Location choices with a non‐linear demand function

This paper introduces a non‐linear hyperbolic demand function in a spatial shipping model. We show that, in contrast with the linear demand case, dispersion of firms emerges in equilibrium both when the firms compete through quantities and when they compete through prices. Further, the impact of the marginal production costs on the degree of firms' dispersion in equilibrium is positive when firms compete with prices, and it is inverse U‐shape when firms compete with quantities.     

Spatial price discrimination in a symmetric barbell model: Bertrand vs. Cournot

This paper investigates the theory of spatial discrimination for general demands and general transportation costs in a barbell model, where markets' locations are assumed to be at opposite endpoints of a line. Duopoly firms in the Bertrand model always differentiate maximally, whereas in the Cournot model the market demand structure is not so critical, but the functional form of the transportation cost plays a crucial role in determining equilibrium location. Non‐maximal distance appears in the Cournot equilibrium when a convex transportation cost is allowed, bringing about the findings that the equilibrium consumer surplus may be higher and the equilibrium profits may be lower under Cournot competition than under Bertrand competition.     

Cournot oligopolistic competition in spatially separated markets: The Stackelberg equilibrium

Consider a two-stage non-cooperative Cournot game with location choice involving r firms. There are n spatially separated markets located at the vertices of a network. Each firm, first selects the location of a facility and then selects the quantities to supply to the markets in order to maximize its profit. Non-zero conjectural variation at the second stage in the model by Sarkar et al. (1997) is studied. When the demand in each market is sufficiently large, equilibrium in the quantities offered by each firm in the markets exists. Furthermore, each firm chooses to locate its facility at the vertices.Partially financed by Ministerio de Ciencia y Tecnología (Spain) and FEDER, grant BFM2002-04525-C02-01.Received: August 2002 / Accepted: May 2003     

Cost differentials and mixed strategy equilibria in a Hotelling model

We introduce heterogeneity of production costs into the location-price Hotelling model discussed by d’Aspremont et al. (Econometrica 47:1145–1150, 1979). Maximum differentiation appears if the cost difference between two firms is small, whereas no pure strategy equilibrium exists if it is large. We examine the mixed strategy equilibria when no pure strategy equilibrium exists. We find that the following simple symmetric mixed strategy equilibrium exists, which never becomes an equilibrium if no cost differential exists: each firm chooses to locate at the two edges of the linear city randomly.     

An application of the Beckmann-Ingene argument to a monopsonist's spatial pricing problem

The purpose of this note is to show that an analogue of the Beckmann-Ingene proposition on price policies of a spatial monopolist applies to a properly formulated profit maximization problem for a spatial monopsonist. The proof of this fact uses the same linear transformation employed in the Beckmann-Ingene argument. Received: 15 October 1998 / Accepted: 9 January 1999     

Potential merger‐forcing entry reduces maximum spacing between firms in spatial competition

In the literature, the range of market sizes (spacings between firms) consistent with free‐entry equilibrium, in various models of spatial competition, extends from the zero‐profit market size, up to the market size for which ‘sophisticated entry’ halfway between two existing firms, by an entrant that correctly foresees post‐entry prices, is marginally deterred. I argue that the upper limit might be the (significantly smaller) market size for which ‘merger‐forcing entry’ by an entrant right next to an existing firm, causing severe price competition and inducing a horizontal merger between the entrant and the existing firm, is marginally deterred.     

Optimal time for implementing cordon toll pricing scheme in a monocentric city

This paper proposes an analytical model to address the timing issue of cordon toll pricing in a monocentric city. The proposed model allows an explicit consideration of the interactions among three types of agents in the urban system: (i) the local authority who aims to jointly determine the optimal time for introducing cordon toll pricing scheme, cordon toll location and toll level to maximize social welfare of the urban system; (ii) property developers who seek to determine the intensity of their capital investment in the land market to maximize their own net profit generated from the housing supply; and (iii) households who choose residential locations that maximize their own utility within a budget constraint. The effects of the cordon toll pricing scheme on household's residential location choice and housing market structure in terms of housing price and space are explicitly considered. A comparison of the toll pricing schemes with a fixed and a mobile cordon location over time and the no toll case is carried out. The proposed model is also illustrated in several Chinese cities. Insightful findings are reported on the interactions among cordon toll pricing scheme, urban population size, household income level, toll collection cost, and urban development.     

Determination of neighbourhood housing amenities: Asymmetric effects of consumers’ choices and multiple equilibria

This paper studies the sizes and rents of housing determined as a result of the choices of consumers whose utility depends on the level of housing amenities in their neighbourhood. The level is, in turn, determined by the sizes of housing there. It is shown that there emerges a possibility of multiple equilibria if the effect of each consumer's choice upon neighbourhood housing amenities is asymmetric.     

Spatial price competition in retail gasoline markets: evidence from Austria

This paper investigates the influence of unbranded stations on the prices charged by branded stations in the retail gasoline sector, using data on 400 stations in Lower Austria. As the market is characterized by spatial competition, a spatial lag model is used to avoid misspecification. The results show that independent retailers generally heighten price competition, as they charge significantly lower prices. At the same time, as consumers might consider gasoline sold at unbranded stations to be inferior, they also reduce price competition for branded stations. Independents therefore ultimately have only a small influence on the prices charged by branded stations.     

Spatial monopoly of multi‐establishment firms: An empirical study for supermarkets in the Netherlands

Multi‐establishment firms can create local spatial monopolies in the form of clusters of own establishments without competition. This paper examines the existence of spatial monopolies for Dutch supermarkets in 2009. It is found that 23 percent of consumers can be qualified as being locked‐in in a spatial monopoly of a specific supermarket brand. Resumen. Las empresas con múltiples establecimientos pueden crear monopolios espaciales locales en forma de conglomerados de sus propios establecimientos sin que haya competencia. Este artículo examina la existencia de monopolios espaciales de supermercados en los Países Bajos en 2009. Se encontró que el 23 por ciento de consumidores pueden clasificarse como cautivos de un monopolio espacial de alguna marca de supermercado específica.      

