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.     

Optimal facility placement and discriminatory congestion pricing in neighborhoods with different time costs

In many urban areas, time costs or wages vary between neighborhoods, but there is little wage variation within a given neighborhood. Neighborhoods are often labelled “working class,”“middle class,” or even “wealthy.” For this reason, there are many efficiency and distributional issues related to location because location largely determines access costs. Congestion also affects time costs and access. Many public policies are geared towards improving access for households in low-wage neighborhoods. Public facilities are built; some firms receive nonprofit status. In order to evaluate these policies, normative theory is needed. This paper develops theory on the optimal placement of facilities and their congestion prices in urban areas with wage variation between neighborhoods. The results show that optimal locations and prices depend on the extent of wage inequality. Received: February 2001/Accepted: September 2001     

Spatial competition with profit-maximising and labour-managed firms

The nature of the equilibria arising under spatial differentiation is investigated here in a duopoly model, where at least one firm maximises value added per worker. The study shows that if firms' objectives differ, there exists a subgame perfect equilibrium in pure strategies, which is possibly characterised by asymmetric locations. If both firms are labour-managed, there exists a (symmetric) subgame perfect equilibrium in pure strategies with firms located at the first and third quartiles, if and only if the setup cost is low enough. Otherwise, undercutting is profitable. Received: 16 March 2000 / Accepted: 15 March 2001     

Spatial duopolistic competition with multipurpose and multistop shopping

This paper explores the impact of multipurpose and multistop shopping behavior on spatial competition among retail firms. The problem deals with a duopoly situation on a line segment. It is shown analytically that a unique location-price Nash equilibrium exists. In equilibrium, the locational configuration is dependent upon consumers' propensity for multipurpose shopping.     

Spatial Cournot competition with non-extreme directional constraints

The circular city model and the linear city model are extended to allow for asymmetric directional transportation costs. A two-stage location-then-quantity model is proposed. We show that in the circular city model, maximal dispersion arises in equilibrium, while in the linear city model, the unique equilibrium is represented by both firms agglomerating in a non-central point of the segment.     

Spatial competition and market interdependence

This paper investigates the optimality properties of interdependent spatial markets in a situation of price-location competition. A framework is developed where interdependences on the demand side of the economy are fully accounted for. It is assumed that goods supplied in the economy are not independent in terms of consumption. In addition, consumers can capture economies of scope in travel by shopping for several goods on one trip. Two goods are available in addition to a composite product. The problem involves two non-cooperative firms that exhibit a Nash behavior in selling their single product to a population uniformly distributed around a circumference. The level of interdependence between markets is expressed by the transportation rate, and by two other parameters indicating the relations of complementarity/substitutability among goods. A numerical analysis of comparative statics is conducted to examine the role of these parameters on firms' optimal location and price configurations.An earlier version of this paper was presented at the 37th North American Meetings, Boston, November 1990.     

Spatial pricing, optimal location and social welfare with consumer arbitrage

This paper provides a comprehensive comparison of the optimal location, output and welfare of spatial discriminatory pricing by integrating consumer arbitrage into the Hwang and Mai (Am Econ Rev 80:567–575, 1990) model. It shows that the presence of arbitrage creates a significant influence on a firm’s locational choice and thus generates different welfare implications. When the discrepancy between the two markets is small, the optimal location and the resulting social welfare level under discriminatory pricing and mill pricing policies remain the same; however, when the discrepancy between the two markets is large, the two pricing policies yield different optimal locations which make the welfare under discriminatory pricing higher than that under mill pricing, hence reversing the support for anti-trust legislation.     

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.     

Spatial competition with quadratic transport costs and one online firm

d’Aspremont (Econometrica 47:1145–1150 , 1979) showed that a Hotelling (Econ J 39:41–57 , 1929) duopoly model with quadratic transport costs yields maximal differentiation. However, the introducing of an online firm ensures that the duopolist will never be located at the end points of the market. In other words, an online firm can raise a market effect that induces two firms to be finitely differentiated. The implication of the socially optimal solution is derived. The results herein can be extended to allow multiple firms. Finally, a free-entry equilibrium and the Stackelberg equilibrium are also discussed.     

