An experiment on spatial competition with endogenous pricing

The Quarterly Review of Economics and Finance, 2005

This paper offers some preliminary steps in the marriage of some of the theoretical foundations of the new economic geography with spatial computable general equilibrium models. Modeling the spatial economy of Brazil using the usual assumptions of CGE models makes little sense when one state, São Paulo, accounts for 40% of GDP and where transportation costs are high and accessibility low compared to European or North American standards. Hence, handling market imperfections becomes imperative as does the need to address internal spatial issues from the perspective of Brazil's increasing involvement with external markets such as MERCOSUL, EU, NAFTA. The paper builds on the B-MARIA-27, a multiregional CGE model of the Brazilian economy; non-constant returns and non-iceberg transportation costs are introduced and some simulation exercises carried out. The results, limited in this paper to short-run considerations, confirm the asymmetric impacts that transportation investment has on a spatial economy in which one state (São Paulo) is able to more fully exploit scale economies vis a vis the rest of Brazil. The analysis also reveals the importance of parameter estimation in handling imperfectly competitive markets.

Regional Science and Urban Economics, 2010

We study the relationship between competition and quality within a spatial competition framework where firms compete in prices and quality. We generalise existing literature on spatial price–quality competition along several dimensions, including utility functions that are non-linear in income and cost functions that are non-separable in output and quality. Our main message is that the scope for a positive relationship between competition and quality is underestimated in the existing literature. If we allow for income effects by assuming that ...

This article provides a general overview of spatial economics, which covers location theory, spatial competition, and regional and urban economics. After a brief review of the main theoretical traditions, the fundamental role of non-convexities and imperfect competition is highlighted. The main challenges faced by theoretical and empirical research are also discussed, followed by a broader discussion of the relationship between this field of research and other subfields of economics and other disciplines. What is spatial economics? In a nutshell, spatial economics is concerned with the allocation of (scarce) resources over space and the location of economic activity. Depending on how this definition is read, the realm of spatial economics may be either extremely broad or rather narrow. On the one hand, economic activity has to take place somewhere so that spatial economics may be concerned with anything that economics is concerned about. On the other hand, location analysis focuses mostly on one economic question, namely, location choice. This is only one decision among a large number of economic decisions. Which boundaries for spatial economics? In practice, we can distinguish three sets of questions for which the importance of the spatial dimension is very different. Consider first the core questions of spatial economics. For example, why are there cities? Why do some regions prosper while others do not? Why do we observe residential segregation? Why do firms from the same industry cluster? These are intrinsically 'spatial' questions, that is, questions in which the spatial dimension plays a dominant

Metroeconomica, 2008

In this paper we investigate the relationship between product market competition and managerial incentives within a circular city model with observable agency contracts. With respect to the case of unobservability studied by Raith , we find that optimal managerial contracts provide lower incentives, and that equilibrium expected prices and profits are higher. Changes in competition fundamentals have ambiguous effects, but observable contracts alleviate their impact on incentives. Finally, observability involves three major implications: managerial incentives are higher under price regulation than under competition; prices may increase with the number of firms; consumer welfare may diminish when competition increases.

ArXiv, 2021

Institutions and investors face the constant challenge of making accurate decisions and predictions regarding how best they should distribute their endowments. The problem of achieving an optimal outcome at minimal cost has been extensively studied and resolved using several heuristics. However, these works usually fail to address how an external party can target different types of fair behaviour or do not take into account how limited information can shape this complex interplay. Here, we consider the well-known Ultimatum game in a spatial setting and propose a hierarchy of interference mechanisms based on the amount of information available to an external decision-maker and desired standards of fairness. Our analysis reveals that monitoring the population at a macroscopic level requires more strict information gathering in order to obtain an optimal outcome and that local observations can mediate this requirement. Moreover, we identify the conditions which must be met for an indiv...

AAMAS

Institutions and investors face the constant challenge of making accurate decisions and predictions regarding how best they should distribute their endowments. The problem of achieving an optimal outcome at minimal cost has been extensively studied and resolved using several heuristics. However, these works fail to address how an external decision maker can target different types of fair behaviour and how limited information can shape this complex interplay. Here, we consider the well-known Ultimatum game in a spatial setting and propose a hierarchy of interference mechanisms based on the amount of information available to the external decision maker and desired standards of fairness. Our key findings show that asymmetric interactions have drastically different dynamics when compared to symmetric games, such as the Prisoner's Dilemma, and discuss why gathering information about the agents' behaviour allows for the most efficient investment strategies.

2011

This critical review focuses on the development of spatial competition models in which the location choice by firms plays a major role. Theref o , 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 r esearch paths within spatial competition modeling. Specifically, the type of strategy (Bertr and vs. Cournot competition) and its implications over location equilibria are discussed . A ditionally, it is presented a comparison of the effects on the location equilibria of the mo st typical assumptions in literature, that respect to the market (linear vs. circular), produc tion costs, transportation costs, as well as the number of firms. Finally, the type of information ( c...

