Spatial Price Competition: A Network Approach

Ohta 1988; Stahl 1989) and locational welfare (Stern 1972; Capozza and Van Order 1977; Benson 1984), we must not forget that the geographic properties of these models invariably have been naive. Besides employing several assumptions of parametric uniformity (for example, identical consumer demand and a constant transportation rate), researchers usually have simplified the geographic context for interfirm competition in two other important ways. First, the boundary or end firm problem has commonly been dealt with by envisaging an infinite (two-dimensional) plane (Liisch 1954; Mills and Lav 1964; Greenhut, Hwang, and Ohta 1975) or finite circle (Chamberlin 1953; Eaton 1976; Novshek 1980) over which competing firms locate. Only in a few cases, apparently, have spatial markets been depicted as both finite and bounded (Hotelling 1929; Eaton and Lipsey 1975; Carruthers 1981; Okabe and Suzuki 1987). As an extension of Eaton and Lipsey (19751, Okabe and Suzuki (1987) have discussed stability conditions and configuration of firms on a bounded two-dimensional space as a function of the number of spatial rivals, noting the instabilities associated with market boundaries. While we certainly agree with Lancaster (1979, p. 191) that it is a judgment call “as to how important events near the boundary are compared to events in the interior,” we feel that since the real world is indeed characterized by a multiplicity of (natural and man-made) boundaries, more effort must be made to accommodate the end (exterior) firm phenomenon in spatial competition models (Coyte et al. 1988; Hay and Johnston 1980; Fik 1989). Second, researchers often have assumed that the unbounded spatial market is in long-run equilibrium without ever establishing just how this equilibrium has been attained (recently, for example, Beckmann 1989; Capozza and Van Order 1989). In other words,

[1]  M. Feldstein.  Social Security and Saving: The Extended Life Cycle Theory , 1976 .

[2]  George Norman.  Spatial competition and spatial price discrimination , 1981 .

[3]  N. Carruthers.  Location choice when price is also a decision variable , 1981 .

[4]  G. Mulligan,et al.  Price variation in spatial markets: the case of perfectly inelastic demand , 1989 .

[5]  R. Lipsey,et al.  The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition , 1975 .

[6]  On the shape and size of market areas , 1989 .

[7]  Observations on the Shape and Relevance of the Spatial Demand Function , 1975 .

[8]  Asymmetrical Price Conjectural Variation in Spatial Competition Models , 1989 .

[9]  Robert Van Order,et al.  SPATIAL COMPETITION WITH CONSISTENT CONJECTURES , 1989 .

[10]  Timothy J. Fik,et al.  Spatial Competition and Price Reporting in Retail Food Markets , 1988 .

[11]  Edward H. Chamberlin.  The Product as an Economic Variable , 1953 .

[12]  H. Hotelling.  Stability in Competition , 1929 .

[13]  Pricing under Spatial Competition and Spatial Monopoly: Reply , 1977 .

[14]  K. Lancaster,et al.  Variety, equity, and efficiency , 1979 .

[15]  H. Ohta,et al.  Theory of Spatial Pricing and Market Areas , 1975 .

[16]  The optimal size of market areas , 1972 .

[17]  W. Novshek.  Equilibrium in simple spatial (or differentiated product) models , 1980 .

[18]  Symposium location, spatial pricing, and spatial competition: Introduction , 1989 .

[19]  Martin J. Beckmann.  Spatial price policies revisited , 1976 .

[20]  B. Eaton,et al.  FREE ENTRY IN ONE‐DIMENSIONAL MODELS: PURE PROFITS AND MULTIPLE EQUILIBRIA* , 1976 .

[21]  SPATIAL VARIATIONS IN GROCERY PRICES: FURTHER ATTEMPTS AT MODELING , 1980 .

[22]  S. Hakimi.  On locating new facilities in a competitive environment , 1983 .

[23]  R. Lipsey,et al.  The Non-Uniqueness of Equilibrium in the Loschian Location Model , 1976 .

[24]  G. Mulligan,et al.  Price variation in spatial oligopolies. , 2010 .

[25]  E. Mills,et al.  A Model of Market Areas with Free Entry , 1964, Journal of Political Economy.

[26]  B. Benson.  Spatial competition with free entry, Chamberlinian tangencies, and social efficiency , 1984 .

[27]  F. Hahn.  Equilibrium and macroeconomics , 1986 .

[28]  Atsuyuki Okabe,et al.  Stability of Spatial Competition for a Large Number of Firms on a Bounded Two-Dimensional Space , 1987 .

[29]  C. Gannon.  Consumer demand, conjectural interdependence, and location equilibria in simple spatial duopoly , 1972 .

[30]  George Norman,et al.  The Economics of Imperfect Competition , 1987 .