Spatial Price Discrimination in the Spokes Model

• Published date: 01 September 2014
• Author: Carlo Reggiani
• Date: 01 September 2014
• DOI: http://doi.org/10.1111/jems.12066

Spatial Price Discrimination in the Spokes Model

CARLO REGGIANI

School of Social Sciences

University of Manchester

Manchester M13 9PL

carlo.reggiani@manchester.ac.uk

The spokes model allows to address nonlocalized spatial competition between firms. In a spatial

context, firms can price discriminate using location-contingent pricing. Nonlocalized competition

implies that neighboring effects are not relevant to firms. This paper analyzes spatial price

discrimination and location choices in the spokes model. Highly asymmetric location patterns are

one outcome if the number of firms is sufficiently high: in that case, one firm supplies a generally

appealing product whereas others focus on a specific niche. Moreover, multiple equilibria arise for

intermediate values of the number of firms. In this case, the location patterns do not always globally

minimize the sum of transport costs: asymmetric configurations distribute more efficiently the

cost between firms.

1. Introduction

Price discrimination is a pervasive practice in many markets: it takes place both in

highly concentrated markets and in more competitive ones, in which several firms are

active. Price discrimination also arises in markets strongly characterized by a spatial

dimension. A feature of these markets is that competition is not necessarily localized:

firms compete to attract a consumer not only with neighboring firms but also with more

distant ones. A number of spatial nonlocalized markets exist where price discrimination

takes place; moreover, if location is interpreted as the space of characteristics, examples

include alcoholic and soft drinks, shoes and clothing, software, and many others: in all

these markets, IT and marketing innovation are leading to wider and more personalized

product lines as firms try to better match consumers’ tastes and extract surplus from

consumers in different segments.

A key strategic decision in these markets is firms’ location and, hence, which

segment of the market to be targeted. A very relevant question is whether firms hit on a

specific niche of the market or adapt their product line in a way that makes it appealing

to a wider segment of consumers, that is, they supply a “general purpose” product line.

The spokes model (Chen and Riordan, 2007a) provides a framework to analyze

markets characterized by spatial but nonlocalized competition between firms: the model

extends the Hotelling (1929) approach to the case of several segments and an arbitrary

number of firms by modeling the market as a collection of spokes with a common core.

Consumers can buy from whichever firm they like: if the firm is not located on their

own spoke, however, either the customer or the delivering firm have to travel through

the center of the market. The spokes model is an important alternative to the circular

I thank Hemant Bhargava, Anindya Bhattacharya, Bipasa Datta, Norman Ireland,Mario Pezzino, Mark Lijesen

Peter Simmons, Klaus Zauner, and specially Ramon Caminal; seminar and conference participants in York,

Manchester,Lecce, and Ljubljana; the editors and the anonymous referees for helpful comments and discussion.

The usual disclaimer applies.

C2014 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume23, Number 3, Fall 2014, 628–649

Spatial Price Discrimination in the Spokes Model 629

city model (Salop, 1979) when the neighboring effects of competition are not particularly

relevant.

This paper addresses the question of what segments of the market firms target by

analyzing optimal location in the spokes model. The analysis shows that, in presence

of price discrimination/product personalization, the equilibrium outcome can be char-

acterized by one firm whose product line is appealing to consumers in all segments of

the market; the remaining competitors target only part of their own market segment,

focusing on a niche of customers with a strong preference for the products supplied by

the firm. In devising the optimal location/product line patterns in the spokes model

with price discrimination, it is also found that multiple equilibria arise depending on

the number of firms in the market. An interesting finding is that, in that case, one of the

outcomes may not globally minimize the sum of transportation costs.

The spokes model has been introduced relatively recently but has already been

widely adopted. Chen and Riordan (2007a) show that the model captures Chamberlin’s

original idea of monopolistic competition; moreover,strategic interaction between firms

may lead to price increasing competition. Caminal and Claici (2007) use the model to

show how the business stealing effect makes loyalty-rewardingschemes mostly procom-

petitive. Chen and Riordan (2007b) illustrate the joint relevance of vertical integration

and exclusive dealing in foreclosing the upstream market and increasing downstream

prices. Germano (2009) and Germano and Meier (2013) adopt the model to address issues

related to the bias of information in media markets. Caminal (2010) analyzes the supply

of content in different languages in bilingual contexts. Caminal and Granero (2012) look

at the provision of variety by multiproduct firms in the spokes model. Mantovani and

Ruiz-Aliseda (2011) analyze cooperative innovation activity of firms producing com-

plementary products. A unifying characteristic of the recalled literature is the focus on

pricing and entry aspects of the interaction between firms. This paper is, to the best of

my knowledge, the first to address the issue of location in the spokes model.

The contribution of this paper is also related to the literature on spatial price dis-

crimination and endogenous location choice. Thisse and Vives (1988) observed that price

discrimination in a spatial market is detrimental to firms’ profits: firms exploit their in-

formation on consumers’ locations and can match any offer made by a rival firm, unless

this is lower than the cost of delivering the good. The classical paper of Lerner and

Singer (1937) established that the optimal location configuration on a line is transport

cost minimizing. Lederer and Hurter (1986) analyze endogenous location and establish

the existence of price-location equilibria in a rather general (e.g., two-dimensional prod-

uct space, generic consumers’ distribution) spatial duopoly. Their results confirm that

the profit maximizing locations chosen by firms correspond to the ones that minimize

the overall transport costs afforded by firms. However, in presence of multiple equi-

libria, the location configuration may not be globally minimizing the sum of transport

costs. MacLeod et al. (1988) consider the price-location equilibria of an n-firms spa-

tial model where the number of firms is endogenously determined by the fixed costs.

Free entry might lead to either a too large or a too small number of varieties. Vogel

(2011) analyzes spatial price discrimination and the location of heterogeneous firms in

the circle finding that more efficient firms are relatively more isolated in equilibrium.

Anderson and De Palma (1988) question Lederer and Hurter’s results by introducing

product heterogeneity: the equilibrium location pattern minimizes the overall transport

costs only in presence of homogeneous or very heterogeneous products. Konrad (2000)

shows that in presence of a contest for consumers, in which firms afford sunk costs, the

equilibrium locations are not minimizing overall transport costs. Finally, Gupta (1992)