ZONE PRICING*

ABSTRACT. Our purpose is to study a spatial price policy often encountered in the real world, known as zone pricing. This price policy consists in determining simultaneously several delivered prices together with the geographical zones in which they apply. It is shown that zone pricing approximates perfect spatial price discrimination and that the firm's profit increases with the number of zones. Furthermore, the number of markets supplied by the firm rises with the number of zones. Finally, zone pricing is compared to other standard spatial price policies and possible extensions are discussed.     

The Modifiable Areal Unit Problem,in a Regression Model Whose Independent Variable Is a Distance from a Predetermined Point

This paper deals with the modifiable areal unit problem in the context of a regression model where a dependent variable is an attribute value (say, income) of an atomic data unit (say, a household) and an independent variable is a distance from a predetermined point (say, a central business district) to the atomic data unit (a disaggregated model). We apply this disaggregated model to spatially aggregated data in which the dependent variable is the average income over a spatial unit and the independent variable is the average distance from each household in a spatial unit to the predetermined point (an aggregated model). First, estimating the slope coefficient by the least squares method, we prove that the variance of the estimator for the slope coefficient in the aggregated model is larger than that in the disaggregated model. Second, focusing on variations in the variance of the estimator for the slope coefficient in the aggregated model with respect to the number of zones, we obtain the number of zones in which the variance is close to that in the disaggregated model. Third, we obtain the zoning system that has the minimum variance for a fixed number of zones. We also calculate the maximum variance in order to examine the range of the variance.     

LÖSCHIAN COMPETITION VERSUS SPATIAL COLLUSION: PRICE AND WELFARE COMPARISONS*

ABSTRACT. Löschian duopoly under heterogeneous cost conditions is examined to show that it is not equivalent, contra past findings, to spatial collusion. Moreover, within the confines of the assumed demand and cost conditions spatial collusion is shown to be superior to Loschian competition in terms of both (aggregate) consumer surplus and producer surplus, which implies a possible welfare gain from collusion. A general, if not the general, prices-and-welfare comparison of alternative pricing schema including collusive, Löschian, and optimal pricing is summarily presented in a table.     

SPATIAL COMPETITION À LA COURNOT: PRICE DISCRIMINATION BY QUANTITY-SETTING OLIGOPOLISTS*

In this paper, we consider oligopolistic competition in a spatial model when firms take care of goods' delivery and discriminate among consumers. Firms compete by setting quantity schedules independently over space. We show that under general conditions a Nash equilibrium in this game exists and is unique. In equilibrium, firms’ markets overlap, a feature which accords with intuition and empirical observations. Over the interval between two firms, the equilibrium spatial price schedule is quasi-concave (quasi-convex) when transport costs are concave (convex). With linear transport costs, the model predicts uniform delivered pricing. Uniform pricing could moreover be obtained by a combination of increasing returns to volume in transportation together with concavity of unit transport costs in distance.     

Crossing Boundaries: Diplomacy and the Global Dimension, 1700–1850

Abstract

This is a comment on the contributions to this special issue (‘Intercultural Diplomacies’) structured around the interactions of cultural zones across Eurasia, the role of intermediaries and networks, and, finally, processes of change 1700–1850.     

Product Differentiation and Location Choice in a Circular City*

Abstract. The paper analyzes spatial competition among firms that sell substitute and/or complementary products. The firms first choose locations on the perimeter of a circular city and then compete in quantities (à la Cournot). Both linear and convex (quadratic) transport costs are considered. In general, multiple location equilibria are encountered. Complete agglomeration, partial agglomeration, and complete dispersion are possible. Convex (quadratic) transport cost substantially shrinks the set of equilibria obtained under linear transport cost. In general, the results obtained for a larger number of firms selling complementary products are strikingly different from those obtained under a duopoly.     

UNIFORM SPATIAL PRICING

ABSTRACT Uniform spatial pricing means that a firm delivers its product to any customer at a fixed price, independent of location. Economic theory explains the use of uniform pricing by the added profit generated by absorbing freight charges of distant customers. I extend this insight by demonstrating that when demand elasticity and transportation cost are positively enough correlated, uniform pricing generates higher profits than mill pricing. I show that this result can better explain observed patterns of price policy choice by mail order and web firms. A second result is application of this idea to firms with many shipping facilities.     

Report of council

The ancient medina of Fes has retained moving through the gates of the medina and suggests much of its traditional craft‐based industrial economy, relying on a flow of raw materials and goods carried within the old city by human and animal porterage. Vehicular traffic is unable to penetrate much of this area, necessitating considerable transhipment between different transport modes at the edge of the medina. This study examines the type of goods and transport that variations in these are related to the location of functional zones within the medina and to the condition of the urban fabric.     

A Note on Trip Benefits in Spatial Interaction Models

We extend the well-known transport users' benefits measure (TUB) for the doubly-constrained spatial interaction model derived by Williams (1976). The original formula expresses the TUB as composed by two terms associated with the origin and the destination zones. First, the TUB is associated here with trips instead of zones, providing a natural interpretation as a rule-of-a-half measure of benefit under inelastic demand (for the short-run case). Second, a TUB formula for the long-run case is derived, that is, when the total number of trips, trip origins, and trip destinations change. We then propose updated measures of accessibility for location behavior.     

