The Theory of Monopolistic Competition: EH

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The Theory of Monopolistic Competition: E.H. Chamberlin's Influence on Industrial Organisation Theory over S i x t y Years by R. Rothschild* University of Lancaster, Lancaster, UK

Introduction In 1933, Edward H. Chamberlin published the Theory of Monopolistic Competition (1962). The work, based upon a dissertation submitted for a PhD degree in Harvard University in 1927 and awarded the David A. Wells prize for 1927-28, has since become a milestone in the development of economic thought. Its impact on industrial organisation theory, general equilibrium and welfare economics, international trade theory and, to a greater or lesser degree, all other branches of economic analysis, has been pervasive and enduring. The ideas set out in the book have been developed, expanded and refined in ways too numerous to be identified precisely, and the books and articles which take Chamberlin's contribution as a starting point arguably exceed in number those on any other single subject in the lexicon of economics[l]. Its status in the history of economic thought notwithstanding, the Theory of Monopolistic Competition is in many ways a rather unsatisfactory work. It rests upon assumptions which describe a world for which there is no empirical analogue: it seems, in its original form at least, to be a solution in search of a problem. Indeed, from a modern perspective, it would appear that the impact of the "Chamberlinian" contribution is due less to the insights contained in the Theory than to the efforts of those whose work has made up the research progamme which was set in train in 1927. The purpose of this paper is to consider some of the links between Chamberlin's ideas and the developments to which these ideas gave rise. In doing so, we shall hope to place in perspective his early contribution to what is now known as "Industrial Organisation" theory, and thereby to demonstrate the power and enduring influence of his role in the evolution of economic thought. Chamberlin's Contribution The Theory of Monopolistic Competition deals with two types of market. The first, to which Chamberlin gave relatively little attention in the book itself, involves a small number of firms (oligopolists) who face a choice between myopic competition of the kind first discussed by Cournot (1838), and joint-profit maximisation. Chamberlin's * This paper was written in large part while the author was Visiting Fellow at the Australian Graduate School of Management, University of New South Wales, Sydney.

Chamberlin and Industrial Organisation Theory

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particular contribution was to show that the recognition of mutual interdependence on the part of firms in the small numbers case is a necessary, if not sufficient[2] condition for the attainment of a Pareto optimal outcome[3]. Although he chose to relegate the discussion of the oligopoly case to a few pages, Chamberlin was in later years to regard this market form as being of central importance in economic analysis (see Chamberlin, 1957, 1961; Kuenne, 1967; and Skinner, 1983). The second type of market which Chamberlin considered — and upon which we shall focus in this discussion — is the "large group". It was in this context that he sought to identify the key features of monopolistic competition. For the purposes of his model Chamberlin regarded industries as being made up of "groups" of products, each in turn being made up of close, but less than perfect substitutes. Groups could themselves be distinguished from one another by the degree of substitutability of their respective products, in this case taken to be smaller than that between varieties within a given group. The classification of industries on this basis was not universally accepted[4], in part because of the marked pervasiveness and complexity of product differentiation in practice. Even after six decades, the problems of definition and the need to find a satisfactory basis for classification remain[5]. However, Bain (1967, p. 153) has observed that, despite its shortcomings, Chamberlin's conceptualisation has: proved formally satisfactory, tractable and productive of meaningful hypotheses...by assuming explicitly that the enterprise economy is made up of industries that are identified and separated by the cross-elasticities of demand among products, and by then classifying such industries according to their market structures The elements of the large group model can be described with the aid of Figures 1 and 2. Let the industry initially comprise N firms, each producing a single variety of the differentiated product. For the sake of simplicity, suppose that at any price p the amount sold by any individual firm is 1/Nth of the total market demand. Let costs be the same for all firms (in this case, the traditional U-shaped average total cost curve is appropriate) and suppose that the prevailing price yields a surplus over costs. Suppose further that, initially, entry into the group is blocked. Under Chamberlin's assumptions, each firm will perceive an opportunity to increase its profits by lowering its price, provided that none of its competitors does the same. On the basis of this belief, each firm will expect to increase its sales by moving down its (relatively elastic) ceteris paribus demand curve (dd); but if all firms were to behave in similar fashion, then each would find that its sales are given by the (more inelastic) "share-of-the market" demand curve (DD). Chamberlin argues that the conjecture of each firm to the effect that it can gain at the expense of its rivals will be rendered invalid by the fact that all behave in this manner, each motivated by the belief that its price reduction will have negligible (and equal) impact upon the sales of all others. The result is that all firms find themselves on their respective DD curves. Yet none is encouraged to revise its expectations: each reduces price still further, until ultimately only normal profits are obtained. When the possibility of free entry and exit is considered explicitly, the process, starting at an arbitrary price above average total costs, is similar, except that now the location of the DD curve is determined by the size of N. Super-normal profits attract new entrants, and the DD curve shifts leftward at the same time as the individual

36 Journal of Economic Studies 14,1

firms undertake their myopic price reductions. The shift is halted when the prevailing market price equals average total costs, but if at this point firms continue to perceive opportunities for profitable price reductions, then these will take place. Eventually, a point is reached at which all firms make losses, yet each conjectures that, provided that none of its rivals behaves as it does, profitability will be restored through one final price reduction. Since all firms entertain this naive expectation the result is that losses are increased for all. The difficulties are resolved through the exit of some firms, an action which has the effect of shifting the DD curve to the right. Eventually, a Cournot equilibrium is attained where the dd curve is tangent to the average total cost curve. At this point, no firm has an incentive to change its price, and neither entry nor exit will take place. Here, a uniform price, equal to average costs, obtains for all firms, but each produces an output smaller than that which would be produced if


