The Max-Min-Min Principle of Product Differentiation

We analyze two and three-dimensional variants of Hotelling's model of differentiated products. In our setup, consumers can place different importances on each product attribute; these are measured by weights on the disutility of distance in each dimension. Two firms play a two-stage game; they choose locations in stage 1 and prices in stage 2. We seek subgame-perfect equilibria. We find that all such equilibria have maximal differentiation in one dimension only; in all other dimensions they have minimum differentiation. An equilibrium with maximal differentiation in a certain dimension occurs when consumers place sufficient importance (weight) on that attribute. Thus, depending on the importance consumers place on each attribute, in two dimensions there is a max-min equilibrium, a min-max equilibrium, or both. In three dimensions, depending on the weights, there can be a max-min-min equilibrium, a min-max-min equilibrium, a min-min-max equilibrium, any two of these, or all three.     

A SPATIAL COMPETITION APPROACH TO CENTRAL PLACE THEORY: SOME BASIC PRINCIPLES*

ABSTRACT. This paper investigates the potential offered by the model of spatial competition for the study of central place theory. We consider n firms selling m substitutable or complementary goods to a continuum of consumers evenly distributed along a linear segment. Consumers have the same income and the same utility function which is quadratic in the goods supplied by the firms and linear in the numeraire. The main results are as follows. (1) In any location equilibrium in which all goods are consumed everywhere, each good supplied by a single firm is sold at the market center. In Christaller's terminology, this means that when the exhaustive principle holds in equilibrium, highest-order goods are made available at the center. (2) When all goods (excluding the numéraire) are complements to each other and each good is sold by a single firm, there always exists an equilibrium in which all the firms locate coincidentally. (3) If the stores selling a given good are under the control of a single owner then, in any equilibrium for which the exhaustive principle holds, the stores are located in a way such that the total transport cost (borne by consumers) is minimized.     

SPATIAL COMPETITION À LA COURNOT: PRICE DISCRIMINATION BY QUANTITY-SETTING OLIGOPOLISTS*

In this paper, we consider oligopolistic competition in a spatial model when firms take care of goods' delivery and discriminate among consumers. Firms compete by setting quantity schedules independently over space. We show that under general conditions a Nash equilibrium in this game exists and is unique. In equilibrium, firms’ markets overlap, a feature which accords with intuition and empirical observations. Over the interval between two firms, the equilibrium spatial price schedule is quasi-concave (quasi-convex) when transport costs are concave (convex). With linear transport costs, the model predicts uniform delivered pricing. Uniform pricing could moreover be obtained by a combination of increasing returns to volume in transportation together with concavity of unit transport costs in distance.     

POLLUTION MOBILITY,PRODUCTIVITY DISPARITY,AND THE SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS

This paper first develops a model to characterize the equilibrium distribution of polluting and nonpolluting firms and then turns to the larger question of whether the equilibrium distribution is socially optimal. We find that the equilibrium distribution of polluting firms differs from the social optimum when they generate a large amount of stationary pollution and have much higher or lower productivity than clean firms. In these cases, conventional pollution control approaches generally do not bring about an optimal distribution. Consideration of transport costs along with productivity and pollution changes some of the classic results of the new economic geography literature.     

SPATIAL PRICING IN INTERDEPENDENT MARHETS*

ABSTRACT. Conditions for spatial price equilibrium are derived for a set of firms in oligopolistic spatial competition, distributed at fixed locations in a heterogeneous region where consumer purchasing patterns are a probabilistic function of the price distribution rather than a deterministic function of proximity to firms. The resulting prices vary with accessibility to consumers or with the degree of local spatial monopoly, and result in non-zero profits for firms. Conditions describing the existence and stability properties of this spatial price equilibrium are defined, and are shown to be equivalent for two different hypotheses concerning disequilibrium pricing behavior: a partial price adjustment model and a Bertrand game. For two different profit goals, total profit maximization and profit rate maximization, it is shown that a spatial price equilibrium exists and is at least locally quasi-stable.     

SPATIAL ENTRY DETERRENCE UNDER OLIGOPOLY*

ABSTRACT. This paper examines colluding, oligopolistic firms in a linear market. By assuming that rivals do not compete for consumers at their market boundaries, it is shown that an equilibrium exists without adopting a convex transportation cost function. Two price profiles are derived. The first describes firm prices in the absence of threatened entry. The second details profit-maximizing prices which forestall entrants. Given infinite relocation costs, threatened entry leads to price adjustments by the incumbent firms.     

