AGGLOMERATION,TRADE, AND SPATIAL DEVELOPMENT: BRINGING DYNAMICS BACK IN*

ABSTRACT The field of spatial economics has made enormous progress in theorizing and measuring agglomeration effects, trade costs, and urbanization. Typical models establish structural determinants by making strong assumptions about which forces are relevant and how these forces interact. But many of these assumptions, about firms, agents, spatial costs, and market structures, are questionable. As a result, the field has a long way to go to establish causality, and to be able to account for spatial economic dynamics.     

A SPATIAL HEDONIC APPROACH ON LAND USE CHANGE ANTICIPATIONS*

ABSTRACT This paper estimates land use conversion anticipation when zoning is the primary tool of land use regulation. Extending the Capozza and Helsey model (1989) to the case of uncertainty in future land use zoning, a spatialized hedonic model is proposed to estimate such anticipation phenomena at a fine level (cadastral unit). Estimations use Mixed Geographically Weighted Regression (MGWR) techniques with a two‐stage model that links agricultural and developable land markets. This allows for mapping varying spatial parameters that measure anticipation effects within the theoretical framework. Results confirm the influence of anticipation on agricultural land prices in the Provence region. Moreover, the level of data spatialization allows us to take into account intra‐municipalities' heterogeneity of land use conversion anticipation.     

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.     

NEW DIRECTIONS FOR URBAN ECONOMIC MODELS OF LAND USE CHANGE: INCORPORATING SPATIAL DYNAMICS AND HETEROGENEITY*

ABSTRACT We review the usefulness of urban spatial economic models of land use change for the study and policy analysis of spatial land use–environment interactions. We find that meaningful progress has been made in econometric and monocentric models extended to account for multiple sources of spatial heterogeneity and in the development of general equilibrium models with spatial dynamics. Despite these advances, more work is needed in developing models with greater realism. Most agent‐based computational models of urban land use change currently lack economic fundamentals, but provide a flexible means of linking microlevel behavior and interactions with macrolevel land use dynamics. In combination with empirical methods to identify parameters, this framework provides a promising approach to modeling spatial land use dynamics and policy effects.     

ON THE VARIABLE SHAPE OF THE FREE SPATIAL DEMAND FUNCTION*

ABSTRACT Analytical evidence is presented confirming variations in the shape of the free spatial demand function under different market conditions. For some simple spatial configurations of consumers, the transformation from convexity to concavity may be conveniently observed using graphical methods. The key criteria for concavity of the free spatial demand function are certain combinations of concave consumer demand, nonuniform consumer density, and/or nonlinear transportation costs. Although findings are confined to free spatial demand, similar variations may be expected to hold for the competitive case.     

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.     

SPATIAL IMPACTS OF AGGLOMERATION EXTERNALITIES*

ABSTRACT This article examines the extent to which agglomeration economies in one location affect employment growth and establishment births, using data from the Dutch province of South‐Holland. The data are of particular interest because they represent a census, rather than a sample, of all establishments and the location of establishments can be pinpointed to within 416 (postal) zip code areas averaging less than 6 km² in size. Results suggest that agglomeration economies positively affect employment growth and the location of new establishments, but with the possible exception of manufacturing, this effect dies out quickly with distance. Thus, the main finding is that for many industries, agglomerative forces may well operate at a geographic scale that is smaller than a city.     

SPATIAL PRICING IN INTERDEPENDENT MARHETS*

ABSTRACT. Conditions for spatial price equilibrium are derived for a set of firms in oligopolistic spatial competition, distributed at fixed locations in a heterogeneous region where consumer purchasing patterns are a probabilistic function of the price distribution rather than a deterministic function of proximity to firms. The resulting prices vary with accessibility to consumers or with the degree of local spatial monopoly, and result in non-zero profits for firms. Conditions describing the existence and stability properties of this spatial price equilibrium are defined, and are shown to be equivalent for two different hypotheses concerning disequilibrium pricing behavior: a partial price adjustment model and a Bertrand game. For two different profit goals, total profit maximization and profit rate maximization, it is shown that a spatial price equilibrium exists and is at least locally quasi-stable.     

SPATIAL ENTRY DETERRENCE UNDER OLIGOPOLY*

ABSTRACT. This paper examines colluding, oligopolistic firms in a linear market. By assuming that rivals do not compete for consumers at their market boundaries, it is shown that an equilibrium exists without adopting a convex transportation cost function. Two price profiles are derived. The first describes firm prices in the absence of threatened entry. The second details profit-maximizing prices which forestall entrants. Given infinite relocation costs, threatened entry leads to price adjustments by the incumbent firms.     

ADDITIVE-INTERACTION MODELS OF SPATIAL AGGLOMERATION*

A wide variety of existing models of spatial agglomeration postulate additive-interaction effects among agents. In this paper, a synthesis of such models is achieved by establishing certain mathematical equivalences between them. In particular, it is shown that Rockafellar's conjugacy theory of concave functions yields a symmetric one-to-one correspondence between three classes of existing models, here designated as spatial-accessibility models, endogenous-contact models, and fixed-contact models. These correspondences not only allow the transference of results between models, but also suggest new economic interpretations of each model in terms of its conjugate model. A series of examples are drawn from the literature to illustrate these results.     

THE FUTURE OF SPATIAL ECONOMETRICS*

ABSTRACT The purpose of this paper is threefold. First, we give an overview of the general direction the spatial econometrics literature has taken without attempting to provide a representative survey of all interesting work that has appeared. Second, we identify a number of problems in spatial econometrics that are as yet unresolved. Finally, we provide advocacy for the notion that new spatial econometric theory should be inspired by actual empirical applications as opposed to being directed by what appears to be the most obvious extension of what is currently available.     

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.     

SPATIAL COMPETITION WITH LOCATION-DEPENDENT COSTS*

This paper investigates the behavior of spatially-competitive firms whose costs depend on their locations. Necessary and sufficient conditions for optimum locations are derived. Comparative-statistics analysis of the equilibrium shows that the responses of firms to changes in input and output transport rates depend on the properties of consumer demand curves or are ambiguous in sign.