Spatial duopoly under uniform delivered pricing when firms avoid turning customers away

This paper studies a spatial duopoly under uniform delivered pricing when firms do not ration the supply of the good, thus extending to a spatial context the analysis of oligopolistic markets with no rationing. The paper shows the existence of the equilibrium in prices under different tie-breaking rules (TBR) and compare the features of the equilibria found under these rules, thereby allowing to highlight the importance of the choice of the TBR in studying these models. When consumers buy from the nearest firm in case of equal prices (efficient TBR), any symmetric price pair within a given range is a Nash equilibrium, with each firm serving exactly half of the market line. If demand in each local market is equally split between the firms charging the same price (random TBR), the only equilibrium price is the one that gives zero profits to each firm. The degree of competitiveness of the market crucially depends on the TBR. Under the efficient TBR, all (but one) price equilibria deliver positive profits to both firms. Under the random TBR, the market outcome is very competitive in that firms make zero profits. None of the equilibria found under any tie-breaking rule are allocatively efficient.This paper is based on my DPhil thesis at the University of York. I would like to thank Gianni De Fraja, Keith Hartley, Peter Simmons, Catherine Waddams, Xavier Wauthy and participants to the 1998 EARIE and ERSA conferences for helpful comments and discussion. The paper has also been improved by the very useful comments of two referees of this journal. The usual disclaimer applies.Received: January 2001 / Accepted: January 2003     

Heterogeneous duopoly, spatially discriminatory pricing, and optimal location

It is found in the literature that if duopolists produce differentiated products and engage in price competition in a linear city model with elastic demand, the two firms necessarily agglomerate at the market center and this is the unique locational equilibrium, irrespective of the pricing policies charged by the firms. Utilizing a more reasonable market-serving assumption, this paper finds that the firms can be either centrally agglomerated or dispersed depending on the magnitude of the transport rate and the degree of product differentiation. Moreover, if the two firms choose quantity instead of price as their decision variables, the two firms become less likely to stay apart. But if they do, the distance of their locations necessarily shrinks. This paper also examines the locational configuration in the absence of the market-serving assumption and finds that spatial dispersion could be the only location pattern.     

Locational competition under environmental regulation when input prices and productivity differ

The purpose of the paper is to outline an analytical framework which captures the ample scope of locational competition: cost differences, resulting from differences in factor prices including taxes, human capital, infrastructure services and total factor productivity. If cost differences are small, locational competition controls excessive government power. We have modeled locational competition by assuming that governments have a vital interest to keep mobile factors of production at home. We represent this aspect by restricting the usage of environmental instruments such that they will at most exhaust the cost difference to a competing foreign firm. If cost differences are large enough there is no binding restriction for the cost-benefit calculus of a national environmental policy. The tax will be below marginal damage due to strategic reasons of rent shifting. If small international cost differences do not allow taxation in accordance with marginal damage considerations, then locational competition restricts the size of the tax rate such that the firm is indifferent in relocating or staying at home.     

Regional competition for the location of new facilities

A model of interregional competition for the location of new facilities is analyzed as a differential game. Two regions try to enhance their attraction by making concessions to a location decision maker in order to raise the probability that a new facility will be located in a specific region. The prospective benefits and costs of exerting influence are decisive for the final outcomes of the model. The open-loop (and feedback) Nash equilibrium solution is inefficient in comparison to the cooperative solution of joint benefit maximization of both regions. Received: May 2000/Accepted: December 2001 I thank Gudrun Bark, Hagen Bobzin, Marc Büdenbender, and Walter Buhr for helpful discussions on the first draft of this paper. The constructive comments of two anonymous referees are gratefully acknowledged. Any errors are my own.     

The impact of revenue-neutral tax policy on plant location under price uncertainty

This research note incorporates price uncertainty into a production- location model and examines the impacts of a revenue-neutral tax policy on production and location decisions. In particular, it is shown that under an assumption of decreasing absolute risk aversion, a revenue-neutral rise in the marginal tax rate increases the firm's output and causes the firm to move its plant closer to (away from) the market center provided that the production function exhibits increasing (decreasing) returns to scale. Nevertheless, the plant location remains unchanged as a result of a revenue-neutral tax policy if the production function is constant returns to scale. A comparison between revenue-neutral and income or lump-sum taxes and hence some important policy implications are also provided in the analysis. Received: 1 March 1997 / Accepted: 18 May 1999     

On the optimal production and location of a labor-managed firm

This paper endeavors to introduce space into the theory of the Labor-Managed firm (LMF) and to investigate its optimal production and location decisions. It is shown that the degree of returns to scale plays a key role in the determination of optimal production and location for an LMF, in particular, that the optimal location of an LMF is farther away from (closer to) the market as compared to a profit-maximizing firm (PMF) if the production function is of increasing (decreasing) returns to scale. We also demonstrate that the optimum location of an LMF moves closer towards the market as demand increases, regardless of whether the production function is of increasing or decreasing returns to scale. This finding is in sharp contrast with that in a capitalist economy. Received: February 2000/August 2000     

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     

Spatial configurations,competition and welfare

Studies into the shapes of market areas abound and emphasize the hexagon as the optimal configuration. This paper demonstrates that a triangular or a square market area can be superior to a hexagonal one under certain behavioural conditions. Spatial configurations are evaluated on the basis of (1) the number of firms required to fill a given market area and (2) the level of welfare per unit area that these firms generate under alternative competitive conditions.     

