THE CORE OF A SPATIAL PRICE EQUILIBRIUM GAME*

ABSTRACT This paper presents a critical appraisal of the use of the core as a solution concept for games involving spatially separated producers. Starting from the classical Samuelson/Takayama-Judge spatial price equilibrium model, the core of a game between the producers of commodities in this economy is defined, the conditions ensuring the nonemptiness of the core are stated, and the problems surrounding the definition and computation of the characteristic function are addressed. An application to the eastern United States’coal market is then presented in order to illustrate the usefulness of the theoretical and algorithmic results of this paper.     

AN ALGORITHM FOR THE SPATIAL PRICE EQUILIBRIUM PROBLEM ON A GENERAL NETWORK IN THE SPACE OF THE PATH FLOWS*

ABSTRACT. The spatial price equilibrium on a general network may be formulated as a nonlinear-cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the origins to all the destinations. In this paper, we develop a Gauss-Seidel-Newton Projection algorithm and combine it with a restriction strategy. That makes it unnecessary to generate a priori all the paths. This algorithm may be further improved by exploiting the equivalence between the spatial price equilibrium on a general network and the network equilibrium. Computational results that we present in this paper demonstrate the efficiency of the proposed solution algorithms.     

COMPUTATIONAL COMPARISONS OF SPATIAL PRICE EQUILIBRIUM METHODS*

ABSTRACT. In this paper we propose new algorithms for the solution of both general and standard spatial price equilibrium problems, and test their performance with existing algorithms on randomly generated problems. For the standard problem, we propose decomposition schemes based on the concept of “equilibration operator” and compare their performance with the Frank-Wolfe method. For the general problem, we present alternative variational inequality formulations defined over Cartesian products of sets and then exploit these formulations to construct Gauss-Seidel-type serial decomposition methods. We then compare their performance with the projection method. Our computational tests suggest that the new schemes are substantially more efficient than earlier ones.     

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.     

DEREGULATING THE DISTRIBUTION OF ELECTRICITY: PRICE AND WELFARE CONSEQUENCES OF SPATIAL OLIGOPOLY WITH UNIFORM DELIVERED PRICES*

ABSTRACT. Theoretical, spatial oligopoly models are developed and calibrated to simulate the price and welfare consequences of deregulating the retail price of electricity (the distribution function), assuming competing sources of generation supply are available. Two types of distribution competition are considered, retaining the currently used uniform delivered pricing structure: competition for customers at neighboring utilities’ borders and franchise competition. Because duplicate facilities are required for borderline competition, short-run price increases ranging between 14 and 37 percent over existing regulated prices are estimated for upstate New York, largely because deregulated prices reflect replacement, not historic, costs of facilities.     

THE SPATIAL STRUCTURE OF HIERARCHICAL INTER-URBAN SYSTEMS: EQUILIBRIUM AND OPTIMUM*

In this paper, I model a simple hierarchical inter-urban system in which the location of business firms is considered together with the determination of residential land-use patterns. By supposing a spatial externality between the business firms and all the residents of the region, three spatial structures are obtained: monocentricity, multicentricity, and a separate pattern where cities are spatially split with an agricultural land existing between them. It is also shown that the spatial structures of monocentric and multicentric patterns formed by the market principle tend to be more concentrated than the optimum.     

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.     

GENERAL EQUILIBRIUM OF SPATIAL PRODUCT AND LABOR MARKETS*

ABSTRACT A simple general equilibrium model relates spatial product markets and spatial labor markets. The firm is treated as being a spatial monopolist or as a Löschian competitor in the output market and as a spatial monopsonist in the labor market. Derived free spatial demand and free regional labor supply are defined, and their properties examined. The model provides the framework for analyzing the impact of a technological improvement in labor productivity on the structure of the spatial markets. The impact of entry on spatial labor supply is an important determinant of whether or not entry lowers wages and raises output prices. Unlike the spaceless competitive paradigm, zero-profit long-run equilibrium can occur in a space economy under conditions of increasing returns to scale.     

THE OUTPUT EFFECTS OF SPATIAL PRICE DISCRIMINATION REVISITED*

ABSTRACT Some prior findings on spatial price discrimination are extended. Under certain spatially defined market conditions, discriminatory pricing is known to yield greater output than does nondiscriminatory f.o.b. mill pricing. However, this seemingly surprising result is based on the form of the basic demand function which is relatively less convex than a certain standard curve. The present paper makes this prior result more general by permitting the assumed basic demand to be relatively more convex.     

THE EFFECT OF RETAIL FIRM OWNERSHIP ON PRICE EQUILIBRIUM*

ABSTRACT. This paper examines the effect of retail firm ownership on price equilibrium using a simple linear-city model. It is shown that price divergence emerges due to the differences in retail firm ownership, because retail firms under different ownership internalize shopping externalities differently. It is also shown that if a commercial center has two specialized retail firms, these stores charge the same markup for different goods at the equilibrium.     

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 CONTEXTUAL ANALYSIS OF THE JOURNEY-TO-SHOP WITH PRICE UNCERTAINTY*

ABSTRACT In this paper we extend the contextual theory of demand to consider rational consumer behavior when the household must deal with some random fluctuation in the prices it faces. Prices at stores reflect “advertised specials,” which are potential cost reductions random across goods, and random in-store price changes, which can only be observed by visiting the store. Our theory of rational behavior includes: (1) calculation by the household of an ex ante plan for its planning period; (2) modification to take account of advertised specials; and (3) rational search behavior to take advantage of random fluctuations observable only on a given day. This theory utilizes an active cash balance as a buffer against random variations from planned daily expenditures, and reformulations of trip circuits to account for patterns of cost-minimizing search.     

GENERAL EQUILIBRIUM ANALYSIS OF URBAN SPATIAL STRUCTURE. THE PORT-CITY MODEL RECONSIDERED*

In this paper, I consider a general equilibrium urban spatial structure in the setting of a port city by adopting Cobb-Douglas type functional forms for production and utility functions. Unlike previous port-city models, this one can generate four land-use patterns, that is, (1) monocentric, (2) completely integrated, (3) partially integrated (with integration at the center), and (4) partially integrated (with integration at the urban fringe) land-use patterns, and the last pattern suggests a new explanation of suburbanization of employment. The existence and uniqueness of each land-use pattern is proven in a simple constructive way.