Heterogeneous households and firms in an urban model with open space and agglomeration economies*

This paper develops a model with heterogeneous households and firms that can locate anywhere in the city. The main features of the model are household preferences for open space which depend on distance to the greenbelts at the city periphery, and agglomeration economies for firms. Numerical results show equilibrium location patterns, rents, and wages under different model specifications. Under most conditions, monocentric location patterns (where there is a higher concentration of firms in the centre zones compared to surrounding zones) are observed, but duocentric location patterns for firms can emerge if both open space values and travel costs are high.     

Spatial price equilibrium and convex duality

This paper presents the duality theory of a class of spatial price equilibrium models characterized by the assumption that the net supply of firms, households, and transport agents can be described by set-valued correspondences, which are subdifferential mappings of convex functions. If the graphs of these correspondences overlap sufficiently in price space and quantity space, an equilibrium exists. Finding an equilibrium allocation is equivalent to the minimization of social costs, and finding an equilibrium price vector is equivalent to the minimization of social surplus under these conditions.Helfpul comments from Tony E. Smith and two anonymous referees are gratefully acknowledged.     

GENERAL EQUILIBRIUM VS. OPTIMUM, AND THE ALLOCATION OF LAND FOR TRANSPORTATION IN A CLOSED INFORMATION-ORIENTED CITY WITH TRAFFIC CONGESTION

ABSTRACT This paper presents a general equilibrium model of the closed city. The households residing in the suburbs are able to supply labor for the firms in the CBD not only by commuting which causes traffic congestion but also by telecom muting which needs an input of telecommunication services. The laissez-faire equilibrium is compared with the optimum. We derive the equilibria by numerical computations using specific utility, production and congestion functions. The results show the allocation of land for transportation based on the social cost-benefit rule, which is different from the allocation of Mills and de Ferranti (1971). This indicates that in the optimum market equilibrium which is maintained by both a congestion tax and subsidy, the city is rather more suburbanized than expected on the basis of previous studies.     

INFRASTRUCTURE PROVISION AND LOCATIONAL EFFICIENCY IN A FEDERATION: A NUMERICAL APPROACH

ABSTRACT How do different strategies of infrastructure provision affect the spatial distribution of firms and households in a federation? The current article analyzes three polar cases: in the first case there is no publicly provided infrastructure at all. The second case is the case of uniform provision, i.e., a federal government provides the same amount of infrastructure to each region, regardless of the initial spatial distribution of firms, households, and tax revenues. The third strategy is decentralized provision, i.e., infrastructure is provided according to regional tax revenues. It is shown that the superior strategy depends on the initial distribution of firms among regions which may reflect historical accidence.     

Cournot competition in spatial markets: Some further results

In contrast to most of the literature on a circular market in which firms choose to disperse equally from each other in equilibrium, this research note shows that the equal-distance dispersion in a circular market results from the substitutability of products produced by two single-plant duopoly firms. Meanwhile, agglomeration at one point results from complementarity. In the multi-plant duopoly case, we find - in contrast to Chamorro-Rivas (2000) - that when firms sell complements, the equilibrium locations tend to exhibit both inter-firm agglomeration and intra-firm dispersion. In other words, the location layout in equilibrium exhibits spatial agglomeration (by pairs) finitely at many points.Received: 8 February 2002, Accepted: 28 October 2002, JEL Classification: D43, L13We would like to thank Chien-Fu Chou, De-Xing Guan, Jacques Poot, and three anonymous referees for their valuable comments. Responsibility for any remaining errors rests with the authors.     

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     

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.     

Spatial economic networks with multicriteria producers and consumers: Statics and dynamics

In this paper, we develop a framework for the formulation, analysis, and computation of solutions to spatial network problems in which the firms are multicriteria decision-makers and the consumers are as well. In particular, the firms, which are involved in the production of a homogeneous commodity, are spatially separated and weight the two criteria of profit maximization and total output maximization in distinct fashion. They are faced with the selection of modes/routes (which are modeled in an aggregated manner) to transport the commodity to the demand markets where consumers, consisting of different classes, consider the price charged by the producers and weight the transportation cost and the transportation time of the product on the links in an individual manner. We derive the governing equilibrium conditions and present the variational inequality formulation. We provide qualitative properties of the equilibrium commodity shipment and generalized price pattern and then propose a tatonnement process, which we formulate as a projected dynamical system. We give an algorithm for computational purposes and apply it to several numerical examples for illustration purposes. This paper is the first to integrate multicriteria decision-making on the production side and on the consumption side in a basic network context. Received: February 2001/Accepted: August 2001     