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the dd curve were horizontal, as it is under conditions of perfect competition. This phenomenon encouraged Chamberlin to the view that monopolistic competition would give rise to a "waste" of resources: too many varieties will be produced, each on too small a scale. The Theory of Monopolistic Competition contains a substantial discussion of selling costs. The ideas put forward by Chamberlin are discussed in some detail in Abbott (1955), but much recent work in this area has departed from Chamberlin's original treatment. For this reason, we shall omit from our review this aspect of the "large group" case. However, it would be inappropriate to accord similar treatment to the question of product variation as a competitive device, and much of the following discussion will address this key issue. For the purposes of this survey, we identify four aspects of the Chamberlin model as it has been set out here:


(3) the assumptions on the nature and consequences of "entry" (and "exit"); and (4) the question of the "optimality" of product variety. Symmetry and Myopia Chamberlin's analysis rests heavily upon two interrelated assumptions. The first is that any firm contemplating a price reduction expects to attract a very small proportion of custom from each of its competitors; the second is that this proportion is the same for all of those competitors. Consequently, every prospective price-cutter believes that other firms will lose so small a proportion of their customers that none will respond by cutting its own price. According to Chamberlin, this belief is correct, but because each acts on this basis market price must fall. These two assumptions are themselves closely linked with, and indeed provide the rationale for, Chamberlin's implicit assumptions about the price cross-elasticities of demand for all pairs of products, and their apparent insensitivity to changes in the number of varieties in the product group. There are two separate issues involved here. The first concerns Chamberlin's assertions about symmetry and the negligible effect of firms' price reductions on the sales made by their rivals. The second concerns the myopia to which these perceptions, when shared by the agents themselves, give rise. These issues are of central importance, because the assumption that firms are myopic in their pursuit of profits is justified only if they consider that their actions have negligible impact upon each and every one of their competitors. Any other conjecture raises the question of structural interdependence, and the notion of comparative anonymity of the individual firm in the large group is replaced by a more complex and less tractable set of relationships. Dixit and Stiglitz (1977) have shown formally that the consumer-theoretic basis of the Chamberlin model requires that demands be generated by an aggregate utility function characterised by a constant elasticity of substitution between any pair of varieties. As Nicols (1947) noted, this may be an unduly restrictive requirement. His alternative is a formulation based on the assumption that customers have scales of preferences, in terms of which they prefer one variety but are indifferent amongst all others. In this case, the ceteris paribus demand curve for each firm can be shown to have an obtuse kink at the going output, and Chamberlin's price cross-elasticity assumptions, yielding as they do a continuous dd curve, turn out to imply a complex and rather special combination of preferences on the part of customers. An extension of the Nicols' model would be one in which the desire for variety on the part of a customer is assumed to diminish continuously with the "distance" of any given variety from his most preferred choice. The idea of distance as a proxy for product differentiation has provided the basis for a substantial body of literature on the subject of spatial competition. Since the appearance of the pioneering work of Hotelling (1929)[6], theorists have recognised that a spatial representation is a tractable and useful way of analysing aspects of the Chamberlin model. Chamberlin himself recognised the potential of the spatial approach in his celebrated "Appendix C" (1962), and also in his discussion of the general applicability of considerations relevant to competition between small numbers (1962, pp. 103, 104). Because differences in "location" may be considered a proxy for product differentiation in general,


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location patterns are analogous to configurations of "variety" in monopolistically competitive markets. Consequently, if the distance between every pair of firms in the spatial market were the same then, in Chamberlin's sense, all products in the group would be equally substitutable for one another. The particular advantage of the spatial representation is that it makes it possible to show the special circumstances under which this will not be so, and the variety of configurations which may arise when different assumptions are made. One of the crucial differences between the Chamberlin and the Hotelling representations of a differentiated market has been identified by Archibald and Rosenbluth (1975), and must be borne in mind. If the distances between all pairs of varieties are not the same, then the impact of both price changes and entry will be asymmetric and dependent upon the "proximity" of given varieties to the source of the perturbation. We shall return to this point below, but it is worth noting here that in this sense, the Chamberlin-Dixit-Stiglitz formulation of the underlying utility function is less useful than that implied by Nicols. In setting out some of the features of models of spatial competition which inform and extend the Chamberlin analysis, we shall assume initially that the number of varieties, N, is fixed. The most appropriate point of departure for those wishing to link the work of Chamberlin with the literature of spatial competition is the "zero variations" conjecture (ZCV). Under ZCV, each firm expects that its rival(s) will not respond to any action on its part. In this sense, ZCV is the natural counterpart of Chamberlin's assumption of myopia. Hotelling assumes a uniform distribution of consumers' preferences over a line of finite length (a "one dimensional market")[7], [8]. There are two firms, both identical in all respects but for their locations on the line. Letting both production costs and elasticity of consumers' demands be zero, he assumes that each buyer purchases from the firm whose price plus transport cost is the lowest. Hotelling allows the firms infinite mobility, so that each is able to adjust its location until no further gain is possible given the choice made by its rival. The equilibrium condition is thus identical to that of the Cournot model. On this basis, he establishes some useful results for the two-seller case. The first is that the introduction of "space" removes some of the discontinuities associated with traditional non-spatial models of interdependence: if one firm undercuts its rival, then the latter will not lose all of its custom. This perception conforms with Chamberlin's model. The second result of interest is that, given identical prices for both firms, there can be found a spatial equilibrium in which the two firms emerge adjacent to each other in the middle of the market. Recent work on the Hotelling model by D'Aspremont et al. (1979) has attempted to show that under ZCV, too great a proximity between the two firms may prevent a simultaneous equilibrium in both price and location from occuring. This result contrasts with those obtained by Neven (1985, 1986) who demonstrates that a pure strategy price equilibrium can be found for this case, and also for the case in which the density of consumer demand is not uniform across the line. In the latter formulation, the tendency of the two firms is however towards dispersion rather than concentration at the midpoint. The two-firm model has also been considered by Smithies (1941). In his framework, elasticity of demand is finite. His results show the crucial role played by the elasticity assumption, and in particular the fact that in this