After flexible manufacturing in the factory...flexible working foroffice staff

Offices are expensive, underused assets that do not deliver the correct working environment for much of the work that is done in them. Changing the work setting improves productivity and saves large sums of money. Here, the author describes how the change is very much more to do with staff and management, than offices and technology. It is also not as disruptive as it is thought to be     

Optimal pricing of public utility service when consumers and producers are spatially diffuse

The demand for public utility services varies temporally as well as spatially. The analysis of the problem of meeting these spatial and temporal variations in system load with optimum plant capacity within the framework of a price determination structure is the objective of this paper. By relying on a mathematical programming model with the objective of maximizing social welfare, the general principles of optimal pricing are derived. No simple cost-based solution proves possible. Price is not set equal to marginal operating cost. Rather the price changes according to the cost and demand conditions.The author is an economist with the federal energy administration. The views expressed are those of the author and do not necessarily represent the policies of the federal energy administration or the views of other federal energy administration staff members.     

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     

Spatial Cournot competition in a circular city with directional delivery constraints

This paper analyzes spatial Cournot competition in a circular city with a directional delivery constraint, which means that a firm can only deliver its product in one direction. It reveals that, contrary to the standard result, the unique location equilibrium involves duopoly firms agglomerating at the same location when they deliver products in different directions or when the direction decisions are made endogenously. We point out that spatial agglomeration emerges from a central point of view for a firm in a circular city, showing relaxing quantity competition through cost differentiation.     

Economically defensible access pricing, competition and preservation of socially desirable cross subsidy

The article describes and evaluates four principles that have been used or proposed to guide regulation of access to essential bottleneck facilities by competitors of the owner of those facilities: fully distributed cost, incremental cost, Ramsey pricing and parity pricing. It is shown that parity prices are the only prices that give no added competitive advantage to the owner of the bottleneck facilities or his rivals. Parity pricing is also shown to permit simultaneous achievement of two objectives previously thought incompatible: unrestricted competitive entry and preservation of cross subsidies that regulators consider socially desirable.     

Spatial concentration of manufacturing firms in China

Applying the methodology developed by Duranton and Overman, we analyse localization and dispersion of firms in China. Using a unique and detailed dataset on manufacturing firms in China, we are able to follow the changes in location patterns of firms between 2002 and 2008. Our analysis shows that firms in China are more localized than in the UK or Japan. Localization is comparable to that in the US, and takes place at relatively small scales that are consistent with the size of Chinese cities. Localization increases rapidly, even in the relative short period between 2002 and 2008, especially new entrants localize. Private firms, firms from Hong‐Kong, Macao and Taiwan, and foreign firms are more localized than state‐owned firms. Our findings are consistent with the notion that China is increasingly liberalizing its economy, enabling (profit seeking) manufacturing firms to benefit from agglomeration economies.     

Spatial competition and contestability based on choice histories of consumers

The paper proposes an empirical framework for measuring competitive interactions between pairs of firms in a certain industry characterized by spatially differentiated firms and heterogeneity in consumer tastes. Recognizing that the degree of competition between firms depends on the extent to which a representative consumer switches among firms, the framework is built on the Latent Class Logit model and on consumer choice histories. It emphasizes the spatial dimension of competition, provides a disaggregated measure of demand contestability, and proposes a network‐based model of supplier competition using a new Global Pairwise Competition Index.     

Spatial Cournot competition and transportation costs in a circular city

We reconsider a Cournot spatial competition in a circular city. We discuss an oligopoly model. We find that two equilibria exist if the transport cost function is nonlinear in distance, while a continuum of equilibria exists if it is linear. Thus, the result of the real indeterminacy of equilibria in the linear transport cost case is knife edge.     

Requirements and applicable standards for design, manufacturing and installation of flexible pipes

A review is given of guidelines and standards for design and operation of high pressure flexible pipes used as pipelines, risers and pipeline/flowline tie-ins, etc. The main emphasis is given to the Veritec Guidelines for Flexible Pipes¹, which are also compared with other standards and regulations for flexible pipes. The final part of the paper discusses possible future Code development to achieve flexible pipe designs having a more consistent safety level with respect to various products, applications, etc.     

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’.