ZONING A CROSS‐BORDER CITY

This paper investigates zoning in a cross‐border linear city that consists of two bordering towns. In each town, a local regulator has a say in the location of the local firm. We find that local regulators may use zoning strategically. The incentive to gain consumers from the other town, or not to lose local consumers, may push regulators to approve only locations for firms close enough to the frontier. When zoning is costly an asymmetric equilibrium may emerge: only one regulator resorts to zoning. In the case of towns of different sizes, the regulator of the larger town is the only one that zones in an asymmetric equilibrium.     

Price Variation in Spatial Oligopolies

The “geography of price” is being given renewed attention by geographers and economists. This paper examines spatial price variation in both unbounded (circular) and bounded (linear) one-dimensional markets. Firms compete for consumers in the short run by adjusting price until the Bertrand equilibrium is reached in the market. While firms act as spatial oligopolists in specific market segments, the profit-maximizing price of any given firm depends directly and indirectly upon the spatial-economic properties (locations, marginal costs) of all other firms in the market.     

THE EFFECTS OF ZONING IN SPATIAL COMPETITION

ABSTRACT This paper considers a location model to illustrate the effect of zoning on competition. A planner is in charge of designing a city in a circular space where firms and consumers are located on different sides. With this type of market configuration, equilibrium in location under concave transport costs is proved. Then, a welfare function with different weights attached to consumer and firm surpluses is introduced to highlight zoning regulation as an influential competition policy tool. Depending on the regulator's political profiles and the demand, it is shown that zoning can lead to strong, weak, or moderate competition.     

A NOTE ON MULTIPURPOSE AND MULTISTOP SHOPPING,SALES, AND MARKET AREAS OF FIRMS*

ABSTRACT. The paper characterizes the aggregate demand addressed to firms in a situation such that consumers are allowed to purchase during the same journey several commodities from several firms located in a one-dimensional space. It is a duopoly in which both firms sell the two commodities. The individual demand is assumed to be price-inelastic.     

An Evolutionary New Economic Geography Model

In this paper we present a general new economic geography model with multiple industries and regions, full labor and capital mobility, land use in production and consumption, and a dynamic adjustment process in which consumers maximize utility and firms respond to nonzero profits. All industries use intermediate inputs as well as land, labor, and capital. Systems of cities form endogenously within this framework, including asymmetrical urban hierarchies and cities of different sizes and industry compositions. Each urban area has a bid-rent gradient and zones with land uses and densities as in the von Thünen model. The equilibrium depends not only on initial conditions but also on speeds of adjustment. The model is a prototype for empirical implementation, as illustrated with a simulation of the effects of transportation cost reductions.     

Hotelling Games with Three,Four, and More Players*

Abstract. This paper extends the interval Hotelling model with quadratic transport costs to the n‐player case. For a large set of locations including potential equilibrium configurations, we show for n > 2 that firms neither maximize differentiation—as in the duopoly model—nor minimize differentiation—as in the multi‐firm game with linear transport cost. Subgame perfect equilibria for games with up to nine players are characterized by a U‐shaped price structure and interior corner firm locations. Results are driven by an asymmetry between firms. Interior firms are weaker competitors than their rivals at the corners. Increasing the number of firms shifts even more power to the corner firms. As a result, there is too much differentiation from the social perspective if n ≤ 3, while adding firms leads to a level of differentiation in equilibrium below the social optimum.     

Beyond the local: places,people, and brands in New England beer marketing

Despite decades of domination by a few large companies, the American beer market has seen a dramatic resurgence of microbreweries. Contrary to conventional oligopolistic market theories, small firms have consistently gained market share from their entrenched competitors. Researchers have attributed this success to “neolocalism.” Through their marketing, microbreweries appeal to consumers’ desire for connections to real people and distinctive products from local places. However, no study has verified whether this pattern is most characteristic of microbreweries. With newer firms threatening their market share, larger firms might adopt neolocal claims, but little empirical attention has been directed at large brewers, and mid-sized, regional firms have been largely ignored by researchers. This paper uses content analysis of beer packaging to investigate the nature of the appeals made to consumers. I find that while microbreweries do make neolocal claims, regional breweries are more likely to associate their products with places on a local scale. Large breweries make few such claims, but instead rely on “reflexive branding”: marketing that refers back to the brand itself rather than borrowing existing symbolism from people or places. These findings partly support the neolocal perspective, but also challenge our expectations of which firms use neolocal appeals the most.     

Regional Competition for Mobile Oligopolistic Firms: Does Public Provision of Local Inputs Lead to Agglomeration?

We develop a model in which two regional governments compete for two mobile oligopolistic firms. Regional governments provide local infrastructure to attract mobile firms in order to increase regional employment and income. Firms face the trade-off between better regional infrastructure and fiercer competition for local workers. Strategic interaction prevails at the regional level as well as at the firm level. We show that an equilibrium with spatial concentration of firms as well as an equilibrium with spatial diversification of firms exists. In almost all cases regional competition leads to a suboptimal provision of local infrastructure.     