Environment and Planning A, 2012

In previous research we argued in favor of an understanding of the capitalist space economy that is grounded in a socio-spatial dialectic and a computationally-based modeling methodology based upon the Goodwin Code . In this paper we extend our argument to illustrate the applicability of both our modeling methodology and ontology when addressing the challenges posed by a probabilistic regional political economy. To ground our discussion, we consider a situation in which the geography of uneven development makes a significant difference to theoretical propositions that are widely accepted by both mainstream and heterodox economists: oligopolistic competition in spatially interdependent markets. We explore the extent to which decisions about whether to treat space as homogenous or uneven have substantive theoretical implications for the set of spatio-temporal trajectories that are possible when total profit maximizing firms follow a 'local' or partial adjustment strategy out-ofequilibrium and are assumed to possess limited computational abilities and only limited information about the pricing strategies of their competitors. We focus on three overlapping questions resulting from the possible set the spatio-temporal trajectories that are generated by our model: (a) under what conditions does a partial adjustment model of price setting result in an equilibrium configuration of prices, outputs, and profits, (b) under what conditions is it rational for retailers to experiment by charging prices other than those prevailing a spatial price equilibrium, (c) to what extent does the nature and degree of spatial interdependencies endogenously generate irregular price structures that can be substantively disrupted by external shocks and display significant dependence on parameter values and initial conditions.

Journal of Urban Economics, 1984

Free entry in Liischian spatial competition leads to a tangency between each firm's negatively sloped average revenue and the downsloping portion of average costs-as in Chamberlin's monopolistic competition. It is generally concluded that this equilibrium involves too many inefficiently small firms. However, this conclusion is incorrect. 'Ihe difference between price and firm marginal production costs in spatial equilibrium is just sufficient to cover the additional marginal cost of output resulting from availability of multiple locations. This Chamberlinian tangency does not imply inefficiency, because it does not include all the social costs and benefits resulting from spatial competition. 'I thank M. L. Greenhut, Thomas Cosimano, and Hiroshi Ohta for helpful comments as I developed this model. 'Spatial competition does not really fit the textbook monopolistic competition model that is most closely associated with Chamberlin [28]. Rather, spatial competition more closely fits the linked oligopoly model which Chamberlin discussed [ll, pp. 103,104]. However, with entry to zero profits these oligopoly firms end up with demand curves tangent to the downsloping section of their average cost curves.

Journal of Regional Science, 1994

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.

Physica A: Statistical Mechanics and its Applications, 2000

We look at price formation in a retail setting, that is, companies set prices, and consumers either accept prices or go someplace else. In contrast to most other models in this context, we use a two-dimensional spatial structure for information transmission, that is, consumers can only learn from nearest neighbors. Many aspects of this can be understood in terms of generalized evolutionary dynamics. In consequence, we first look at spatial competition and cluster formation without price. This leads to establishement size distributions, which we compare to reality. After some theoretical considerations, which at least heuristically explain our simulation results, we finally return to price formation, where we demonstrate that our simple model with nearly no organized planning or rationality on the part of any of the agents indeed leads to an economically plausible price.

Journal of Regional Science, 1989

Equilibrium in spatial models invariably depends on firms' conjectures about how competitors will react to their price changes. This paper analyzes spatial price and location equilibrium when firms hold consistent (i.e. correct) conjectures. Most spatial models assume an exogenous conjecture. Consistent conjectures are one method, albeit a controversial one, for endogenizing the conjecture. We show that the consistent conjecture about a competitor's reaction to a price change in the simplest case is 1, ' s. When demand is elastic the consistent conjecture is a decreasing function of the radius. It is always below 1/3 and can be negative. In the third model, we show that the consistent conjecture declines as the number of dimensions and the number of competitors increases. *We acknowledge with thanks the helpful comments of Ralph Braid and anonymous referees.

Papers in Regional Science, 2013

This critical review focuses on the development of spatial competition models à la Hotelling in which the location choice of firms plays a major role. We start by quantifying the research in this field by using bibliometric tools. Thereafter, this study identifies the main research paths within spatial competition modelling. Specifically, the type of strategy (Bertrand vs. Cournot competition), the assumptions that are made in respect to the market (linear vs. circular), production costs, transportation costs, the number of firms and the type of information (complete vs. incomplete) and their effects on the location equilibria are also discussed.

Journal of Urban Economics, 1989

Belenky is correct in pointing out that certain derivations presented in Benson [3] are incorrect. That does not mean that the implications of [3] are incorrect, however. The intention of was to characterize the long-run zero profit equilibrium in Liischian spatial competition. Unfortunately the derivation of that characterization involved an analytical short cut and some intuitive discussion which were misleading and indeed invalid. Belenky accurately points out that the results claimed in [3] are not derived therein. Thus, the purpose of the following presentation is to correct that derivation by explicitly characterizing the long-run equilibrium rather than describing a movement to that equilibrium. The key to the Benson [3] analysis is (24)-hereafter all equations from [3] will be labeled as in Belenky, with a B preceding the equation number, e.g., (B24). This equation, which says that price equals long-run marginal cost in a Liischian equilibrium, is incorrectly derived through (B22), depicting the movement from one long-run equilibrium to another. Belenky notes that such a movement requires an additional term 6'(Nv)/6e # 0 (see Belenky's (5) or Benson [2] for correction of a similar model). Belenky thus contends that (aN~/aPm)(dPm/de) + (aZV~/aN)/(dhr/de) must balance off the a( Nr)/ae # 0, and that the analysis involving (B24) does not follow. However, (B24) does characterize the long-run equilibrium, even though it does not hold for a movement to that equilibrium. *We thank M. L. Greenhut for helpful comments and suggestions.

Review of Regional Studies, 1987

A rather large body of recent literature has explored the implications of various conjectural variations in spatial pricing models. Very different conclusions have been reached as to which conjecture is appropriate for spatial modeling. The purpose of this paper is to add to this debate through application to a spatial model of two sets of arguments which stress that entrepreneurs learn.