SPATIAL COMPETITION WITH CONSISTENT CONJECTURES*

ABSTRACT 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 1/3. 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.     

INTERDEPENDENT BEHAVIOR WITH RELOCATION COSTS: THE COMPARATIVE STATICS OF SPATIAL HISTORY*

Relocation costs are a form of sunk costs because they are relevant to new entrants, not to agents at their existing locations. With sufficiently high relocation costs, initial (historically given) locations and other conditions determine the equilibrium assignment of agents to locations. Comparative static results depend on initial conditions, i.e., history matters and historical persistence can be characterized. The model suggests empirically-relevant results which can be tested by collecting data on relocation and transportation costs. For example, appropriate levels of these costs imply that suburbanization always occurs with the entry of new firms. Sequential entry strategies may be adopted by existing firms which earn pure profits. This may be contrasted with traditional NUE models which predict changes in the boundaries of central zones.     

SPATIAL COMPETITION AND THE JOINT CONSUMPTION OF SERVICES*

In Hotelling location models, an implicit assumption has been made that a customer uses the service provided by the firm, independent of other customers. However, for firms that supply meeting rooms, wedding halls, tennis courts, and golf links it is essential to incorporate the fact that the customer only uses the service in conjunction with other customers. The objective of this paper is to formulate the Hotelling location model n consideration of the interdependence among customers in one-dimensional space, and to characterize the state of equilibrium. In our model, each group of members within a given distance enjoys a fixed amount of service of the firms, under the assumption that the travel cost incurred by each group is defined as the travel cost of the farthest customer in the group.     

A NOTE ON THE STABILITY PROPERTY OF SPATIAL COMPETITION*

ABSTRACT. Our study extends the standard comparative static analysis to allow for dynamic aspects of equilibrium in spatial competiton. We investigate dynamic stability properties via the Routh-Hurwitz criterion. Nontrivial equilibria in the so-called Löschian, Hotelling-Smithies, and Greenhut-Ohta models are shown to be stable even under heterogeneous cost conditions among competing firms, conditions not considered hitherto. We can thus provide powerful support to the comparative static analyses which can only be developed via equilibrium concepts with stability properties.     

SPATIAL PRICE COMPETITION WITH CONSUIMERS ON A PLANE,AT INTERSECTIONS,AND ALONG MAIN ROADWAYS*

ABSTRACT. This paper examines two-dimensional price competition on a plane, with a block metric and a square grid of main roadways. One store is located at each intersection of main roadways. Consumer locations include a uniform distribution over the plane, linear concentrations along main roadways, and point concentrations at intersections. Bertrmd-Nash mill price competition is examined first. The equilibrium price depends on the relative numbers of consumers in the three types of locations (and on travel costs per mile and the spacing between stores). If too many consumers are in each point concentration, then the price equilibrium is undermined by a high-price strategy or by mill-price undercutting. Spatial competition with price discrimination is examined next, and compared to Bertrand-Nash mill price competition.     

SPATIAL EQUILIBRIUM WITH FOOTLOOSE FIRMS*

ABSTRACT. We determine the location equilibria in a duopoly model under a novel solution concept. Typically, spatial equilibrium is described as either a simultaneous price and location game, or else as a two-stage location-then-price game. We introduce a new alternative, a two-stage price-then-location game. It is well known that no (pure strategy) equilibrium usually exists under the two standard solution concepts when products are homogeneous. We show this is also true for the new concept. We then provide numerical results for a specific functional form (the logit model) which introduces product heterogeneity into the standard framework, restoring equilibrium when the degree of substitutability between products is not too small.     

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.     

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.     

LÖSCHIAN COMPETITION VERSUS SPATIAL COLLUSION: PRICE AND WELFARE COMPARISONS*

ABSTRACT. Löschian duopoly under heterogeneous cost conditions is examined to show that it is not equivalent, contra past findings, to spatial collusion. Moreover, within the confines of the assumed demand and cost conditions spatial collusion is shown to be superior to Loschian competition in terms of both (aggregate) consumer surplus and producer surplus, which implies a possible welfare gain from collusion. A general, if not the general, prices-and-welfare comparison of alternative pricing schema including collusive, Löschian, and optimal pricing is summarily presented in a table.     