case the tendency will be towards dispersion. In this sense, his result appears to offer some support for Chamberlin's implicit assumption that, in differentiated markets, varieties will be symmetrically dispersed[9]. Unfortunately, however, the introduction of larger numbers of varieties makes matters very much more complex. Chamberlin (1962) has shown that there is no stable (pure strategy) equilibrium in locations (given identical prices) when N = 3. A similar result has been proved by Shaked (1975) and Graitson (1979), although Shaked (1982) has shown that, for this case, there does exist an equilibrium in mixed strategies. Lerner and Singer (1937) and Eaton and Lipsey (1975) have shown that a purely locational equilibrium can, however, be found for any A7 greater than 3. The results confirm a tendency towards dispersion, but in general the distance between adjacent firms is not uniform. Other formulations of the N-firm problems under ZCV include Carruthers (1981), who models a case in which each firm assumes that its rivals' locations are fixed, but that they will adjust their prices to his choice of price and location. This has the effect of bringing the firms located towards the end of the line somewhat closer to the interior than is the case in the models of Lerner and Singer and Eaton and Lipsey[10]. The analyses presented above are based upon a somewhat restrictive assumption. Novshek (1980), for example, has observed that in spatial markets where marginal costs are constant, ZCV may be an inappropriate concept: the fact that firms whose markets overlap must always affect each other means that no equilibrium of interest can occur. According to Novshek it is, not surprisingly, only monopolies (whose markets are, by their nature, distinct from others) for whom ZCV is a legitimate operational assumption, and for these firms it is largely irrelevant in any case. A similar conclusion can be found in Kohlberg and Novshek (1982), who show that the existence of equilibrium depends in a crucial way upon the length of the market relative to the number of firms. Quite apart, however, from the restrictions necessary to secure equilibria of interest, there is the objection raised by Kamien and Schwartz (1983), who point out that the logic of ZCV is itself suspect: if each firm conjectures that rivals will not respond to its actions, how does the firm justify its own response to theirs? A wide variety of possibilities arises once the ZCV assumption is relaxed. Gannon (1972) has argued that equilibrium in the two-firm case may be anywhere in the market, depending upon the conjectures of the firms. His general principle is that firms will emerge closer to each other if each believes that the other will respond "weakly" (ie. to a smaller extent) to any change in its own location, and vice-versa for "strong" expected reactions. D'Aspremont et al. (1979) and Graitson (1980) have proposed a modified concept, the "maximim" conjecture, for which an equilibrium in both prices and locations (each firm at the midpoint of its respective market) may be found. Rothschild (1976, 1979) has investigated the application of the maximin concept to the case where N is fixed and greater than 2, and demonstrates a general tendency towards dispersion[ll]. Perhaps the most important, yet least developed, of the analytical issues arising from an explicitly spatial representation of the work of Chamberlin is the problem of "chain-linked" markets. A market may be said to be chain-linked if a cut in price by one firm affects more strongly its proximate rivals, leaving relatively unaffected those further away. Here, proximity encompasses both physical proximity (as in the


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case of gasoline filling stations) and similarity in characteristics (as in the case of varieties of cider). Either way, the argument that proximate competitors will be more affected by a price reduction, and hence will be more likely than others to respond, is an intuitively and empirically appealing one. Kaldor (1935) was the first to raise the objection that markets are typically chain-linked rather than symmetrical in Chamberlin's sense. Chamberlin's symmetry assumption makes it unnecessary for him to consider this important question, but he shows himself to be aware of it (Chamberlin, 1962, pp. 103, 104). A brief discussion of chain-linking can be found in Copeland (1940) and Henderson (1954), but the idea is not developed. Lancaster (1966) has dealt with the concept in the course of setting out his "characteristics" approach to the theory of demand. This framework, which Lancaster (1966), Baumol (1967), Salop (1979) and Archibald, et al. (1986) have shown to be similar to the one-dimensional spatial models, rests upon the assumption that consumers typically demand characteristics of products rather than products themselves. Competition between firms is thus seen to be competition between "bundles" of characteristics. The analogy with spatial representations of horizontally differentiated products is readily apparent, and writers in this area have emphasised the localised (non-symmetrical) nature of competition in markets defined in this way, Archibald and Rosenbluth (1975) have integrated Lancaster's approach to demand with Chamberlin's large group model, and show that the latter's ceteris paribus demand curve (dd) is an absurd construct if the products in question have fewer than four distinguishing characteristics. The principal reason is that, in Lancaster's formulation, such a situation would give rise to a series of chain-linked markets. However, if the number of characteristics identifying each product exceeds four, then although the likelihood of discontinuities in competitors' reactions is increased, the possibility that these might be small or mutually offsetting is sufficient to provide a rationale for Chamberlin's implicit assumptions. In similar vein, Capozza and van Order (1982) suggest that, even when competitors are few, price reductions may not be followed. In this sense, the effect of chain-linking may be less serious than might be expected. The problem of chain-linking nevertheless remains one of quite crucial importance in industrial organisation theory. As Friedman (1977, 1983) has argued, the concept provides a sensible view of monopolistically competitive markets, and one which is in many ways superior to that commonly found in the literature. However, although the question is addressed in Friedman (1983), he offers few results apart from a formalisation of some of the relationships. Perhaps the most detailed analysis of the phenomenon to date can be found in Rothschild (1982, 1986), who shows, on the basis of a particular set of expectations, how an equilibrium in prices may emerge in a chainmarket in which all adjacent firms are equidistant. The natural extension of the analysis of chain-markets is to the question of the effect of changes in N. In Chamberlin's formulation, the cross price-elasticity of demand for each existing variety remains unchanged in the face of entry and exit. The spatial analogy, and in particular the phenomenon of chain-linking suggests that changes in the number of firms must be expected to change the relative proximities of the available varieties. If this occurs, then individual price cross-elasticities must also change. The problem remains an important and potentially fruitful one for further research.


