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Spatial price discrimination and the locations of firms with different product selections or product varieties
Abstract
The equilibrium locations of two firms are partially centralized to the socially optimal extent if there is spatial price discrimination, and if each firm has two out of three products, or else one variety of a differentiated product with some consumers indifferent between varieties.
... In this paper, we extend Braid (2008) to capture the sensitivity of equilibrium locations of downstream firms, selling different varieties of a product, to the vertical structure of an industry when spatial moves are sequential. Braid (2008) showed that the equilibrium locations of two firms are partially centralized to the socially optimal extent if there is spatial price discrimination, and if each firm has two out of three products, or else one variety of a differentiated product with some consumers indifferent between varieties. ...
... In this paper, we extend Braid (2008) to capture the sensitivity of equilibrium locations of downstream firms, selling different varieties of a product, to the vertical structure of an industry when spatial moves are sequential. Braid (2008) showed that the equilibrium locations of two firms are partially centralized to the socially optimal extent if there is spatial price discrimination, and if each firm has two out of three products, or else one variety of a differentiated product with some consumers indifferent between varieties. In what follows, we demonstrate the effect of sequential moves by downstream firms engaged in spatial competition in a vertically related industry where no firm can produce all the varieties that consumers demand. ...
We demonstrate the sensitivity of the location of downstream firms, engaged in sequential spatial competition, to the vertical structure of an industry where no downstream firm can produce all varieties demanded.
... Papers subsequent to Hotelling (1929) have also addressed suppliers' location choices (e.g., Anderson and De Palma, 1988;Anderson and Neven, 1991;Braid, 2008;Gupta, 1992;Hamilton et al., 1989;Hurter Jr. and Lederer, 1985;MacLeod et al., 1988; for an overview, see Biscaia and Mota, 2013). The results of these studies indicate that suppliers tend to choose the socially optimal locations if they can use spatial price discrimination, and if suppliers-instead of consumers-incur the transportation costs. ...
In order to reduce the high level of concentration in the market segment of statutory audits of listed companies and to improve audit quality, new audit market regulations have been introduced (e.g., the mandatory rotation of the audit firm in the EU and the prohibition of single-provider auditing and consulting in the EU and in the U.S.). Other measures are currently discussed (e.g., joint audits or shared audits in the UK). However, the empirical evidence as to whether such regulations have the expected effects and whether there is actually a negative correlation between concentration and audit quality is mixed. This could be because the effects of regulatory measures on auditor and auditee incentives and their effects on market structure are interdependent, and, moreover, simultaneously determine audit quality. We therefore do not only provide a structured overview of the empirical literature on the effects of audit market regulations, but also discuss how to analyze these effects based on analytical models.
... Under mill (discriminatory) pricing, besides transportation cost, the firm charges the same (different) product price p m (p d ) to each individual regardless of (depending on, respectively) his location. Following models of spatial competition with endogenous location and prices, we assume a sequential-move model, with location chosen in the first stage and prices chosen in the second stage (Hwang and Mai 1990;Braid 2008). 12 In the following sections, we employ backward induction to solve for the equilibrium. ...
We analyze a two-stage sequential-move model of location and pricing to identify firm’s location, output, and welfare. We consider two pricing regimes (mill pricing and spatial price discrimination) and, unlike previous literature, allow in each of them for a non-uniform population density, non-constant location costs (i.e., the setup costs, such rental costs and land prices, differ by firm’s location), and endogenous market boundaries. Under constant location costs, our results show the firm locates at the city center under both mill and discriminatory pricing, and that output is larger under spatial price discrimination. Welfare comparisons are, however, ambiguous. Under non-constant location costs, we find the optimal location can move away from the city center, and does not coincide across pricing regimes. Compared with mill pricing, spatial price discrimination generates a higher level of output. We also find that welfare is higher (lower) under mill than under discriminatory pricing when transportation rates are low (high, respectively).
... Consumers incur linear transportation costs, in addition to the product price. Hotelling (1929) focused on the Nash equilibrium in the price-setting stage of the game; subsequent papers have investigated suppliers' location choices in more detail (Hurter and Lederer 1985;Anderson and De Palma 1988;MacLeod, Norman, and Thisse 1988;Hamilton, Thisse, and Weskamp 1989;Anderson and Neven 1991;Gupta 1992;Braid 2008; for an overview, see Biscaia and Mota [2013]). When suppliers can set prices contingent on consumers' locations (spatial price discrimination) and suppliers-instead of consumers-incur the transportation costs, the suppliers tend to choose the socially optimal locations. ...