Organisational motives and spatial effects in Internet adoption and intensity of use: evidence from French industrial firms

The aim of this study is to examine the reasons why firms use ICTs at varying rates, by making a distinction between the two stages of their diffusion: their adoption and the intensity of their use. What are the differences between Internet adopters (in terms of their internal organization and external environment) that explain the intensity with which they use this technology? Furthermore, do these processes vary according to the type of area in which firms are located (urban vs. rural)? A model of technological diffusion is constructed that merges two types of models: those that concentrate on epidemic effects and the so-called equilibrium models that consider the decision to adopt new technologies as a result of an economic calculation by firms. To test this model, we use data drawn from a recent French national survey of 5,200 industrial firms (“ICT and E-commerce”, 2002). One striking result of this study is that we do not obtain a significant positive correlation between firm’s size and Internet intensity of use. Moreover, though spatial disparities related to ICT adoption are no longer significant in France, they remain very important in the processes of ICT appropriation and use by firms. The results also indicate that the determinants of the intensity of Internet use vary significantly according to the firms’ location: epidemics effects play an essential role in the case of urban the firms, while rank effects are essential in low density areas.     

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.     

Hotelling was right with decreasing returns to scale and a coalition-proof refinement

This paper provides a simple, realistic, and very slightly modified version of the production technology in Hotelling’s (Econ J 39:41–57, 1929) spatial model with linear transportation costs to overcome the nonexistence problem of equilibrium—decreasing returns to scale. It is shown that a pure strategy Nash equilibrium in price competition always exists for all location pairs and guarantees uniqueness if we utilize a coalition-proof refinement introduced by Bernheim et al. (J Econ Theory 42:1–12, 1987). Decreasing returns to scale reduce the profit a firm can capture through price undercutting and stabilize the price equilibrium due to the increasing average production cost of firms. As a consequence, duopoly firms agglomerating at the center of a line are shown to be at the unique location equilibrium. This paper confers a new validity to the so-called principle of minimum differentiation, in some sense, with the least deviation from the original Hotelling (Econ J 39:41–57, 1929) model.     

Modeling competition in electric energy markets by equilibrium constraints

Throughout the world, the electricity industry is currently undergoing significant restructuring towards deregulation and competition. Under this new framework, electric firms assume more risk, and are more responsible for their own decisions. Utilities need original models that fulfil these new requirements. This paper presents a novel conceptual approach to modeling the newly deregulated power markets. It combines powerful traditional tools related to the detailed system operation with techniques for modeling economic market equilibria. The proposed approach models the competitive behavior of the electric firms by incorporating a set of constraints, namely the equilibrium constraints, into a traditional production cost model. These constraints reproduce the first order optimality conditions of the strategic companies. Thus the approach achieves a profit maximization objective while keeping the system operation details. This model has been implemented in GAMS. An application to a sample case study is also presented.     

SPATIAL CONSEQUENCES OF CHANGES IN THE TRANSPORTATION NETWORK: THEORETICAL ANALYSIS AND NUMERICAL EXPERIMENTS WITHIN A MULTIZONAL THREE SECTOR MODEL

ABSTRACT: In this article a model is presented that is directed toward analysis of spatial consequences of changes in the transportation network. The model is based on a variant of Lowry's economic base model, with three sectors and two nested levels of spatial dis-aggregation. Changes in the locational structure are explained through the interdependency between households and local sector firms. As a numerical experiment, the model is applied to estimate locational impacts of some large-scale investments in transportation infrastructure along the Western coast of Norway.     

Consistent price and location conjectures in spatial competition models

Remarkable advances have been made in spatial competition theory during the past three decades. Only in recent years, however, have the implications of firms' conjectural responses become well understood. Here research has largely focused on analyzing markets where prices (short run) or prices and locations (medium and long run) are exogenous. This paper examines the equilibium properties of spatial firms when prices and locations are consistent or endogenous. Price reaction equations are complemented with location reaction equations, consistency conditions are introduced, and numerical solutions are then given. While the simulations are confined to one-dimensional markets, equilibrium solutions unambiguously indicate how prices, locations, and profits are related to the costs of firms, the elasticity of consumer demand, and the presence or absence of market boundaries.     

