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.     

SPATIAL PRICING IN INTERDEPENDENT MARHETS*

ABSTRACT. Conditions for spatial price equilibrium are derived for a set of firms in oligopolistic spatial competition, distributed at fixed locations in a heterogeneous region where consumer purchasing patterns are a probabilistic function of the price distribution rather than a deterministic function of proximity to firms. The resulting prices vary with accessibility to consumers or with the degree of local spatial monopoly, and result in non-zero profits for firms. Conditions describing the existence and stability properties of this spatial price equilibrium are defined, and are shown to be equivalent for two different hypotheses concerning disequilibrium pricing behavior: a partial price adjustment model and a Bertrand game. For two different profit goals, total profit maximization and profit rate maximization, it is shown that a spatial price equilibrium exists and is at least locally quasi-stable.     

PRODUCT DIFFERENTIATION,PRICING POLICY AND EQUILIBRIUM*

ABSTRACT. This paper studies the price-location equilibrium of duopolists supplying differentiated goods and competing in a spatial market with elastic demand. We show that a price-location equilibrium exists under all three pricing policies traditionally considered by the literature: f.o.b. mill, uniform delivered, and spatially discriminatory pricing. We also show that firms always cluster at the market center. The second part of the paper studies the endogenous choice of pricing policy. A surprising feature of the resulting equilibrium is asymmetry. The greater the extent to which the goods are substitutes, the more likely is it that one firm will choose f.o.b. pricing and the other price discrimination. Finally, the welfare consequences of the analysis show some interesting trade-offs.     

THE EFFECT OF RETAIL FIRM OWNERSHIP ON PRICE EQUILIBRIUM*

ABSTRACT. This paper examines the effect of retail firm ownership on price equilibrium using a simple linear-city model. It is shown that price divergence emerges due to the differences in retail firm ownership, because retail firms under different ownership internalize shopping externalities differently. It is also shown that if a commercial center has two specialized retail firms, these stores charge the same markup for different goods at the equilibrium.     

Determining Market Areas Captured by Competitive Facilities: A Continuous Equilibrium Modeling Approach

Many existing models concerning locations and market areas of competitive facilities assume that customers patronize a facility based on distance to that facility, or perhaps on a function of distances between the customer and the different facilities available. Customers are generally assumed to be located at certain discrete demand points in a two-dimensional space, or continuously distributed over a one-dimensional line segment. In this paper these assumptions are relaxed by employment of a continuum optimization model to characterize the equilibrium choice behavior of customers for a given set of competitive facilities over a heterogeneous two-dimensional space. Customers are assumed to be scattered continuously over the space and each customer is assumed to choose a facility based on both congested travel time to the facility and on the attributes of the facility. The model is formulated as a calculus of variations problem and its optimality conditions are shown to be equivalent to the spatial customer-choice equilibrium conditions. An efficient numerical method using finite element technique is proposed and illustrated with a numerical example.     

The Max-Min-Min Principle of Product Differentiation

We analyze two and three-dimensional variants of Hotelling's model of differentiated products. In our setup, consumers can place different importances on each product attribute; these are measured by weights on the disutility of distance in each dimension. Two firms play a two-stage game; they choose locations in stage 1 and prices in stage 2. We seek subgame-perfect equilibria. We find that all such equilibria have maximal differentiation in one dimension only; in all other dimensions they have minimum differentiation. An equilibrium with maximal differentiation in a certain dimension occurs when consumers place sufficient importance (weight) on that attribute. Thus, depending on the importance consumers place on each attribute, in two dimensions there is a max-min equilibrium, a min-max equilibrium, or both. In three dimensions, depending on the weights, there can be a max-min-min equilibrium, a min-max-min equilibrium, a min-min-max equilibrium, any two of these, or all three.     