Recently, a system of audit firm rotation has been implemented for the audits of listed companies conducted in the EU. In the US, in contrast, the regulator decided against such rotation. Whereas proponents argue that rotation would strengthen independence and decrease audit market concentration, opponents stress the importance of auditors' learning effects, which would be eliminated by a change in auditors.
In extending the market matching model of Salop (1979), we provide an analysis that integrates these contradictory views. We assume that both auditors' industry expertise and their experience in auditing a client decrease audit costs. We investigate the bidding strategies applied to re-acquire clients that were lost due to rotation, auditors' profit contributions, the equilibrium number of auditors (i.e., audit market concentration), and the economic importance of specific clients.
Our findings indicate that the regulators' goals of simultaneously decreasing client importance and audit market concentration are in direct conflict, and therefore the rotation system might have unintended consequences. Our model thus suggests how different institutional parameters give rise to economic forces that can support diverging decisions regarding the implementation of MAR.
... In their paper Beladi et al. (2010) attempt to extend the work of Braid (2008) to demonstrate the e¤ect of a cross-border merger between upstream …rms on the equilibrium locations of downstream …rms selling di¤erent varieties of a product. They claim that the pre-merger autarkic Nash equilibrium locations of two downstream retailers coincide with the Nash equilibrium locations of the same …rms in the post-merger free trade case. ...
The aim of this paper is to revise and correct the results obtained in Beladi et al. [Beladi, H., Chakrabarti, A., Marjit, S., 2010. Cross-border merger, vertical structure, and spatial competition. Economics Letters 109, 112-114]. Speci
fically, we prove that the Nash equilibrium locations of the downstream fi
rms are the same in the pre-merger free-trade case as they are following a cross-border upstream merger.
... JEL classi…cation: L13, L42, D43, R32, F10, F12 Keywords: Price-discrimination; Spatial-competition; Firm-location; Cross-border merger In 2010, Beladi, Chakrabarti and Marjit attempted to generalize results previously obtained by Braid (2008) to the case of a vertically structured industry. They published two papers, one in February 2010 ( Beladi et al., 2010a) and a second one in November 2010 (Beladi et al., 2010b). ...
Following the publication of Eleftheriou and Michelacakis (2016a), it was brought to our attention that the problem identified and corrected in Eleftheriou and Michelacakis (2016a) affects more papers than just the Beladi et al. (2008). Two such instances of published papers that we know of are the Beladi et al. (2010a) and Beladi et al. (2010b). The aim of this short addendum is to warn the reader against the validity of the results in these two papers and perhaps others using the same basic duopoly model as in Beladi et al. (2008). We look into the origins of the fallacy and make an announcement of corrected versions of some of the affected conclusions referring elsewhere for precise details.
... While the current global crises have dampened this trend, there is a growing consensus 2 that " a new wave " of cross-border mergers will be triggered by the imminent exit of public funds from ailing industries in the immediate aftermath of the crises 3 . With this backdrop, in this paper, we extend 4 the work of Braid (2008) to demonstrate the effect of a cross-border merger between upstream firms on the equilibrium locations of downstream firms selling different varieties of a product. ...
We look at the implications of a cross-border merger upstream in a vertically related industry where no downstream firm can produce all varieties demanded.
The welfare effects of regulation are of crucial importance to policy makers. To this end, we present a model of n firms with differentiated costs competing in a linear market within the framework of spatial price discrimination. We prove that the Nash equilibrium locations of firms are always socially optimal irrespective of the number of competitors, the distribution of consumers, firms' cost heterogeneity, the level of privatization, and the number and/or the varieties of the produced goods. We also provide an algorithm on how to find the unique Nash equilibrium in the case of uniformly distributed consumers.
The analysis in this chapter focuses on how enterprises make strategic decisions regarding their future development in an environment of uncertainty. The strategic planning of enterprises on issues involving long-term investment activity, R&D, innovation, identification, and exploitation of entrepreneurial opportunities is based on a background comprising various sociological, psychological, and economic starting points. Simultaneously, issues are highlighted in relation to the identification of uncertainty that can alter strategic planning and cause the failure of traditional investment evaluation methods.
The aim of this paper is to revise and correct the results obtained in Beladi et al. (2008). Specifically, we prove that in the pre-merger case, Nash equilibrium locations are socially optimal, whereas a vertical merger will relocate downstream firms by making them move to the right of their old socially optimal positions while keeping their in-between distance intact.
We show that, in a vertically linked duopoly where neither firm can produce all varieties demanded, spatial competition between a public and a private firm induces them to deviate from the socially optimal location. We identify specific conditions under which a change in the degree of privatization induces one firm to move toward, while the other moves away from the socially optimal location. There exists a critical level of privatization above (below) which the public and private firms will come close (drift apart) with a rise in the degree of privatization.