Uniformity and Excess Capacity Chamberlin's assumptions of uniformity in demand and costs have also received a great deal of critical attention. Stigler (1950), for example, noted that product differentiation and uniformity of cost and demand curves across all firms are mutually exclusive concepts: differentiation, by its very nature, serves to make firms dissimilar, and dissimilarities manifest themselves most commonly in non-uniform costs. The point was not lost on Chamberlin, who made a number of attempts[12] to modify the assumption. A recent contribution may have provided a basis for countering Stigler's objection. Sher and Pinola (1981) have argued that a sufficient condition for the existence of both of Chamberlin's demand curves (dd and DD) is that the prices of products stand always in the same proportional relation to one another. Extending this argument to cases in which the respective cost curves of the producers stand in the same proportional relation to one another as do their prices, would make it possible to identify an equilibrium for the group at some configuration of these prices. This modification of the Chamberlin uniformity assumption, valuable though it is, does not take account of the effect of entry and exit. Irrespective of whether costs and demands are identical or merely infixedproportions to one another, the important questions in this context are firstly whether group equilibrium will be characterised by excess capacity in Chamberlin's sense and secondly whether the process will lead to the zero-profit outcome predicted for the large group case. We turn first to the question of excess capacity. In a series of papers, Demsetz (1959, 1964, 1968, 1972) addressed Chamberlin's assertion that, in equilibrium, firms would produce a smaller output than that necessary to minimise average total costs. The essence of Demsetz' argument is that when a profit-maximising firm changes its output, it will also attempt to shift its demand curve through increased selling expenditure. When this occurs, the demand curve ceases to be fixed in the sense assumed by Chamberlin. As an alternative to Chamberlin's demand curve, Demsetz introduces the concept of a mutatis mutandis average revenue curve which depicts the optimum price for each quantity sold. On the assumption that returns to selling expenditure initially increase and subsequently decrease, the Demsetz curve acquires an inverted U-shape. On the further assumption that firms will always wish (or be forced by competition) to choose the most efficient available process, the tangency of the mutatis mutandis curve with the average total cost curve ensures that the locus of market equilibria will be horizontal, thus permitting the attainment of a zero-profit equilibrium at the level of minimum average cots. Although the Demsetz contribution has been extensively criticised (see for example Archibald, 1961; Barzel, 1970, Perkins, 1972; Schmalensee, 1972; Ohta, 1977 and Murphy, 1978) it has, together with the work of Dewey (1958) and Fama and Laffer (1972), formed the foundation for the development of a new and potentially exciting research area known as the Theory of Contestable Markets. Dewey argued that Chamberlin's tangency position would be inherently unstable. If competition is imperfect, then rationalisation of the industry must be expected to lead ultimately to production at minimum average costs. A necessary condition here, as Dewey points out, is that entry into the market must be an instantaneous possibility. The leading contributors to the contestability literature (Panzar and Willig, 1977; Baumol et al., 1982 and Baumol, 1982, characterise a contestable market as one which permits


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absolutely free (and instantaneous) entry and costless exit. The entrant suffers no disadvantages relative to incumbents and can, upon leaving the market, recover all costs incurred on entry, subject, of course, to adjustment for any normal user costs and depreciation. Since this condition serves to eliminate all risks involved in entry, markets defined in this way are vulnerable, irrespective of the time period under consideration. Because of the absence of barriers to entry and exit, contestable markets are characterised by zero economic profits, no matter how many firms operate. In such markets there exists no inefficiency, however defined, for the reason that inefficiency constitutes an invitation to entry and will thus be eliminated. Moreover price can never be less than marginal costs, since potential entrants could, in those circumstances, obtain higher profits than incumbents by shading price and eliminating unprofitable units. It follows that, in contestable markets, price must always equal marginal costs, so that the necessary conditions for Pareto optimality are satisfied. The results reported here introduce explicitly the question of entry, and the issue of whether it will give rise to equilibrium. This is itself an important subject and, despite the vigour with which the contestability argument has been pursued, by no means a settled one. Even if the symmetry and uniformity assumptions were valid in general, the likelihood of a zero-profit group equilibrium under free entry and any imaginable conjectures on the part of firms would remain a separate and controversial issue Kaldor (1935) argued that zero-profit equilibrium might not occur in the presence of indivisibilities and economies of scale. In this case, entry will not lead ultimately to a Chamberlinian tangency, but rather, will cease prematurely because of high costs. Using the spatial analogy, the "interpolation" of a producer "between" any two others might actually cause profits to become negative, thus deterring entry and yielding monopoly advantage to pre-existing firms. This argument has found broad acceptance, although Capozza and van Order (1982) have observed that it is weakened somewhat if capital is mobile and the market is large relative to the indivisible unit of capital. However their results also show that if capital is not mobile, then Kaldor's objection cannot be so easily dismissed. A similar conclusion can be found in Eaton and Lipsey (1976, 1978). Peles (1974) also concludes that pure profits may exist in equilibrium, and argues that the presence of untransferable fixed assets allows firms to enjoy monopoly power. But he shows that the quantity produced by these firms may correspond to that associated with minimum average costs, so that in this sense production is efficient. Similar ideas have been put forward by Tullock (1965), Telser (1969) and Salop (1979). With the aid of a spatial analogy, Tullock shows that a Chamberlinian zero-profit equilibrium is indeed possible, and that it will also be Pareto optimal if consumers' tastes are taken explicitly into account. In the same vein, Telser distinguishes between markets of finite and infinite length. In the former, entry will lead to a Chamberlinian equilibrium. In this sense, the restriction imposed by the finite nature of the market gives rise to inefficiency. However, where the market is infinite, efficiency can in principle be achieved. Salop investigates the problem using the framework of a Chamberlinian "group" and an "outside" market. In his formulation, consumers buy either one unit or none of the differentiated product, and spend the remainder of their income on the homogeneous outside good. The differentiated product is produced