LOCATING OUTSIDE A LINEAR CITY CAN BENEFIT CONSUMERS*

ABSTRACT We investigate the effects of restricting the locations of firms in Hotelling duopoly models. In standard location‐price models, the equilibrium distance between firms is too great from the viewpoint of consumer welfare. Thus, restricting the locations of firms and shortening the distance between them improves consumer welfare by reducing prices and transport costs. We introduce strategic reward contracts into location‐price models and find that, in contrast to the above result, restrictions on the locations of firms reduce consumer welfare. These restrictions reduce transport costs but increase prices by changing the strategic commitments of the firms.     

PRICE AND LOCATION CONJECTURES IN MEDIUM- AND LONG-RUN SPATIAL COMPETITION MODELS*

ABSTRACT. This paper examines medium-run and long-run equilibria in unbounded (circular) and bounded (linear) one-dimensional multifirm markets. A price-location adjustment model is outlined that dows simulation of the spatial equilibrium when these firms anticipate reactions from their nearest spatial rivals. Thus, the market equilibrium is derived from the interdependent but atomistic decisions of the competing firms and is not imposed by some outside observer or agency. Ail conjectures are exogenous; the three well-known price conjectures (Greenhut-Ohta, Hotelling-Smithies, and Losch) are highlighted; and the relevant comparative statics are provided.     

THE EFFECT OF RETAIL FIRM OWNERSHIP ON PRICE EQUILIBRIUM*

ABSTRACT. This paper examines the effect of retail firm ownership on price equilibrium using a simple linear-city model. It is shown that price divergence emerges due to the differences in retail firm ownership, because retail firms under different ownership internalize shopping externalities differently. It is also shown that if a commercial center has two specialized retail firms, these stores charge the same markup for different goods at the equilibrium.     

HOTELLING'S “MAIN STREET” WITH MORE THAN TWO COMPETITORS*

ABSTRACT. I analyze oligopolistic competition among three or more firms located on Hotelling's (1929) Main Street and show that in contrast with Hotelling's duopoly, the symmetric locational structure supports a noncooperative equilibrium in prices. However, in a two-stage game of location choice in the first stage, and price choice in the second stage, there exists no subgame-perfect equilibrium where the whole market is served. This is because, starting from any locational pattern, firms have incentives to move toward the central firm. This strong version of the Principle of Minimum Differentiation destroys the possibility of a locational equilibrium. The results are a direct consequence of the existence of boundaries in the space of location. The sharp difference between these results and those of the standard circular model (whose product space lacks boundaries) shows that the general use of the circular model as an approximation to the line interval model may be unwarranted.     

Innovation projects and local production networks: A case study of Hertfordshire

This paper evaluates some of the key arguments underlying what is called here the local production network paradigm (LPNP). These are presented as three interlinked hypotheses that turn on the idea that firms competing in world markets need to accommodate continuous change by fostering product or process innovation. The definition of innovation used in this study is “the commercially successful exploitation of new technologies, ideas or methods through the introduction of new products or processes, or through the improvement of existing ones” (EC DG XIII, 1996, p. 54).

One conventionally described organizational response to this requirement to accommodate continuous innovation is to dis‐integrate firms and set up local production networks. Local production networks are defined in this study as “collaborative linkages between local firms and local factors of production”. Such networks are said to rely on local resources of various kinds to enable them to innovate on a continuous and incremental basis. As a result of such dependencies on local factors, and their interconnectedness with each other, the local production network (LPN) firms then become ‘embedded’ in their localities. Such networked economies have been variously described as new industrial districts, areas of flexible specialization, and innovative milieux.

The evidence presented to test these hypotheses is based on a case study of innovative, award‐winning firms in Hertfordshire. The findings show that although these firms do compete successfully in fast‐moving international markets, they do not rely much on local production networks, as defined here, to enable them to do so. The findings call into question the general applicability of the LPNP. Questions are raised particularly with respect to innovation in the important minority of highly innovative core metropolitan regions.

Innovation is argued to be an interactive process that is both driven by a steady supply of technological advances and stimulated by different types of consumer demand. In the case of the firms interviewed in Hertfordshire, most of their innovative projects were developed by the firms working individually, and in isolation, from other local businesses using high quality, knowledge, information, human resources and venture capital. At the same time, these firms were also pulled by demands from military, health and company consumers. Only in the case of the minority of innovations that were purchased in the first instance by private final consumers were local production networks of some significance.     

Periodicity and Market Interactions

This paper develops two systems of modeling periodic shopping behavior. The first approach uses a system of Volterra equations to define interactions between populations of consumers and firms in a special market. The second approach develops the relationship between trip length, frequency, and time for consumers in the context of the place utility model. The final section investigates ways of integrating the two approaches.