This paper examines the socially optimal (and also equilibrium) locations of two stores or libraries on a linear market of unit length. If each consumer has probability of finding a desired product at each store, then the socially optimal locations are never completely centralized for full information, but are completely centralized for when costly visit search is necessary. The Nash equilibrium locations of two stores, and various alternative models for the socially optimal locations of two stores, are also examined.
We visit the role of privatization in the location decision of firms in an industry where no firm can produce all varieties demanded. We demonstrate that the Nash equilibrium locations are socially optimal, in the presence of a publicly owned firm, notwithstanding the degree of privatization.
We consider a standard linear city model with two firms, where firms and consumers both incur transport costs. This is done by assuming that the total transport cost is shared by the buyers and sellers according to an exogenously given rule. In the model, firms choose locations and prices, with the transportation cost being linear in distance. We first derive the profit function for the two-stage transport cost sharing game and find that it has a complex form. We then invoke simplifying assumptions and solve for two different games. We provide a complete characterization for the equilibrium of the location game between the two firms by assuming fixed prices. We then examine the price game when the two firms are constrained to locate at the same spot. The equilibria of these two games provide insights about the complex two-stage game.
With Bertrand-Nash mill-price competition, travel costs proportional to distance squared, and three firms on an interval, the equilibrium locations of the peripheral firms are further from the center than is socially optimal. If there is a central intersection, with four (or more) finite roadway segments radiating outward from the center (a small city spread along two intersecting roadways), and with one firm at the center and one on each radial segment, then the equilibrium locations of the peripheral firms are closer to the center than is socially optimal. Extensions include competition with spatial price discrimination, a more complicated system of intersecting roadways, and more than one firm on each roadway segment.
This critical review focuses on the development of spatial competition models in which the location choice by firms plays a major role. Therefore, after a brief review of the roots of spatial competition modeling, this paper intends to offer a critical analysis over its recent developments. The starting point is the recognition of the increased importance of this topic through the quantification of the research in this field by using some bibliometric tools. After that, this study proceeds by identifying the main research paths within spatial competition modeling. Specifically, the type of strategy (Bertrand vs. Cournot competition) and its implications over location equilibria are discussed. Additionally, it is presented a comparison of the effects on the location equilibria of the most typical assumptions in literature, that respect to the market (linear vs. circular), production costs, transportation costs, as well as the number of firms. Finally, the type of information (complete vs. incomplete) and its effects over the equilibria are also discussed.
This paper assumes Bertrand‐Nash‐mill‐price competition between two firms on a unit interval, with each firm selling two out of three products, and transportation costs that are proportional to distance squared. If c consumers per unit length desire each monopoly product, and b per unit length desire the duopoly product, then the equilibrium locations of the two firms are more centralized the higher the ratio c/b , more centralized than the socially optimal locations for c/b above a critical value, and completely centralized for c/b above a different critical value. A number of variations of the model are also presented.
Resumen
Este artículo asume la competencia Bertrand‐Nash para precios en fábrica entre dos empresas con intervalo de una unidad, que cada empresa vende dos de un total de tres productos, y que los costos de transporte son proporcionales al cuadrado de la distancia. Si c consumidores por unidad de longitud desean cada producto de un monopolio, y b por unidad de longitud desean el producto del duopolio, entonces las localizaciones del equilibrio de ambas empresas estarán más centralizadas cuanto mayor sea la razón c/b, más centralizadas que las localizaciones socialmente óptimas para c/b por encima de un valor crítico, y completamente centralizadas para c/b por encima de un valor crítico diferente. Se ofrece además una serie de variaciones del modelo.
We show how, in an industry where no downstream firm can produce all varieties demanded, a vertical merger with a monopoly upstream will induce each downstream firm (inside and out of the merger) to deviate from the socially optimal location.
In this paper, the authors investigate the implications of flexible manufacturing for market structure. In the received theory of market structure, based largely on inflexible techniques of production, a number of well-known forces work to limit concentration. In the authors' model, none of these forces exists. Hence, they conclude that flexible manufacturing promotes concentration through preemption and mergers, or equivalently through cartels. Interestingly, the concentrated market structures associated with flexibility may or may not be welfare-dominated by a regime in which monopolization is not allowed. Copyright 1994 by American Economic Association.