Duopoly prices under congested access*

Abstract. Consider two firms, at different locations, supplying a homogenous good at constant marginal production cost. Consumers incur travel costs to the firm for each unit purchased, and the travel costs increase with the amount of travel to each firm (congestion). When all traffic and all congestion are generated by travel to a duopolist, both the Nash–Bertrand equilibrium prices and the Nash–Cournot equilibrium prices exceed the sum of the marginal production cost and the marginal external travel cost. However, when the road is shared by travelers to the duopolists' facilities and travelers in competitive markets, the Nash–Bertrand duopoly price equals the competitive price and the Nash–Cournot price contains a markup.     

TRAFFIC CONGESTION,POLYCENTRICITY, AND INTRAURBAN FIRM LOCATION CHOICES: A NESTED LOGIT MODEL FOR THE LOS ANGELES METROPOLITAN AREA

This study empirically investigates traffic congestion effects on agglomeration through the lens of firm location decisions. A discrete choice model is applied to examine new establishments’ location choices within the Los Angeles metropolitan area. Employment centers are defined as the choice set to explore the nature and role of intraurban agglomerations. The results show that metro‐wide congestion negatively affects the location choices of firms in the high‐order office‐related activities, while local congestion have positive impacts on those firms’ location decisions. In contrast, firms in production‐related activities are positively influenced by regional congestion but are negatively affected by local congestion levels.     

A MODEL OF SHOPPING CENTERS*

ABSTRACT In this paper, we propose a model of developers' strategies for tenant mixes and the locations of shopping centers (SCs). Consumers have preferences for product variety, and tenants in the SCs sell differentiated goods. The consumers can choose two shopping behaviors: patronizing one or both of the two SCs. We show that if the consumers have strong preferences for product variety, the SCs agglomerate to free‐ride on the rivals' product varieties, and the consumers patronize both SCs. On the other hand, if consumer preferences are weak, the SCs locate at different locations, and the consumers patronize one of the two SCs.     

Pricing Road Congestion: Recent Evidence from Singapore

The role of road pricing in travel demand management and congestion mitigation has been gaining support in many countries. Although the theory of congestion pricing is persuasive and straightforward, successful application of road pricing mandates that congestion externalities be estimated. Using data from a recent traffic survey in Singapore, this paper estimates congestion prices for alternative time values and vehicle types. These estimates are compared with the existing cost of area licenses, from which implications for economic efficiency and resource allocation are drawn.     

The Location-Production-Allocation Problem With Nonlinear Production Costs

This paper develops a location-production-allocation model for the multiplant producer selling under the conditions of nonlinear production costs and a uniform pricing system. The primary goals of this paper are to incorporate the following criteria into a model: (1) production factors and location factors should be synthesized into a location-production-allocation problem; (2) the production function is nonlinear, implying economies and diseconomies of scale; (3) a systems approach should be utilized to solve for a global optimum. Within the context of these criteria, equilibrium conditions are derived for a location-production-allocation model. Finally, a heuristic technique to solve this problem is derived from the equilibrium conditions.     

The Optimal Nodal Location of Public Facilities With Price-Sensitive Demand

The purpose of this paper is to present some models for the location of public facilities in nodal networks that explicitly maximize social welfare by accounting for price-elastic demand functions. The models presented here are general; yet they are mathematically equivalent to the plant location problem and are therefore amenable to solution procedures developed for the plant location problem. The models presented here distinguish between two institutional environments that reflect the degree of power of the consumer to choose which facility to patronize. If consumers can be assigned arbitrarily to facilities and can be denied service, then the environment is one of public fiat. If consumers must be served at the facility of their choice, then a “serve-allcomers” environment exists. Separate models for each environment are specified, and the relationship between optimal assignments and pricing policies is developed.     

Facility Location Under Zone Pricing

Zone pricing consists in determining simultaneously several delivered prices together with the zones where these prices apply. A model and algorithm are proposed to determine optimal facility locations, prices, tariff-zones, and market areas in order to maximize the firm's profit under zone pricing. The resulting nonlinear mixed-integer program is tackled by projecting the objective function on the price space, solving repeatedly uncapacitated facility location problems for fixed values of the prices. The implicit profit function so defined is optimized by branch-and-bound. Computational results are reported.     