On the social significance of spatial location; Spatial segregation and social inclusion

This article gives an overview of the positive and negative aspects of spatial concentration and segregation. We argue that much of the literature is biased; it emphasizes the drawbacks of spatial concentration and segregation of low-income groups in general and immigrants in particular. The opportunities offered by concentration and segregation, which almost always depend on the presence of local solidarity networks, are given less attention. These opportunities are mainly treated in the literature on ethnic entrepreneurs. Much of the literature on the effects of spatial concentration and segregation is based on research in the United States. Thus, we have to be very careful when we apply the results to West European countries. The overview concludes with some suggestions for further research. This paper was first presented at the COST-CIVITAS Conference on Social Fragmentation, Social Cohesion and Urban Governance in Oslo, 5–7 June 1997. Gideon Bolt is a PhD researcher at the Urban Research Centre Utrecht, Faculty of Geographical Sciences, Utrecht University. His work concerns the importance of the neighborhood with regard to the migration patterns of Turks. Jack Burgers is an associate professor of sociology at the Erasmus University of Rotterdam. Ronald van Kempen is an associate professor at the Urban Research Centre Utrecht, Faculty of Geographical Sciences, Utrecht University, the Netherlands.     

Logistics cost, consumer demand, and retail establishment density

This article develops models to formulate the optimal density of retail establishments by considering interactions between logistics cost and consumer demand. Commodities are assumed to be distributed from a depot directly or through single intermediate terminal to many retail establishments. Average logistic cost per item, consumer demand, and the interrelationship between them are analyzed. The optimal density of retail establishments and local terminals are determined by minimizing average logistic cost, or maximizing total supply subject to the demand-supply equality. The envelope curves for the optimal configuration strategies corresponding to different values of total market area and terminal cost are derived. Received: 3 October 1996 / Accepted: 29 January 1999     

Modelling residential location choice in an area with spatial barriers

A model is presented for residential location choice in rural areas with spatial barriers. We address the problem through comparative static analysis focusing on how residential location choices are affected by a new road link across the spatial barrier. We proceed through a probability theoretical approach: choose a family of utility functions representing every possible location, and equip this family with a probability measure. Then choose a representative within an equivalence class of utility functions, and represent the probability distribution by a parametrized family of distributions. Our analysis demonstrates that investments in new road links do not necessarily represent an adequate instrument for achieving ambitions in regional policy. We identify reasonable situations where a new road link could just as easily generate net migration from the area in which the investments are directed. In general, our analysis demonstrates how agglomeration and centralisation tendencies can be considerably affected by transportation infrastructure innovations. Received: June 1999/Accepted: June 2001 This paper benefited from comments by Bj?rn Sandvik and Lars-G?ran Mattsson.     

Spatial prices,search behavior and location

This paper presents a model that links spatial prices with search behavior and location. Consumers are assumed to search for a product at the lowest overall costs where suppliers are spatially distributed. The expected result of this “shopping decision” is linked with a longer term “quantity decision” relating the customer’s location via bid prices for land with the expected costs of buying the product. We demonstrate various characteristics of this model via numerical simulations.     

Spatial externalities, neighbourhood rules and CA land-use modelling

This paper investigates which, how and to what extent land-use related neighbourhood effects play a role in urban dynamics. To justify the use of cellular automata land-use models for spatial policy support, existing neighbourhood rules need to be better founded. This research eliminates a number of uncertainties in the land-use model outcomes by introducing improved empirically founded and regional-specific neighbourhood rules. This allows for a better evaluation and justification of spatial policy scenarios and their effects on future land-use dynamics.     