The paper is divided into two parts: one-dimensional markets and two-dimensional markets. Also, we develop both one and two-dimensional models. Within each, we distinguish (a) bounded, (b) unbounded but finite, and (c) unbounded, infinite spaces. Among other things, we show: in one dimension, the nature of the space is not, as many investigators have thought, critical; in two dimensions, however, the very existence of equilibrium is seen to depend upon the nature of the space; the commonly-used rectangular customer density function yields results that do not generalize to any other density function; the existence of multiple equilibria in both one and two dimensions is a pervasive phenomenon in any of the spaces studied, and MD occurs only when the number of firms is restricted to two. Although the analysis and discussion are in terms of location theory and are concerned with the relationship between equilibrium configuration of firms and the transport-cost minimizing configuration, many of the results generalize to other forms of differenciation. The conditions under which the results generalize are considered in the concluding section of the paper. (This abstract was borrowed from another version of this item.)
After the work of the late Professor F. Y. Edgeworth one may doubt that anything further can be said on the theory of competition among a small number of entrepreneurs. However, one important feature of actual business seems until recently to have escaped scrutiny. This is the fact that of all the purchasers of a commodity, some buy from one seller, some from another, in spite of moderate differences of price. If the purveyor of an article gradually increases his price while his rivals keep theirs fixed, the diminution in volume of his sales will in general take place continuously rather than in the abrupt way which has tacitly been assumed.
This paper analyzes sequential entry with perfect foresight in a competitive spatial price discrimination model, with both an exogenous and an endogenous number of firms. The SPNE locations do not coincide with the social cost minimizing locations.
Modern theories of monopolistic competition have borrowed extensively from techniques developed in location theory and the theory of spatial pricing: the monopolistically competitive firm is assumed to choose a ‘location’ and price for its product. A subject that has been of increasing concern in this corpus of theory is that there exists no free-entry price-location equilibrium. In this paper we demonstrate that free-entry price-location equilibrium exists provided only that producers are allowed to price discriminate among customers in a reasonable manner. Equilibrium is modelled as a two-stage game using the Selten concept of subgame perfect Nash equilibrium. It is shown that the equilibrium discriminatory price system is one initially identified by Hoover. In addition, we show that equilibrium is not unique. The precise nature of equilibrium in a particular market will be dependent upon the history of that market.
A model with two firms competing in location and sales is analyzed for the case of spatial discrimination. Consumers are uniformly distributed along a line segment and have identical downward sloping demands. Two games are solved and results are compared. In one game, firms first choose locations and then quantity schedules; in the other, the final stage is choice of price schedules. Prices and transport costs are lower under Bertrand competition. Profits are higher under Cournot competition for low transport costs, but the reverse holds for larger values of these costs. Aggregate welfare is higher in the Bertrand competition case. In both games, firms locate in such a way as to minimize their own transport costs for the sales pattern arising in equilibrium, but the equilibrium configurations are quite different.
The equilibrium locations of three stores may be completely centralized (in the absence of price competition) if different stores sell different varieties of a differentiated product or different combinations of varieties that are partially overlapping.
The socially optimal locations of three stores (or facilities) may be relatively centralized if stores are not certain to have what consumers want due to stockouts or limited product selections.
A partly analytical, partly computational approach is used to study mixed strategy equilibria of Hotelling's model of sp atial competition in which each of two firms chooses a location in a line segment and a price. There is a unique (up to symmetry) subgame perfect equilibrium in which the locations choices are pure. In it, t he locations are close to the quartiles of the market, and the suppor t of the equilibrium mixed-price strategy of each firm is the union o f two short intervals. There is also a subgame perfect equilibrium in which the firms randomize over locations. Copyright 1987 by The Econometric Society.
Two costlessly mobile firms are to be located in a market region, a subset of the plane. The firms compete by setting locations and delivered price schedules. To study this competitive situation an appropriate extensive form game is defined, along with an appropriate noncooperative solution concept. Existence and general properties of the equilibrium are demonstrated. Among the results are: Each firm increases its profit by locating so as to decrease total cost to both firms of serving the market. Firms will never locate coincidentally if they have identical production costs and transport cost rates, or if these are different and the firms are located in a circular market region having a uniform demand distribution.
The purpose of this note is to show that the so-called Principle of Minimum Differentiation, as based on Hotelling's 1929 paper "Stability in Competition," is invalid.
In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. In contrast with the principal-agent models that are extended within, here the presence of ties in the agents' best-response correspondences yields discontinuous payoff functions for the agencies. These discontinuities are dealt with via efficient tie-breaking rules. The main results of this paper are a proof of existence of (mixed-strategies) Nash equilibria in the case of profit-maximizing agencies, and of socially efficient allocations when the firms are risk minimizers. It is also shown that in the particular case of the entropic risk measure, there exists an efficient "fix-mix" tie-breaking rule, in which case firms share the whole market over given proportions.
Stability in competition
- Hotelling