subject to decreasing costs; the other is produced under competitive conditions. For this case there can be shown to exist a variety of zero-profit equilibria, two of which are of particular interest. The first is a confirmation of the existence of the traditional Chamberlinian equilibrium; the second is an equilibrium in which profits are zero but the demand curve is kinked because of the conjectures of the firms involved. The result is similar to that of Sweezy (1939), although the conjectures of the agents are somewhat different. While Salop does establish conditions under which profits in equilibrium will be zero, he also provides an insight into the circumstances under which this outcome will not necessarily occur. In particular, he notes that the existence of indivisiblefixedcosts may require that the number of varieties in the market be integer valued, thus preventing a zero-profit equilibrium from being attained. In this sense, his results may be seen as being in the tradition of Kaldor[13]. Some of the problems of indivisibility, monopoly and efficiency which arise in the context of a partial equilibrium formulation of the Chamberlin model disappear when the framework is that of a general equilibrium. Hart (1978, 1980, 1982) has argued that a monopolistically competitive equilibrium can exist given correct conjectures on the part of firms about the demand for all potential differentiated goods, and that this equilibrium will be approximately Pareto optimal if the economy is sufficiently "large". This result does, however, turn crucially upon certain restrictions on consumers' preferences. Novshek (1980) offers similar results to Hart on the basis of a modified ZCV assumption. Gabszewicz and Thisse (1980) also address the relationship between the size of the market and the nature of the resulting equilibrium. They show that increases in the number of differentiated products ultimately bring about a perfectly competitive outcome, provided that the firms choose prices non-cooperatively. But there exists an upper bound to the number of firms which can be active in such a market. It will be clear from the foregoing discussion that no unambiguous conclusions can be drawn as to the existence or otherwise of a zero-profit equilibrium under monopolistically competitive conditions. The question of whether or not such an equilibrium would be characterised by the existence of excess capacity merely serves to complicate the issue. The mobility of capital will doubtless be a factor of importance in both respects. But even if capital is perfectly mobile, the characteristics of equilibrium prices will depend upon the conjectures of firms, the preferences of consumers and the size of the economy. Variety, Market Pre-emption and Welfare The issues raised in this section relate to the optimal provision of variety from the perspective of both firms and consumers. As already noted, Chamberlin gives explicit attention to the question of entry. However, in his model firms already in the market do not anticipate new competition and so make no provision for it when deciding upon the location of the products in the spectrum of varieties. In practice, of course, existing firms must be expected to devote considerable resources to the matter of selecting varieties and, in particular, to pre-empting the choices of potential competitors. The need to do so arises in large part from the commitment which a particular choice of variety imposes upon firms. In Chamberlin's model the entry


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of new firms cannot be prevented and, once it occurs, the market shares of all incumbents are reduced by equal amounts. Using the analogy of the spatial market, the implicit assumption in this case is that firms are "infinitely mobile" in the Hotelling sense, and can adjust to the new entrant by establishing an accommodating set of equidistant locations post entry. In practice, of course, such possibilities are severely restricted by the existence of relocation costs[14]. Once the possibility of entry is introduced explicitly, firms face the need to choose product varieties subject to expectations of the behaviour of both existing and potential rivals. The anticipation of the choices to be made by subsequent entrants is a necessary condition for securing optimal provision of variety ex post from the firms' point of view. The analysis of the problem has proceeded along two distinct lines. The first assumes that N is determined exogenously and that firms attempt only to ensure their maximum attainable advantage given the certainty that the industry will contain that number. The second assumes that N is determined endogenously and that firms deter entry by means of appropriate choices of location on the variety spectrum. Perhaps the earliest discussion of the first version of the problem is to be found in Rothschild (1976, 1979), who considers a case in which N is exogenously determined but firms enter sequentially. All firms are assumed to sell at the same price, so that only location is a choice variable. The market is taken to be the circumference of a circle, with each consumer buying from the nearest seller. Firms choose their locations on the assumption that succeeding entrants (whose number is known with certainty) will choose the most unfavourable location from their point of view; each assumes further that all rivals entertain precisely the same maximin conjecture. The pattern of locations which results depends upon the elasticity of demand for each variety: if elasticity is zero, then the first N-l entrants will locate equidistant, while the Nth will choose a location arbitrarily; if elasticity is finite, then all firms emerge more or less at the midpoints of their respective markets, but the early entrants obtain larger markets than those who enter later. In both models there is a tendency towards a dispersion of varieties over the variety spectrum. The second of the two lines of analysis has been dealt with by Hay (1976), Prescott and Visscher (1977) and Lane (1980). All analyse the strategic aspects of entry deterrence under sequential entry. In Hay's model, new entry is prevented by a process of brand proliferation, in which firms leave insufficiently large gaps in the spectrum of product varieties to support newcomers. In Chamberlinian terms, the profits obtainable by new firms are less than those at the tangency of average revenue and costs. When entry is deterred in this way, the general tendency is for incumbents to disperse rather than cluster, but in this they are constrained by the need to ensure that the interstitial market segments are kept sufficiently small. The important insight obtained by Hay is that it is minimum market size rather than price which constitutes the effective deterrent to new competition. In his formulation, once entry has been deterred, the prices of all firms adjust so as to maximise the profits of each. He shows that similar conditions apply, and similar market configurations emerge, when the market is growing. Moreover, the analysis can be shown to proceed as before even when demand is not uniformly spaced, except that under these circumstances the spacing of firms in equilibrium will be irregular.


