Spatial competition theory
Because consumers are dispersed across space, they differ in their access to the same firm. In such a context, firms anticipate accurately that each consumer will buy from the firm posting the lower full price, namely, the price at the firm’s gate, called mill price, augmented by the travel costs that consumers must bear to go to the firm they patronize.
As a consequence, firms have some monopoly power over the consumers located in their vicinity, which enables them to choose their price. Of course, this choice is restricted by the possibility that consumers may decide to supply themselves from competing firms. This process of competition among spatially dispersed firms has been described by Launhardt (1885 [1993]) who proposed a model of price formation, in which he anticipated the concept of Nash equilibrium. In particular, he was the first to show what came to be known as the principle of differentiation in industrial organization: “the improvement of means of transport is dangerous for costly goods: these lose the most effective protection of all tariff protections, namely that provided by bad roads” (p.150 of the English translation). In other words, firms want to be separated to relax price competition.Launhardt’s contribution remained ignored outside the German-speaking scientific community until recently. Hotelling (1929), more than 40 years later, has had more impact although the path-breaking nature of his paper was more fully recognized when economists became aware of the power of non-cooperative game theory. The value and importance of Hotelling’s contribution was brought to light in the 1980s by showing that its use exceeds the original geographical interpretation to accommodate various dimensions that differentiates firms and consumers. To be precise, the spatial framework may serve as a powerful metaphor for dealing with issues involving heterogeneity and diversity across agents in a host of economic, political and social domains.
In addition, Hotelling’s paper may be viewed as one of the prototypes of the modern economic literature: it is self-contained and focuses on a specific problem, which is studied by means of a simple and elegant model.Because any single consumer is negligible to firms, Hotelling assumed that consumers are continuously distributed along a linear and bounded segment - think of Main Street. Two stores, aiming to maximize their respective profits, seek a location along the same segment. Each firm being aware that its price choice affects the consumer segment supplied by its rival, spatial competition is, therefore, inherently strategic. This is one of the main innovations introduced by Hotelling who uses a two-stage game to model the process of spatial competition: in the first stage, stores choose their location non- cooperatively; in the second, these locations being publicly observed, firms select their selling price. The use of a sequential procedure means that firms anticipate the consequences of their location choices on their subsequent choices of prices, thus conferring to the model an implicit dynamic structure. The game is solved by backward induction. For an arbitrary pair of locations, Hotelling starts by solving the price sub-game corresponding to the second stage. The resulting equilibrium prices are introduced into the profit functions, which then depend only upon the locations chosen by the firms. These functions stand for the payoffs that firms will maximize during the first stage of the game. Such an approach anticipates by several decades the concept of sub-game perfect Nash equilibrium introduced by Selten in the 1960s.
Hotelling’s conclusion was that the process of spatial competition leads firms to agglomerate at the market center. If true, this provides us with a rationale for the observed spatial concentration of firms selling similar goods (for example, restaurants, movie theaters, and fashion cloth shops). Unfortunately, Hotelling’s analysis was plagued by a mistake that invalidates his main conclusion: when firms are sufficiently close, the corresponding sub-game does not have a Nash equilibrium in pure strategies, so that the payoffs used by Hotelling in the first stage are wrong (d’Aspremont et al., 1979).
This negative conclusion has led d’Aspremont et al. (1979) to modify the Hotelling setting by assuming that the travel costs borne by consumers are quadratic in the distance covered, instead of being linear as in Hotelling. This new assumption captures the idea that the marginal cost of time increases with the length of the trip to the store. In this modified version, d’Aspremont et al. show that any price sub-game has one and only one Nash equilibrium in pure strategies. Plugging these prices into the profit functions, they show that firms choose to set up at the two extremities of the linear segment. Firms do so because this allows them to relax price competition and to restore their profit margins. Therefore, the slight change made by d’Aspremont et al. leads to conclusions that completely differ from those obtained by Hotelling.
In his review of Chamberlin’s book, The Theory of Monopolistic Competition, Kaldor (1935) forcefully argued that, once it is recognized that firms operate in space, each one competes directly with only a few neighboring firms regardless of the total number of firms in the industry. The very nature of competition in space is, therefore, oligopolistic, thus casting serious doubt on the relevance of monopolistic competition as a market structure. Beckmann (1972b) has developed a full analytical treatment of spatial competition in a well-crafted paper that went unnoticed, probably because it was published in a journal having a low visibility in the economics profession. In addition, Beckmann’s main results were rediscovered by Salop (1979) in a paper that became famous in industrial organization. These two authors show how free entry may determine the equilibrium number of firms operating under increasing returns and competing oligopolistically with adjacent firms. Among other things, their analysis shows in a very precise way how the market solves the trade-off between increasing returns (internal to firms) and transport costs.
Building respectively on Kaldor and Hotelling, Eaton and Lipsey (1977) and Gabszewicz and Thisse (1986) have provided syntheses that help to clarify what spatial competition theory is about and what it can accomplish. This work was timely. Indeed, Salop was not aware of the contributions made by his four predecessors (Launhardt, Hotelling, Kaldor, and Beckmann), who all had a clear understanding of the nature of competition in space. This list of unrelated contributions, which cover almost one century, provides evidence of the very dispersed and fragmented nature of research in spatial economics until the emergence of new economic geography, which has served as a catalyst.
Increasing returns and strategic competition are, therefore, the basic ingredients of a relevant theory of spatial equilibrium. The difficulty of the task has put off more than one scholar. Exaggerating a little, we may say that the inability of the competitive model to tackle various issues as well as the absence of alternative models have generated a lock-in effect that economists had a lot of trouble escaping. It is, therefore, not totally surprising that the surge of new economic geography took place a few years after the revival of monopolistic competition.
As seen above, when firms sell a homogeneous good, they want to avoid spatial clustering because price competition has devastating effects upon them. It should be kept in mind, however, that this result is based on an extreme price sensitivity of consumers: if two firms are located side by side with identical prices, a small price reduction of one firm will attract all the customers. Such an extreme behavior seems unwarranted. When the product is differentiated and when consumers like product variety, the aggregate response to a price cut will not be so abrupt because the quality of product match matters to consumers. By turning the picture around, this observation suggests that firms selling differentiated goods may want to gather at some central market location, because price competition is now weakened (de Palma et al., 1985).
When transport costs are low, the benefits of geographical separation are reduced and prices are lower. Firms then choose to reconstruct their profit margins by differentiating their products along some non-geographical characteristics that are tangible or intangible. Stated differently, product differentiation is substituted for geographical dispersion. In this case, firms no longer fear the effects of price competition and strive to be as close as possible to the consumers with whom the fit is the best. Because these consumers are spread all over the market space, firms set up at the market center and, therefore, minimize their geographical differentiation.