A Note on the Extremities of Local Moran's Iis and Their Impact on Global Moran's I

By defining local Moran's I_i as a ratio of quadratic forms and making use of its overall additivity to match global Moran's I, we can identify spatial objects with a strong impact on global Moran's I. First, we concentrate on the spatial properties of local Moran's I_i expressed by the local linkage degree. Depending on whether we use the W- or C-coding of the spatial connectivity matrix, the variance of local Moran's I_i for a small local linkage degree will be either large or small. Note that spatial objects associated with a local Moran's I_i with a large variance affect the global statistic much more than spatial objects associated with a local Moran's I_i with a small variance. Counterintuitively, global Moran's I defined in the W-coding is most influenced by spatial objects with a small number of spatial neighbors. In contrast, spatial objects with a large number of spatial neighbors exert more impact on global Moran's I setup in the C-coding. Second, we investigate the impact of the empirical data on local Moran's I_i and show that local Moran's I_i will only be significant for extreme absolute residuals at and around the reference location. Clusters of average regression residuals cannot be detected by local Moran's I_i. Consequently, spatial cliques of extreme residuals contribute more to significance tests on global autocorrelation.     

The influence of poorly interconnected fault zone flow paths on spring geochemistry

Thermal springs commonly occur along faults because of the enhanced vertical permeability afforded by fracture zones. Field and laboratory studies of fault zone materials document substantial heterogeneities in fracture permeabilities. Modeling and field studies of springs suggest that spatial variations in permeability strongly influence spring locations, discharge rates and temperatures. The impact of heterogeneous permeability on spring geochemistry, however, is poorly documented. We present stable isotope and water chemistry data from a series of closely spaced thermal springs associated with the Hayward Fault, California. We suggest that substantial spatial variations observed in δ¹⁸O and chloride values reflect subsurface fluid transport through a poorly connected fracture network in which mixing of subsurface waters remains limited. Our measurements provide insight into the effect of fracture zone heterogeneities on spring geochemistry, offer an additional tool to intuit the nature of tectonically induced changes in fault zone plumbing, and highlight the need to consider local variations when characterizing fracture zone fluid geochemistry from spring systems with multiple discharge sites.     

Geometry‐coupled reactive fluid transport at the fracture scale: application to CO2 geologic storage

Water acidification follows CO₂ injection and leads to reactive fluid transport through pores and rock fractures, with potential implications to reservoirs and wells in CO₂ geologic storage and enhanced oil recovery. Kinetic rate laws for dissolution reactions in calcite and anorthite are combined with the Navier‐Stokes law and advection–diffusion transport to perform geometry‐coupled numerical simulations in order to study the evolution of chemical reactions, species concentration, and fracture morphology. Results are summarized as a function of two dimensionless parameters: the Damköhler number Da which is the ratio between advection and reaction times, and the transverse Peclet number Pe defined as the ratio between the time for diffusion across the fracture and the time for advection along the fracture. Reactant species are readily consumed near the inlet in a carbonate reservoir when the flow velocity is low (low transverse Peclet number and Da > 10^?1). At high flow velocities, diffusion fails to homogenize the concentration field across the fracture (high transverse Peclet number Pe > 10^?1). When the reaction rate is low as in anorthite reservoirs (Da < 10^?1), reactant species are more readily transported toward the outlet. At a given Peclet number, a lower Damköhler number causes the flow channel to experience a more uniform aperture enlargement along the length of the fracture. When the length‐to‐aperture ratio is sufficiently large, say l/d > 30, the system response resembles the solution for 1D reactive fluid transport. A decreased length‐to‐aperture ratio slows the diffusive transport of reactant species to the mineral fracture surface, and analyses of fracture networks must take into consideration both the length and slenderness of individual fractures in addition to Pe and Da numbers.     

Opening up the Compendium: An Evaluation of International Comparative Planning Research Methodologies

It is two decades since the European Compendium of Spatial Planning Systems and Policies was conceived. Since its publication in 1997, the Compendium has become a widely cited reference in comparative planning literature.¹ It remains one of the few comprehensive reviews of spatial planning policy and practice across western Europe. The Compendium also represents one of the few studies to develop a typology for distinguishing between national planning systems. A number of comparative research studies on spatial planning have since built on the methodological foundations laid by the Compendium although its typology of national planning systems is not always used or interpreted as originally intended for a variety of reasons. In the context of extensive reform of planning approaches in Europe, the paper examines what can be learned about methodologies for international comparative research in planning based on the experience of the Compendium study and subsequent major comparative planning studies. We conclude that while broad typologies remain useful in explaining general trends, they may hide as much as they reveal. Future studies should widen the criteria used to build ideal types beyond formal characteristics in order to address planning in practice.     

