of the entire set of firms in an industry are maximized when they act together as a monopolist. At 1 I am indebted to Claire Friedland for the sta- tistical work and to Harry Johnson for helpful criti- cisms. least in the traditional formulation of the oligopoly problem, in which there are no major uncertainties as to the profit-maxi- mizing output and price at any time, this familiar conclusion seems inescap- able. Moreover, the result holds for any number of firms. Our modification of this theory con- sists simply in presenting a systematic account of the factors governing the feas- ibility of collusion, which like most things in this world is not free. Before we do so, it is desirable to look somewhat critically at the concept of homogeneity of prod- ucts, and what it implies for profit-maxi- mizing. We shall show that collusion normally involves much more than "the" price. Homogeneity is commonly defined in terms of identity of products or of (what is presumed to be equivalent) pairs of products between which the elasticity of substitution is infinite. On either defini- tion it is the behavior of buyers that is decisive. Yet it should be obvious that products may be identical to any or every buyer while buyers may be quite different from the viewpoint of sellers. This fact that every transaction in- volves two parties is something that economists do not easily forget. One would therefore expect a definition of homogeneity also to be two-sided: if the products are what sellers offer, and the purchase commitments are what the buyers offer, full homogeneity clearly in- volves infinite elasticities of substitution between both products and purchase 44
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A THEORY OF OLIGOPOLY 45 commitments. In other words, two prod- ucts are homogeneous to a buyer if he is indifferent between all combinations of x of one and (say) 20 - x of the other, at a common price. Two purchase commit- ments are homogeneous to a seller if he is indifferent between all combinations of y of one and (say) 20- y of the other, at a common price. Full homogeneity is then defined as homogeneity both in products (sellers) and purchase com- mitments (buyers). The heterogeneity of purchase com- mitments (buyers), however, is surely often at least as large as that of products within an industry, and sometimes vastly larger. There is the same sort of per- sonal differentia of buyers as of sellers- ease in making sales, promptness of pay- ment, penchant for returning goods, like- lihood of buying again (or buying other products). In addition there are two differences among buyers which are per- vasive and well recognized in economics: 1. The size of purchase, with large differences in costs of providing lots of different size. 2. The urgency of purchase, with possibly suf- ficient differences in elasticity of demand to invite price discrimination. It is one thing to assert that no im- portant market has homogeneous trans- actions, and quite another to measure the extent of the heterogeneity. In a regime of perfect knowledge, it would be possible to measure heterogeneity by the variance of prices in transactions; in a regime of imperfect knowledge, there will be dispersion of prices even with trans- action homogeneity.2 The relevance of heterogeneity to col- lusion is this: It is part of the task of maximizing industry profits to employ a 2 Unless one defines heterogeneity of transactions to include also differences in luck in finding low price sellers; see my "Economics of Information," Journal of Political Economy, June, 1961. price structure that takes account of the larger differences in the costs of various classes of transactions. Even with a single, physically homogeneous product the profits will be reduced if differences among buyers are ignored. A simple illus- tration of this fact is given in the Appen- dix; disregard of differences among buyers proves to be equivalent to imposing an excise tax upon them, but one which is not collected by the monopolist. A price structure of some complexity will usually be the goal of collusive oligopolists. II. THE METHODS OF COLLUSION Collusion of firms can take many forms, of which the most comprehensive is outright merger. Often merger will be inappropriate, however, because of dis- economies of scale, and at certain times and places it may be forbidden by law. Only less comprehensive is the cartel with a joint sales agency, which again has economic limitations-it is ill suited to custom work and creates serious ad- ministrative costs in achieving quality standards, cost reductions, product inno- vations, etc. In deference to American antitrust policy, we shall assume that the collusion takes the form of joint deter- mination of outputs and prices by osten- sibly independent firms, but we shall not take account of the effects of the legal prohibitions until later. Oligopoly existed before 1890, and has existed in countries that have never had an antitrust policy. The colluding firms must agree upon the price structure appropriate to the transaction classes which they are pre- pared to recognize. A complete profit- maximizing price structure may have 3 If the firms are multiproduct, with different product structures, the diseconomies of merger are not strictly those of scale (in any output) but of firm size measured either absolutely or in terms of variety of products.
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46 GEORGE J. STIGLER almost infinitely numerous price classes: the firms will have to decide upon the number of price classes in the light of the costs and returns from tailoring prices to the diversity of transactions. We have already indicated by hypothetical exam- ple (see Appendix) that there are net profits to be obtained by catering to dif- ferences in transactions. The level of col- lusive prices will also depend upon the conditions of entry into the industry as well as upon the elasticities of demand. Let us assume that the collusion has been effected, and a price structure agreed upon. It is a well-established proposition that if any member of the agreement can secretly violate it, he will gain larger profits than by conforming to it.4 It is, moreover, surely one of the axioms of human behavior that all agreements whose violation would be profitable to the violator must be enforced. The liter- ature of collusive agreements, ranging from the pools of the 1880's to the elec- trical conspiracies of recent times, is re- plete with instances of the collapse of conspiracies because of "secret" price- cutting. This literature is biased: con- spiracies that are successful in avoiding an amount of price-cutting which leads to collapse of the agreement are less likely to be reported or detected. But no conspiracy can neglect the problem of enforcement. Enforcement consists basically of de- tecting significant deviations from the agreed-upon prices. Once detected, the deviations will tend to disappear because they are no longer secret and will be matched by fellow conspirators if they are not withdrawn. If the enforcement is weak, however-if price-cutting is de- tected only slowly and incompletely- 4 If price is above marginal cost, marginal reve- nue will be only slightly less than price (and hence above marginal cost) for price cuts by this one seller. the conspiracy must recognize its weak- ness: it must set prices not much above the competitive level so the inducements to price-cutting are small, or it must re- strict the conspiracy to areas in which enforcement can be made efficient. Fixing market shares is probably the most efficient of all methods of combat- ing secret price reductions. No one can profit from price-cutting if he is moving along the industry demand curve,' once a maximum profit price has been chosen. With inspection of output and an appro- priate formula for redistribution of gains and losses from departures from quotas, the incentive to secret price-cutting is eliminated. Unless inspection of output is costly or ineffective (as with services), this is the ideal method of enforcement, and is widely used by legal cartels. Un- fortunately for oligopolists, it is usually an easy form of collusion to detect, for it may require side payments among firms and it leaves indelible traces in the output records. Almost as efficient a method of elimi- nating secret price-cutting is to assign each buyer to a single seller. If this can be done for all buyers, short-run price- cutting no longer has any purpose. Long- run price-cutting