Prescott and Visscher consider a number of different formulations of the sequential entry problem and show that, for each, the tendency is towards a dispersion of varieties. When N isfixed,a Hotelling-type approach yields a result similar to that of Rothschild (1976); when waiting time is introduced explicitly, a Cournot equilibrium in both price and location is obtained; when there is waiting time and prices can be chosen (and costlessly varied) after the choices of others have been observed, then there also exists an equilibrium; finally, when production capacities are chosen sequentially under conditions of restricted entry and firms are permitted to choose plant in any number of locations, complete monopoly results. The idea of plant proliferation as a tactical device is also explored by Peles (1974). Results of the latter type are of some interest when the social optimality of product variety is being considered. We return to this topic below. Lane offers an analysis which draws on elements in the work of both Hay and Prescott and Visscher. On the assumptions that firstly each consumer has a unique set of preferences and secondly both prices and locations are endogenously determined, he sets out a model in which firms enter sequentially and cluster in the centre of the market. A firm's optimal location will be found at the point where there exists a balance between the tendency to cluster in this way, and the pressure to disperse which results from competition in price. The patterns of location which characterise Lane's sequential entry equilibrium yield to early entrants higher profits than those obtained by others. The level of fixed costs for the firm will be a factor in the decision to deter new entry: if these costs are high, then entry deterrence is possible; if they are low, then the profit maximising strategy for the firm may require that new entrants be accommodated. A similar result has been obtained by Dixit (1979) in a somewhat different context. The natural extension of the arguments contained in some of the work outlined here is the use of brand proliferation as an element of strategic behaviour. A discussion of the issue can be found in Archibald and Rosenbluth (1975) and Schmalensee (1978), who uses the principle in his analysis of entry deterrence in the "ready-to-eat" breakfast cereal industry. Recent work of a similar kind is to be found in Lyons (1986). In turning to the question of the optimality of product variety from the point of view of the consumer, we address the welfare implications of monopolistic competition. Some early writers, such as Kahn (1935) concerned themselves exclusively with the relationship between price and marginal costs which characterises the equilibrium of the large group. Kahn argued that, where price exceeds marginal cost, Pareto optimality can still be achieved if the ratio of these variables is uniform throughout the economy. But, as Bishop (1967) has observed, this approach to the question of optimality neglects the important relationship between variety and welfare, which in his view remains indeterminate as long as Chamberlin's uniformity assumption is retained, even if other, more traditional optimality conditions are met. The problem, although partly eased if the uniformity assumption is abandoned, is never entirely eliminated. In similar vein, Kaldor (1935) has argued that it is impossible to draw any general conclusions about the implications of excess capacity for welfare. Chamberlin's own views on the welfare implications of large group equilibrium are to be found in a number of sources. His exposition in Chamberlin (1950) is perhaps the best known of these. There he observes that the consequences of monopolistically competitive elements had either been "ignored or seriously misunderstood", and that


47

the view of perfect competition as an ideal (as, for example, in Kahn, 1935) reflected an underestimate of the pervasiveness of monopoly in the real world and a consequent failure to incorporate it into a workable definition of welfare. In essence, whenever diversity is demanded, marginal cost pricing ceases to be a basis for welfare judgements, and comparisons of the state of affairs in large group equilibrium — which he terms "a sort of an ideal" — with the prescriptions of the perfectly competitive model are therefore meaningless. Chamberlin is equally clear about the difficulties involved in establishing the optimality of product variety. In his view, no unambiguous statements are possible a priori. Whilst no recent contributions to the subject have developed the issues raised by Kahn (1935), a number of writers have attempted to show that, in monopolistically competitive markets, variety will be over-, under-, or optimally-provided[15]. Lewis (1945), for example, argues that monopolistic competition may lead to either excess capacity or optimal provision, depending upon the circumstances surrounding the particular class of trade. Spence (1976a) suggests that product selection failures ("too many, too few, or the wrong products") may be a significant part of the overall costs of market imperfection, but concludes that these costs are not currently measurable. In Spence (1976b) he shows that, given monopolistically competitive pricing, high own price and price cross-elasticities are likely to lead to the production of too many products, while the converse is probable when both of these elasticities are low. A similar result can be found in Dixit and Stiglitz (1977), who distinguish between the "market" solution and the socially optimal outcome. The basis of their analysis is the conflict between the objectives of producers (profit maximisation) and those of the consumer (consumer's surplus), and they demonstrate that under certain conditions on consumers' utility functions free entry will lead to the provision of a less than optimal number of varieties[16]. The relationship between economies of scale and the extent of product differentiation has been investigated by Meade (1974). He recognises a general need for variety, which he regards as being greater the smaller the degree of substitutability among products. But he argues also that the benefits of variety must be set against the opportunity costs involved in its provision, measured here in terms of the economies of scale which derive from concentration on the production of a narrower range of products. He observes that, as a general principle, if costs of production are high while substitutability is low, then firms will concentrate upon a smaller number of varieties. In such circumstances, cost considerations will dominate the need for substitutability even though the socially optimal solution demands variety. Koenker and Perry (1981) consider circumstances under which scale economies will give rise to excessive variety. The problem has been approached from an explicitly spatial perspective by Stern (1972), who shows that monopolistic competition may lead to market areas of above optimal size (too little variety) as well as to market areas of below optimal size (too much variety) according to circumstances. In similar vein, Heal (1980) has observed that small markets will be under-served in terms of variety, while the reverse is true for larger markets. In this sense, the extent to which variety is provided is determined by the size of the market. Another approach to the question of optimal variety stresses the importance of market structure in general. Lovell (1970) argues that both price and variety may be