Road pricing with limited information and heterogeneous users: A successful case

Since strictly optimal (first-best) road pricing policies require information that we will probably never have, it is important to investigate what can be done under more restrictive assumptions as to what information is available. One such case is examined in this paper, where the main restrictive assumptions are that all users have the same choice set and that all alternatives have the same monetary cost. Individuals have utility functions with constant marginal utilities of time and money, but these marginal utilities vary across individuals, and are assumed to be unobservable.  We show that for this model, any toll reform that reduces aggregate travel time and redistributes the toll revenues equally to all users makes everyone better off. This holds regardless of the distribution of marginal utilities of time and money, and for any road network. Received: November 1999/Accepted: July 2001     

Knowledge spillovers, location of industry, and endogenous growth

A Grossman–Helpman–Romer-type (Grossman and Helpman in Innovation and growth in the world economy, 1991; Romer in J Polit Econ 98:71–102, 1990) endogenous-growth model is developed in this study. This model has two countries in which there are knowledge spillovers that are partially local. Owing to these spillovers, the innovation costs in a particular country decrease as the number of firms locating in both that country and the other country increases. If international knowledge spillovers are symmetric, the innovation sector is in the country with the larger market. However, if international knowledge spillovers are asymmetric, the innovation costs may be in the small-market country. When innovation costs are lower in the country with a large market, the growth rate increases with a reduction of transportation costs. However, when innovation costs are lower in the country with the smaller market, the growth rate decreases with a reduction in transportation costs. We are grateful to Marcus Berliant, Masahisa Fujita, Koichi Futagami, Tatsuo Kinugasa, Takuo Imagawa, Tomoya Mori, Se-il Mun, Hisahiro Naito, Ryoji Ohdoi, Tatsuyoshi Saijyo, and Akihisa Shibata for their helpful comments and suggestions. Any remaining errors are the responsibility of the authors.     

Spatial competition and flexible manufacturing with spatially discriminatory pricing

This paper develops a two-dimensional spatial framework, in which firms have the technique of flexible manufacturing and engage in spatially discriminatory pricing, in order to explore the firms’ optimal locations and optimal attributes of basic products under linear transportation costs. The paper shows that the two firms will agglomerate at the center of the location line and the optimal attributes of the two basic products will be located at the first and third quartiles of the attribute line, respectively, when the ratio of the marginal modification rate to the transport rate is high. It also shows that the two firms will locate separately on the location line and that the optimal attributes of the two basic products will remain at the first and third quartiles, when this ratio is moderate. Moreover, this paper proves that the two firms will locate at the first and third quartiles of the location line, respectively, and that the attributes of the basic products will agglomerate at the center of the attribute line, when this ratio is low.     

Networks and firm location

This paper models the decision of vertically linked firms to build either partitioned or connected networks of supply of an intermediate good. In each case, there is a correlation between the locations of upstream and downstream firms. Input specificity is related to both variable costs (transport costs of the input) and fixed costs (learning costs of the use of the input). When both are low, a connected network emerges, whereas, in the opposite case, we find a partitioned pattern. In the boundary region, there are multiple equilibria, either asymmetric (mixed network) or symmetric.     

Spatial location patterns of Spanish manufacturing firms*

In this paper, we evaluate the spatial location patterns of Spanish manufacturing firms in each industry. We use a distance‐based method, Ripley's K function, which allows us to treat space as continuous. With ‘complete spatial randomness’ as benchmark, every sector presents significant concentration whatever the distance considered. If we use the locations of all manufacturing firms as a benchmark, we find dispersion in some sectors and concentration in others, finding also differences in the spatial scale at which clustering occurs. Finally, the use of cities as a benchmark reveals that not only is ‘first nature’ among the location determinants of manufacturing firms but they also include the self‐reinforcing advantages of ‘second nature’. Resumen. En este artículo evaluamos los patrones de localización espacial de empresas de manufacturas en cada industria. Utilizamos un método basado en la distancia, la función K de Ripley, que nos permite tratar el espacio como un continuo. Tomando la ‘aleatoriedad espacial completa’ como cota de referencia, todos los sectores presentan una concentración significativa, independientemente de la distancia considerada. Si empleamos las localizaciones de todas las empresas manufactureras como cota de referencia, encontramos dispersión en algunos sectores y concentración en otros, así como diferencias en la escala espacial a la que ocurre la formación de conglomerados (clusters). Finalmente, el emplear ciudades como cota de referencia revela que entre los determinantes de localización de empresas manufactureras no solo está la ‘primera naturaleza’ sino que también se incluyen las ventajas de retroalimentación positiva de la ‘segunda naturaleza’.      

Endogenous determination of historical amenities and the residential location choice

Brueckner et al. (Econ Rev 43:91–107, 1999) remark that city’s historical amenities, which are considered exogenous today, may have been formed endogenously over time. This paper develops a simple two-period model based on this idea. It assumes there are two locations in a city and two income types. Lot sizes are decided myopically in the first period and cannot be adjusted later. Without historical amenities, locations of the rich and the poor are never reversed (the poor always locate closer to the center) for increasing population, income and utility levels of each type. If the rich leave some “historical amenity” behind for the residents in the second period, locations are reversed when the population of the first period is moderate, income disparity between the two types is low and the rich is sensitive to amenity. An earlier version of this paper was presented at International Symposium on Spatial Economics and Transportation, Sendai, Japan, June 13, 2005. The paper has benefited greatly from the comments of Dr. Jan Brueckner, who participated in the symposium, and Dr. Charles de Bartolomé, my academic adviser in the University of Colorado at Boulder.