Modelling dynamics of knowledge networks and local connectedness: a case study of urban high-tech companies in The Netherlands

There are increasing doubts on the importance of localized knowledge and learning as benefits from a clustered location. Some empirical studies indicate that the influence of local proximity in knowledge networks stretches over larger distances than in previous times, while others suggest that local and global knowledge networks coexist. This study seeks to fill a gap in understanding how knowledge networks are shaped and how global networks may affect strength of local connectedness in a cluster. The study adopts an entrepreneurial view, drawing on a selected sample of urban innovators in the Netherlands, and employs rough set analysis and various other learning experiments. The results suggest that local/regional and global networks coexist in the urban places; this as a result of the interplay of spatial focus in the overall strategy, network capabilities and innovation intensity. With regard to local connectedness, our tentative results indicate a limited, but differentiated weakening of local linkages if knowledge networking is predominantly global. Overall, in balancing global with the local, young high-technology companies seek different ways dependent on progressing in their lifecycle and specific strategic choices.     

Price‐sensitive demand and market entry

This paper revisits the optimal entry decision in a differentiated product market where customer demand is price‐sensitive and depends on a per‐unit transport cost. We show that compared to the socially optimal outcome, too few firms may enter when entry costs and transport costs are high.     

Search costs decrease prices in a model of spatial competition

This paper examines the Nash equilibrium prices of stores in a spatial search model. By assumption, a large store is certain to have the particular product a consumer wants, whereas a small store has it with probability w. Large and small stores alternate with each other on a circular roadway. Consumers must search by visiting stores. In the Nash price equilibrium, large stores charge higher prices than small stores. Perhaps surprisingly, all Nash equilibrium prices are lower than in the corresponding perfect‐information‐no‐search model (for a given value w). This last result is also demonstrated in a model with only small stores.     

Spatial patterns of adoption of just‐in‐time manufacturing *

We study the spatial pattern of just‐in‐time (JIT) adoption for a sample of medium‐sized and large Spanish manufacturing firms. JIT differs from other advanced manufacturing technologies because it relates directly to the spatial co‐ordination of firms' internal production organisation with the external productive environment and depends on the quality of the transport system. Our results confirm the distinctive role of location for JIT adoption even after controlling for industry and plant‐specific differences. We find that JIT adoption is greater in smaller cities but with higher transport accessibility indicating that urban congestion in larger urban areas likely reduces the benefits that firms may obtain from JIT implementation.     

R&D competition in a spatial model with technical risk*

Abstract. In this paper, we introduce stochastic R&D into a Hotelling model with two duopolists. With an emphasis on the interaction between firms' R&D decision and location choice, we compare socially and privately optimal locations and levels of R&D. We show that, depending on R&D cost and the degree of technical risk, equilibrium location varies from minimum differentiation to maximum differentiation. From a welfare perspective, the equilibrium distance between the two firms could be either closer, farther or socially best. Moreover, depending on cost structure, firms' R&D expenditures could be either higher, lower or socially optimal, from a welfare viewpoint.     

Spatial pattern and domestic tourism: An econometric analysis using inter‐regional monetary flows by type of journey*

In this paper, we develop an econometric analysis of the intra‐ and interregional trade flows of the accommodation, restaurant industry, and travel agency sectors in Spain by means of several specifications of the gravity model and three alternative databases containing the monetary flows for 2001 and 2007. The results obtained show the existence of an important border effect in favour of the intraregional trade of tourism, and verify a minor elasticity of the trade flows in some characteristic tourism sectors in relation to distance. Finally, the two main typologies of flows – tourist establishments and second homes – are modelled separately, identifying specific factors for explaining each category. En este artículo desarrollamos un análisis econométrico de los flujos comerciales intra e interregionales de los sectores hotelero, restauración y agencias de viajes en España, mediante varias especificaciones del modelo de gravedad y tres bases de datos alternativas que incluyen los flujos monetarios en 2001 y 2007. Los resultados obtenidos muestran la existencia de un importante efecto frontera favorable al comercio intrarregional de turismo y corroboran una elasticidad menor de los flujos comerciales en ciertos sectores de turismo característicos en relación a la distancia. Finalmente, se modeliza por separado las dos tipologías principales de flujos – establecimientos turísticos y segundas residencias, mediante la identificación de factores específicos para cada categoría.      

Tax effects in a two‐region model of monopolistic competition

I examine how unit tax and ad valorem tax affect firm location in a monopolistic‐competition model with asymmetrically sized regions and a quasi‐linear preference. Tax revenue is evenly distributed to all workers or evenly distributed to the workers residing in the region generating the tax revenue. When a homogeneous good is traded, despite reimbursement systems, the ad valorem tax retains the firm share, while the unit tax accelerates firm agglomeration in the larger region. When the homogeneous good is nontradable, despite taxation schemes, the intraregional distribution retains the firm share, while the interregional one accelerates agglomeration in the larger region.     

Spatial fixed effects and spatial dependence in a single cross‐section

We investigate the common conjecture in applied econometric work that the inclusion of spatial fixed effects in a regression specification for a single cross‐sectional data set removes spatial dependence. We demonstrate analytically and by means of a series of simulation experiments how evidence of the removal of spatial autocorrelation by spatial fixed effects may be spurious when the true data generating processes (DGP) takes the form of a spatial lag or spatial error dependence. In addition, we also show that spatial fixed effects correctly remove spatial correlation only in the special case where the dependence is group‐wise, with all observations in the same group as neighbours of each other.