inappropriate in some sense. In particular, to the extent that the variety being offered reflects the dominant market form and also the conjectures of the firms involved, socially optimal provision is unlikely except in unique circumstances. Swan (1970) shows that a monopolist operating under conditions of constant returns to scale will offer optimal variety. On the same subject, but for a more general case, Lancaster (1975) has shown that, under imperfect competition and increasing returns to scale, differentiation will not in general be socially optimal, but the precise direction of bias depends upon the particular market structure. In his view, if returns to scale are increasing, then monopolistic competition gives rise to excessive differentiation, and monopoly to too little. However, if returns to scale are constant, then market imperfections are not in themselves a cause of sub-optimal provision of variety. The inference for both writers is thus that market conditions do not matter when constant returns prevail. The point is disputed by White (1977), who shows that a monopolist working under such conditions will offer optimal variety only if allowed to discriminate on the basis of price. Otherwise, some of the products desired by consumers may not be offered. Using a similar argument, Gabszewicz (1983) has shown that, even if overhead costs are excluded, a monopoly may produce less variety than is socially optimal. The review of the literature in this section suggests that no firm conclusions should be drawn as to the optimality or otherwise of product provision in differentiated markets, from either the producers' or the consumers' points of view. Whether or not variety will be over- or under-supplied depends upon the technical conditions in production, the structure of the market, the conjectures and strategic behaviour of firms, and the utility functions of the consumers. Concluding Comments The nature and significance of the Chamberlinian contribution are best judged in terms of the literature which his original work has inspired. On this criterion, as our brief review will have demonstrated, Chamberlin's impact upon the evolution of economic analysis must be beyond dispute. Although his view of the world, as expressed in the Theory of Monopolistic Competition, has been shown by subsequent writers to have been overly simple and, in places, crucially flawed, the insights upon which it was based have themselves formed the foundation for much of what is today called Industrial Organisation theory. Viewed in this light, Chamberlin's contribution must be regarded as a cornerstone of economic analysis and a guarantee that his name will enjoy a permanent place on the roll of the great economic theorists. Notes 1.

2. 3.

Although Joan Robinson's celebrated book, The Economics of Imperfect Competition (1933), appeared at the same time as the work of Chamberlin, it is undoubtedly the latter which has received more attention. In this review we shall address ourselves exclusively to his contribution. For a discussion of the intellectual background to Chamberlin's work see Chamberlin (1961) and papers in Kuenne (1967). See Fellner (1967) for a discussion of this point. See Friedman (1977) for an analysis of the conditions under which noncooperative behaviour may yield outcomes which are Pareto optimal, and Formby and Smith (1979) for an exposition and critique of Chamberlin's cooperative outcome in the two-firm case.


4. 5. 6. 7.

8.

9.

10. 11.

12. 13.

49

See Bain (1967). See Bishop (1952), Heiser (1955), Bishop (1955), Fellner (1953), Chamberlin (1953) and Bishop (1953). Similar analysis can be found in Launhardt (1885) and Zeuthen (1929). This particular form has been widely used as an analogue for monopolistic competition, even though in such a market all firms can never be equidistant from all others. The point, however, is that the absence of symmetry of this kind from the one-dimensional market must imply its absence from an N-dimensional one. The basic Hotelling model has attracted some criticisms which we shall not develop here. Hartwick and Hartwick (1971) have shown that the equilibrium price in such a market may not be unique, but will depend upon the initial price and location choice of the first firm to act. Devletoglou (1965) bases his characterisation on a slightly different set of assumptions. He identifies a "minimum sensible" constraint of indifference on the part of buyers. Given the existence of such a constraint, it can be shown that firms will be repelled from the centre. Models similar to that of Smithies have been investigated by Lerner and Singer (1937), Webber (1972), Eaton and Lipsey (1975), Graitson (1979) and Economides (1982), who assume rectangular demand functions with the particular property that consumers buy one unit of the product up to some price, and nothing above it. In this case, depending upon the size and shape of the market area, different equilibria can be found, their number and character depending, in turn, upon the number of firms in the market. Vickrey (1963) has considered the Hotelling/Smithies problem in the context of a circular, rather than a linear market, and confirms the tendency to dispersion when elasticity of demand is finite. A number of writers have argued that the tendency will be toward agglomeration, rather than dispersion. Lewis (1945) has suggested that larger retail firms will tend to cluster together. Stahl and Varaiya (1978) attribute such behaviour to imperfections in information on the side of firms, while Stuart (1979) argues that clustering is more likely to be due to uncertainty on the part of consumers. Although we shall not develop these issues here, their importance for the theory of location, especially retail location, should be noted. Ali and Greenbaum (1977) consider a similar case involving sequential entry into the market for banking services. Teitz (1968) shows that, iffirmsare permitted to own multiple plants, then an equilibrium in locations will only be likely to occur if maximin location strategies are adopted. Variations on this gametheoretic approach include Stevens (1961), who models the Hotelling/Smithies framework as a zero-sum game, and shows that if the location points are discrete and choices simultaneous, then their results hold. Gal-or (1982) considers the possibility of mixed strategies, showing that when firms choose a distribution of prices (rather than a single price), equilibria may exist where otherwise none would be possible. Kohlberg (1983) has shown that if the Hotelling problem is modeled as an N-person game in which strategies are location choices and the payoffs are market shares, then relocation gives rise to jump discontinuities. But if consumers choose outlets on the basis of travel time plus waiting time (the latter being a function of the market shares of firms) then market shares become continuous functions of the firms' locations. Unfortunately, no equilibria exist for the case where N > 2. See, for example, Chamberlin (1962, p. 82ff). The work of Losch (1954) is in many ways a parallel to that of Chamberlin. Using a spatial framework (in this case, an areal market), Losch shows that a system of regular hexagonal markets, one for each firm, yields a unique zero-profit equilibrium under conditions of free entry. In contrast to these findings, and on the basis of rather different assumptions on costs, Mills and Lav (1964) have shown that there may be a wide variety of market shapes consistent with free entry, so that profits in equilibrium may not be zero. Extending their analysis to include the question of efficient allocation, and comparing theirfindingswith those of Chamberlin, they conclude that equilibrium may be characterised by a misallocation of resources especially where de-centralised processes are involved. (A discussion of this point can be found in Samuelson, 1967; and Grace, 1970). Eaton (1976) and Eaton and Lipsey (1978) provide a rationalisation and confirmation of the Mills and Lav "positive profit" argument in the context of a one-dimensional market in which firms entertain ZCV with respect to rivals' locations and the expectations that their respective mill prices will not be undercut. Niedercorn (1981) offers a similar result.