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.     

ANALYSIS OF A DYNAMIC RESIDENTIAL LOCATION CHOICE MODEL WITH TRANSACTION COSTS*

ABSTRACT. This paper incorporates transaction costs in a residential location choice model. An individual's choice is assumed to be an outcome of a two-stage process: a decision to change, or to undertake a transaction and, conditional on a change occurring, a choice of a new alternative. The dynamic choice model is aggregated to yield a Markovian model of residential location patterns. It is shown that recent contributions to dynamical urban modeling correspond to special cases of the deterministic version of this model. The Markovian model is used in a theoretical analysis of the influence of transaction costs on the properties of the stationary state. The effects of residential mobility rates and of interdependencies among individuals, caused by supply-side and density-related interactions, are also analyzed. It is shown how these dynamical factors modify the stationary state, thereby demonstrating the type of errors which may occur with static models that omit them.     

MILL PRICING AND SPATIAL PRICE DISCRIMINATION MONOPOLY PERFORMANCE AND LOCATION WITH SPATIAL RETAIL MARKETS*

ABSTRACT. Most of the monopoly spatial price discrimination literature explicitly assumes uniform population density over space. It also implicitly assumes that firms (plants) are spatially isolated from each other with production and retail points that coincide in location. While departures from these assumptions have been explored separately in the literature, it remains to examine performance and location when these assumptions are relaxed simultaneously. What emerges in this paper is a model where density functions approximate a pair of cities isolated from other cities. Each city has its own retail market, while the location of a single production or wholesale point is determined by characteristics of the two markets. Comparisons of mill pricing and spatial price discrimination found in the spatial monopoly literature can be interpreted as special cases of the more general framework provided here.     

PRICING POLICY REACTIONS TO AGGLOMERATION IN A MARKET WITH SPATIAL SEARCH*

ABSTRACT. Price dispersion (variation) and agglomeration are common characteristics of spatial markets, in particular, markets with imperfect consumer information and search. However, pricing and location strategies in these markets are not well analyzed since spatial search is difficult to model without restricting the spatial dimension of the problem. This paper analyzes pricing and location strategies in a market with spatid search using a probabilistic modeling strategy that does not restrict search patterns in the plane. Specifically, the analysis considers the pricing strategy of an isolated firm in response to the agglomeration of competing firms. Results indicate that spatial and temporal price dispersion are effective responses to competitors'agglomeration. However, the relative effectiveness of these strategies varies with market conditions. In addition, agglomeration can have some counterintuitive effects. This paper also provides insights into existing theories of spatial search and spatial competition in spatially-restricted (linear and circular) markets.     

AGGLOMERATION AND REGIONAL COSTS OF LIVING*

ABSTRACT Standard models of the new economic geography predict that costs of living are lower in the core than in the periphery. But in reality they tend to be higher in agglomeration areas, mainly because of regional differences in housing costs. In this paper, we add a home goods sector to the seminal NEG model of Krugman (1991) . We show that a core–periphery structure can endogenously emerge in which the core is the more expensive area. This result has an important normative implication. Since higher costs of living imply falling real wages if there is no nominal wage premium, it is not desirable for everybody to live in the core region.     

THE BEHAVIORAL COSTS OF ECONOMIC INSTABILITY*

This paper reviews the literature reporting a connection between economic change and behavioral disorder. The literature is separated into individual and aggregate based research and the methodological issues raised by each approach are described. The implications of the research findings for illness prevention, remedial services and economic policy making are discussed. The authors argue that the social costs of mobile capital should be accounted and internalized because social justice as well as Economic and Psychological theory assume that an individual should bear the costs of his or her behavior.