Vertical differentiation in a generalized model of spatial competition

In a duopoly model of spatial competition where consumer's surplus function contains both a linear and a quadratic disutility component, it is shown that the nature of differentiation at equilibrium depends on the distribution of roles across firms and the relative weight of linear and quadratic components in the transportation cost function. Vertical differentiation is more likely to obtain the lower the weight attached to the linear component and the higher the advantage enjoyed by one firm over the rival. Received: August 1998/Accepted: January 2000     

“Signal-jamming” leads to “minimum differentiation” under demand uncertainty

This paper analyzes the location equilibrium when three firms choose a location sequentially under demand uncertainty in spatial competition. If subsequently entering firms can predict new information concerning demand by observing the demand signal that arises after preceding firms enter the market, then the three firms choose the same location at the midpoint of the expected demand; this is known as “minimum differentiation.” The reason for this is that preceding firms behave in a manner such that subsequent firms cannot predict the exact demand. This behavior of firms might present a new interpretation of “mimic behavior.”     

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     

Aging in place and housing over-consumption

Societies are aging and the number of households with heads or even all members over 65 is increasing rapidly. Many of these households are well established in the housing market and occupy housing at the apex of the housing choice process. These houses are large, nearly always owned and with substantial equity value. The households that occupy such dwellings have lower mobility rates than households in general and are likely, with low mobility rates, to continue to occupy their houses even when they no longer need the same space as when they were raising families. The paper examines the extent of this phenomenon in the Netherlands and traces under what circumstances older households are exchanging these large houses. The data, derived from the Housing Demand Survey in the Netherlands, reveal that older households occupy very spacious housing, that they have relatively long durations of stay, and that owners over 60 are nearly certain to be ‘over-consuming’ housing with respect to equilibrium consumption. At the same time, when older households do move, they reduce the amount of space they consume. The issue for society at large is whether the low mobility rates create a bottleneck in access to spacious housing by younger families.This paper was originally designed and initiated in collaboration with Frans Dieleman. We wish to acknowledge our long time collaboration with Frans. We will miss his insight and creativity.     

Shifting Trajectories of Homeownership in Japan

In contemporary Japanese society, ‘post-bubble’ housing debates are being shaped by labour market restructuring, demographic change and policy shifts. In this context, this paper explores shifting trajectories of homeownership using three specific housing debates: ‘the emergence of a gap society’, ‘increasing single-person households’ and ‘housing assets in later life’. By exploring these various debates, it attempts to highlight how housing, demography and social policy interact at different levels and in different areas to produce dynamic shifts away from the conventional post-war housing trajectory. Current trends have exhibited shifts away from: the linear upward housing trajectory; the family-centred housing model; the land-orientated housing system; and homeownership dominance per se. The concept of generation is used as a thread to tie the different debates together. Each housing issue is often more relevant to a particular generation, but relationships between generations within families and society add to the dynamism to the current shifts.     

An intra-industry trade model in a vertical differentiation framework

We developed a partial equilibrium model in which intra-industry trade arises as a result of utility maximization of consumers and profit maximization of firms. The driving force for intra-industry trade is non-homothetic preferences of consumers. We utilized a vertical differentiation framework, in which consumers have the same tastes for quality but different income levels determining their non-homogeneous choices. All firms in all countries have access to the same production technology, and there are no differences in factor endowments. Intra-industry trade arises as a result of each firm specializing on a certain segment of the market in all countries. We solved the model numerically for a two-country two-firm setup. In this setup, firms choose their product quality level and their price by maximizing their profits in a two-stage optimization problem. They also decide whether to export to the foreign market or to concentrate only on the domestic market in a standard two-by-two game. With introduction of non-zero transportation costs, trade volumes in both directions decrease. Transportation costs are shared between consumers and firms according to the marginal demand in the domestic versus in the foreign country. This model supports Krugman’s home market effect: In case of non-zero transportation costs, firms want to locate their production site in the country where there is higher marginal demand for their product.