Endogenous product differentiation and product R&D in spatial Cournot competition

We investigate in a spatial Cournot competition setting how much product research and development (R&D) investment firms make in order to differentiate their goods. The model features a location competition in the first stage, R&D competition in the second stage, and Cournot competition in the third stage. There are two differentiation methods in the model??spatial differentiation affecting the firm costs, and differentiation in the demand function affecting the demand levels. We find that comparing to the setting with no spatial connotation, the firms tend to invest less in product R&D. We also consider welfare implications. Although the firms employ maximum differentiation in equilibrium, there are cases in which welfare can be improved if the firms are to locate closer to each other.     

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.     

Location, agglomeration and infrastructure

Abstract. In this article we discuss the relationships between transportation infrastructure, firm location, agglomeration and regional development. We will argue that the spatial transaction costs faced by modern firms have changed over recent decades, and that this has changed the ways in which transportation infrastructure contributes to form location behaviour and regional economic development. Therefore, in order to analyse these issues, it is necessary to consider the spatial transaction costs faced by modern firms and to investigate the conditions under which reductions in these costs due to infrastructure improvements will allow firms to move. These complex relationships are seen to be mediated via different geography-firm-organisation structures and consideration of these is essential for any realistic evaluation of the role of transportation infrastructure.     

“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.”     

Collusion in two models of spatial competition with quantity-setting firms

We use the linear city model and the circular city model to investigate the relationship between collusion sustainability and firms’ distance, and between collusion sustainability and transportation costs when firms can sell different quantities at each location. We find that when transportation costs are low, collusion sustainability monotonically increases with firms’ distance, while when transportation costs are high, the relationship is non-monotonic. Higher transportation costs increase collusion sustainability. Finally, in the circular city model, welfare is higher under collusion than under competition when transportation costs are high and firms are distant enough.     

Location,agglomeration and infrastructure

In this article we discuss the relationships between transportation infrastructure, firm location, agglomeration and regional development. We will argue that the spatial transaction costs faced by modern firms have changed over recent decades, and that this has changed the ways in which transportation infrastructure contributes to form location behaviour and regional economic development. Therefore, in order to analyse these issues, it is necessary to consider the spatial transaction costs faced by modern firms and to investigate the conditions under which reductions in these costs due to infrastructure improvements will allow firms to move. These complex relationships are seen to be mediated via different geography-firm-organisation structures and consideration of these is essential for any realistic evaluation of the role of transportation infrastructure.JEL Classification: D21, D23, L1, R12, R3     

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.     

Network facility-location models in Stackelberg-Nash-Cournot spatial competition

A hierarchical mathematical programming approach is combined with sensitivity analysis (of variational inequalities) to formulate a facility-location model for a firm competing on a discrete network. It is assumed that the locating firm will act as the leader firm in an industry characterized by Stackelberg leader-follower(s) oligopolistic competition. The othern competitors in this industry are assumed to act as Cournot firms that each operate under the Cournot assumption of zero conjectural variation with respect to theirn — 1 Cournot competitors. It is further assumed that then Cournot firms will react to the location/production/shipping activities of the Stackelberg firm. Therefore, when the Stackelberg firm makes its location, production, and shipping decisions it takes into account the reaction of then Cournot firms to its (the Stackelberg firm's) integrated location and distribution decisions. Specifically, a Cournot reaction function is developed and imbedded in the Stackelberg firm's profit-maximizing objective function to project the anticipated reaction of the Cournot firms to the Stackelberg firm's location decision.An earlier version of this paper was presented at the 37th North American Meetings, Boston, November 1990.     

The locations of firms on intersecting roadways

With Bertrand-Nash mill-price competition, travel costs proportional to distance squared, and three firms on an interval, the equilibrium locations of the peripheral firms are further from the center than is socially optimal. If there is a central intersection, with four (or more) finite roadway segments radiating outward from the center (a small city spread along two intersecting roadways), and with one firm at the center and one on each radial segment, then the equilibrium locations of the peripheral firms are closer to the center than is socially optimal. Extensions include competition with spatial price discrimination, a more complicated system of intersecting roadways, and more than one firm on each roadway segment.     