The relationship between the monopoly and competitive prices posited by Losch has itself attracted considerable attention, and is relevant to the work of Chamberlin. Greenhut et al. (1975) have pointed out that the Loschian equilibrium will be characterised by higher prices than would spatial monopoly, and that the more intuitively plausible outcome associated with traditional (non-spatial) theory requires the explicit assumption that firms' prices at their respective market boundaries befixed.The Greenhut-Hwang-Ohta interpretation differs from that of Beckman (1970), who argues that Loschian free entry will reduce prices to the minimum level consistent with zero profits. However, as Capozza andvanOrder (1977) have pointed out, the debate hinges upon different interpretations of "equilibrium". If the equilibrium condition requires profits to be zero, then Loschian competition yields this outcome, but only at a "high" price; alternatively, if the condition requires all firms to have equal market shares, then the Greenhut-Hwang-Ohta approach yields a more satisfactory result. Capozza and van Order (1978) employ ZCV to show that Losch's perverse results obtain only in exceptional cases, and not in the more traditional (Chamberlinian) framework of monopolistic competition. 14. The processes involved in product selection by firms have been the subject of study for some time. Brems (1951) addressed the question but found it to be largely intractable. It is only since the work of Baumol (1967) that potentially fruitful analysis has been possible. His model employs the techniques of integer programming to establish optimal strategies of product design. On the assumption that no retaliation by rivals is possible, he shows that the optimal strategy of a firm involves making its product more, rather than less, similar to existing varieties. In contrast, Schuster (1969) has considered a case in which the preferred strategy involves the production of varieties which are quite distinct from those of rivals. Reichardt (1962) has cast the analysis in explicitly game-theoretic terms. Lancaster (1966) has also studied the problem in a "characteristics" framework. Valuable though these contributions have been, all are restricted to the analysis of product selection in markets where N is fixed. 15. For a diagrammatic exposition of some of the models set out here, see de Meza (1983). 16. But see Pettengill (1979) for a counter argument. References Abbott, L., Quality and Competition, New York, Columbia University Press, 1955. Ali, M.M. and Greenbaum, S.I., "A Spatial Model of the Banking Industry", Journal of Finance, Vol. 32, 1977, pp. 1283-1303. Archibald, G.C., "Chamberlin versus Chicago", Review of Economic Studies, Vol. 29, 1961, pp. 2-28. Archibald, G.C. and Rosenbluth, G., "The 'New' Theory of Consumer Demand and Monopolistic Competition", Quarterly Journal of Economics, Vol. 89, 1975, pp. 569-590. Archibald, G.C, Eaton, B.C. and Lipsey, R.G., "Address Models of Value Theory", in Stiglitz, J.E. and Mathewson, G.F., (Eds.), New Developments in the Analysis of Market Structure, London, Macmillan, 1986. Bain, J.S., "Chamberlin's Impact on Microeconomic Theory", in Kuenne, R.E., (Ed.), Monopolistic Competition Theory: Studies in Impact, New York, John Wiley and Sons, 1967. Barzel, Y., "Excess Capacity in Monopolistic Competition", Journal of Political Economy, Vol. 78, 1970, pp. 1142-1149. Baumol, W.J., "Calculation of Optimal Product and Retailer Characteristics: the Abstract Product Approach", Journal of Political Economy, Vol. 75, 1967, pp. 674-685. Baumol, W.J., "Contestable Markets: An Uprising in the Theory of Industrial Structure", American Economic Review, Vol. 72, 1982, pp. 1-15. Baumol, W.J., Panzar, J.C. and Willig, R.D., Contestable Markets and the Theory of Industrial Structure, New York, Harcourt Brace, Jovanovich, 1982. Beckman, M.J., "Equilibrium vs. Optimum: Spacing of Firms and Patterns of Market Areas", Discussion Paper 16, Brown University, 1970. Bishop, R.L., "Elasticities, Cross-Elasticities, and Market Relationships", American Economic Review, Vol. 42, 1952, pp. 781-803.


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