UPWARDS,OUTWARDS AND WESTWARDS: RELOCATION OF ETHNIC MINORITY GROUPS IN THE OSLO REGION

Our purpose in this article is to examine socio‐economic and spatial integration of ethnic minorities in the Oslo region. We analyse relocation between 1998 and 2008 for members of ten minority groups along three overlapping dimensions: upwards in the neighbourhood hierarchy, outwards from the inner city to all suburbs, and westwards from a less affluent to a more affluent part of the region. The results provide some limited support for spatial assimilation theory. Two minority groups, Iranians and Vietnamese, comply partly with the theory. Another group, Filipinos, has stagnated in its socio‐economic and spatial integration. The remaining groups do not relocate in accordance with the native pattern, or fail to integrate in socio‐economic terms. The discrepancy between theory and results is most pronounced along the westward axis. We interpret the results in a broader context of regional and national circumstances: spatial assimilation theory may have different utility in different welfare regimes, depending on spatial inequality and the politics of place.     

Locating Vehicle Inspection Stations to Protect a Transportation Network

We develop a new conceptual approach to locating inspection stations for hazardous vehicles, prevention, and compare it to the previous, punitive, philosophy of the flow-capturing location model. We implement this preventive protection philosophy with a new mixed integer program that maximizes hazard avoidance by locating a number of inspection stations to detect and remove hazardous vehicles as early in their trips as possible. We test the model's performance and analyze the spatial characteristics of solutions simulating several potential applications. Our computations demonstrate that a relaxed integer-linear program is overly demanding computationally and that a simple greedy heuristic lacks robustness. We suggest further approaches to developing more powerful and efficient solution methods.     

Power of the Rank Adjacency Statistic to Detect Spatial Clustering in a Small Number of Regions

The rank adjacency statistic D is a statistical method for assessing spatial autocorrelation or clustering of geographical data. It was originally proposed for summarizing the geographical patterns of cancer data in Scotland (IARC 1985). In this paper, we investigate the power of the rank adjacency statistic to detect spatial clustering when a small number of regions is involved. The investigations were carried out using Monte Carlo simulations, which involved generating patterned/clustered values and computing the power with which the D statistic would detect it. To investigate the effects of region shapes, structure of the regions, and definition of weights, simulations were carried out using two different region shapes, binary and nonhinary weights, and three different lattice structures. The results indicate that in the typical example of considering Canadian total mortality at the electoral district level, the D statistic had adequate power to detect general spatial autocorrelation in twenty‐five or more regions. There was an inverse relationship between power and the level of connectedness of the regions, which depends on the weighting function, shape, and arrangement of the regions. The power of the D statistic was also found to compare favorably with that of Moran's I statistic.     

What Makes SMEs more Likely to Collaborate? Analysing the Role of Regional Innovation Policy

The last 20 years have witnessed the diffusion of regional innovation policies supporting networks of innovators. The underlying aim of these policies is to encourage firms, particularly small and medium-sized enterprises (SMEs), to undertake collaborations with organizations possessing complementary knowledge. Focusing on a set of SMEs that have participated, over time, in several innovation networks funded by the same regional government, the paper investigates how their relationships have evolved with respect to the following aspects: (i) reiteration of pre-existing relationships as opposed to experimentation with new relationships; (ii) collaboration with organizations possessing complementary rather than similar knowledge and competencies; (iii) creation of local relationships rather than experimentation with extra-local collaborations; (iv) reliance upon intermediaries to connect with other organizations. Our findings reveal that the involvement in these policy-supported networks changed the firms' relational patterns, leading them to collaborate with a wider variety of agents than those with whom they were linked before the policies. Sectoral heterogeneity had a negative effect on the probability of collaborating, while co-localization increased the likelihood of collaborating. Mutual involvement with intermediaries also had a positive effect. However, in the case of firm-to-university relationships only specialized intermediaries were likely to perform a positive role and, therefore, encourage networking.     

Hypermobility and the governance of global production networks: The case of the Canadian cycle industry and its links with China and Taiwan

Western firms engaged in mass retailing and in product assembly make frequent changes to their global production networks (GPNs). Indeed, some GPNs show a tendency to hypermobility, which we define as a rapid switching of economic links among manufacturers, importers, and retailers. This theme is explored in the context of the Canadian bicycle industry where domestic production collapsed between 1980 and 2008, following a century of remarkable stability. After a period of flux when Taiwan was the key player, China has emerged as the dominant original equipment manufacturer (OEM) of bicycles sold in Canada, with big‐box stores accounting for the great majority of sales. We connect this increasing fluidity in supply arrangements and in the global organization of the industry with the governance of these GPNs. Several aspects of governance are considered, including the Sloanist practices of the largest Canadian retailers, and the activist role of the Chinese state in directing regional patterns of manufacturing in China.     

SPATIAL ECONOMETRIC MODELING OF ORIGIN‐DESTINATION FLOWS*

ABSTRACT Standard spatial autoregressive models rely on spatial weight structures constructed to model dependence among n regions. Ways of parsimoniously modeling the connectivity among the sample of N=n² origin‐destination (OD) pairs that arise in a closed system of interregional flows has remained a stumbling block. We overcome this problem by proposing spatial weight structures that model dependence among the N OD pairs in a fashion consistent with standard spatial autoregressive models. This results in a family of spatial OD models introduced here that represent an extension of the spatial regression models described in Anselin (1988) .