Industrial configuration in an economy with low transportation costs

We examine how the spatial economy with multiple industries is shaped when interregional trade costs and intraregional commuting costs are low. All industries are characterized by increasing returns to scale and monopolistic competition, and they are differentiated by their trade costs and the degree of intra-industry competition measured by their firm numbers. We find some distinct rules in industrial location. First, at most, one industry disperses, while others agglomerate in a region according to their ratios of relative trade costs to firm numbers. Second, industries with stronger competition constitute a smaller region, while those with higher trade costs compose a larger region. The results are consistent with the classical Weberian location theory and suggest that the degree of intra-industry competition also becomes an essential factor to determine industrial location when transportation costs are small. Finally, the population differential between the regions monotonically decreases in the relative commuting cost.     

Industrial location,spatial discrete choice models and the need to account for neighbourhood effects

This research, following the original contributions of Vichiensan et al. (J East Asia Soc Trans Stud 6:3789–3802, 2005) and Autant-Bernard (Eur Plan Stud 14:1187–1208, 2006), employs a spatial conditional logit framework in order to explore the role that inter-territorial spillovers play in driving the location choices of industrial firms. After introducing neighbourhood effects into the theoretical model, we test the methodology using data on 8,429 firms established in the municipalities making up the Spanish region of Murcia. Our results show that human capital, agglomeration economies and industrial land availability are the main factors driving entrepreneurs’ decisions. Estimates of the spatial component of the model indicate that spillovers or externalities taking place between municipalities (inter-territorial spatial effects) have a remarkable influence on the location decisions of the firms, thus confirming the need to account for such spatial dependence pattern when studying location decisions of industrial companies at a local level.     

Hierarchies of cities and the spatial filtering of industrial development

ABSTRACT The spatial division of labor and external economics associated with the nation's hierarchical system of cities are postulated to be part of the process involved in the spatial filtering of industrial development. In this process high labor costs in metropolitan areas cause less competitive industries to restructure their operations or be priced out of the larger labor markets. The industries priced out of the markets locate all or some of their operations in smaller settlements in more distant areas where labor costs are lower, given sufficient external economics. The research supports this general proposition but reveals differences based upon the types of industries and the location of their headquarter facilities. It also reveals significant differences in the locational patterns and site selection criteria of different types of plants established by local, national and foreign firms; these differences foster the development of spatially bifurcated or dual labor markets that are associated with regional city size distributions.     

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.     

A note on “Price variation in spatial markets: the case of perfectly inelastic demand”

Summary These considerations are based on the need for consistent models. If we look at the spatial oligopoly approach of Mulligan and Fik from this point of view, we draw two conclusions. First, their model does not indicate any reasons for asymmetrical conjectural or actual price reactions in the market, as they are not influenced by any different marginal production costs and different locational distributions. Second, exactly one conjectural reaction coefficient is consistent with the profit-maximizing behavior of the firms, and this coefficient is identical for all firms in the market. Consequently, the alternative market results for different reaction coefficients in the paper of Mulligan and Fik are reduced toone result atconsistent conjectural reaction coefficients.     

Tariff policy and transport costs under reciprocal dumping*

This paper proposes a framework, based on a reciprocal dumping model, that assesses the effects of tariff competition for mobile firms on the location patterns of the industry as well as welfare implications. While high transport costs encourage geographic dispersion in the industry, sufficiently low transport costs result in a core‐periphery location where nobody bears tariff burdens. We show that the world economy would be in a much better position under an international co‐ordination scheme, which differs from models proposed in previous studies.     

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.     

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.     

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     

Demand creation and location: a variable consumer-distribution approach in spatial competition

This paper deals with a variable spatial distribution of consumers according to the location decisions of firms in spatial competition. Specifically, we present a location-then-quantity game in which some of the consumers are attracted to the firms’ locations. We show that all firms agglomerate in a circular city when the transport cost is low. This is in sharp contrast to the results shown in previous studies with fixed distributions of consumers, where such a full agglomeration never occurs in equilibrium. Welfare analysis shows excess dispersion compared with the second-best scenario.     

Myopic spatial competition: Boundary effects and network solutions

Recent findings suggest that spatial competition studies should focus more on markets having numerous firms and realistic topologies. Eventually clarification is needed of the existence conditions and properties of multi-firm equilibria in network markets. This paper uses a traditional conjectures approach to examine long-run equilibria in a variety of one-dimensional markets. In all cases consumer demand is perfectly inelastic, price conjectures are exogenous, and (interior) firms show maximum locational differentiation. The attitude of firms is always myopic and never strategic, however. In a linear market the analysis discloses that firm price depends upon price in the counterpart circular market, a boundary effect, the spatial aggression of exterior firms, and the location of the firm. In a network market the analysis discloses that multiple equilibria occur and that the existence conditions for these equilibria depend upon both the geometric properties of the network and the price conjectures of the firms.