Dynamic road pricing and the value of time and reliability

High Occupancy Toll (HOT) lanes that use dynamic pricing to manage congestion and generate revenue are increasingly popular. In this paper, we estimate the behavioral response of drivers to dynamic pricing in an HOT lane. The challenge in estimation lies in the simultaneity of price and demand: the structure of dynamic tolling ensures that prices increase as more drivers enter the HOT lane. Prior research has found that higher prices in HOT lanes increase usage. We find that after controlling for simultaneity HOT drivers instead respond to tolls in a manner consistent with economic theory. The average response to a 10 percent increase in the toll is a 1.6 percent reduction in usage. Drivers primarily value travel reliability over time savings, although there is heterogeneity in the relative values of time and reliability based on time of day and destination to or from work. The results highlight the importance of both controlling for simultaneity when estimating demand for dynamically priced toll roads and treating HOT lanes with dynamic prices as a differentiated product with bundled attributes.     

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.     

Congestion Pricing and Demand Management: A Discussion of the Issues

This article reviews the political, technological, and economic issues involved in the formulation of congestion pricing policy. Increased urban congestion combined with increasingly scarce resources is making policymakers consider congestion pricing as an alternative to expanding highway capacity. Past experiences with congestion pricing and other types of demand management are discussed in an attempt to identify problems policymakers may expect to encounter in the US.     

SHOPPING AND LEISURE: IMPLICATIONS OF WEST EDMONTON MALL FOR LEISURE AND FOR LEISURE RESEARCH

In the context of three alternative approaches to the meaning of leisure (activity, time, and experience), this article uses West Edmonton Mall (with its vast array of shops and unique complex of recreational facilities) as a starting point to explore four relationships between shopping and leisure. These are: independence (shopping as purchasing); shopping for leisure (the purchase of goods for use in subsequent leisure time); shopping and leisure (when shops and leisure facilities are juxtaposed in a single facility like West Edmonton Mall); and shopping as leisure (when shopping begins to take on the attributes of leisure as an experience). It is concluded that the last category offers the most interesting questions for future research.     

Maximizing Accessibility on Congested Networks

The problem of locating facilities to maximize their accessibility on networks where costs are functions of flow volume is considered. In particular, an accessibility model developed by Leonardi is extended to bipartite and tree networks whose arc costs are determined by a flow-dependent congestion function. The resultant nonseparable equilibrium problem is solved heuristically, and numerical simulations are used to explore the model's behavior under varying conditions.     

Probing A Traffic Congestion Controversy: Density and Flow Scrutinized

Probing a die-hard traffic congestion controversy, this paper scrutinizes two key variables, density and flow, under equilibrium versus optimal states. Optimization requires equilibrium flow to decrease under mild congestion, but increase under hyper-congestion. However, both increasing flow needed under hypercongestion and decreasing flow needed under mild congestion should be accompanied by decreasing density. Thus, inflow of vehicles should always be discouraged to either increase or decrease flow of vehicles for economic efficiency. Moreover, even when optimal policy requires equilibrium flow to increase, the optimal flow itself must decrease eventually as demand increases beyond a critical level.     

CAN REGIONALIZATION OF LOCAL PUBLIC SERVICES INCREASE A REGION'S WEALTH?*

ABSTRACT. In the presence of agglomeration and congestion externalities the sequence of location choices made by firms results in an inefficient distribution of economic activity, since individual firms do not bear the congestion costs they impose on other firms. In this paper, we model the interaction of public authority service strategies and firm location choices. We show that a self-interested regional authority can effect a welfare-improving distribution of economic activity when compared with an economy without an authority or an economy with local authorities. However, we also show that the conditions under which the authority would induce a welfare enhancing distribution depends on the authority's strategic posture, as well as the nature and size of public subsidies for the authority. The conditions necessary for a regional authority to choose an efficiency enhancing strategy may be difficult to achieve.