MILL AND UNIFORM PRICING A COMPARISON*

ABSTRACT. In this paper we examine profit, price, output and welfare under mill and uniform pricing in a monopolistic spatial market with nonlinear demand, a general consumer distribution function, and a general transportation cost function. We show that if demand is convex (concave) then the optimal uniform price minus the average unit transportation cost is lower (higher) than the optimal mill price, output under uniform pricing is lower (higher) than output under mill pricing, and welfare under uniform pricing is lower (higher) than welfare under mill pricing, provided other respective conditions are satisfied.     

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.     

THE SCOPE FOR PURE PROFITS IN A STANDARD LOCATION MODEL*

ABSTRACT. This paper examines the possibility of sustaining a collusive equilibrium in a standard location model. Drawing on recent developments in game theory, it is suggested that collusion is only feasible if market areas lie within a certain range. When market areas are large the threat of entry is likely to undermine any collusive agreement. In contrast when market areas are small, defection from the cartel is shown to be profitable. Thus collusion is shown to be feasible only when market areas and demand lie within certain bounds. More generally, this result appears to be consistent with the somewhat ambiguous empirical evidence which suggests that competitive pricing behavior is likely to prevail in periods of excessively high demand and during recessions.     

A Spatial Price Determination Model for Multi‐Market Heterogeneously Distributed Resources: An Application to Forestry Markets in Sweden

The spatial dimension is a key paradigm in price determination, as attested by recent studies in the literature that highlighted the differential in market behavior between spatial and non‐spatial pricing settings. In this paper, we develop a model of spatial pricing for multi‐market heterogeneously distributed resources, with an application to the Swedish forestry sector. The focus of the model is to estimate the impact of spatial interaction on the demand for resources in terms of resource allocation, competition, and pricing. In its core, the pricing mechanism relies on a supply–demand framework. Using disaggregated data at the gridcell level for forest feedstock supply and harvesting costs in Sweden, we construct regional supply curves for each gridcell assuming a maximum transportation distance to delimit the potential market. Demand nodes are exogenously determined and are adjusted using a distance‐decay model to assess demand pressure across locations. We apply the model empirically to assess the impact on forest feedstock prices of a 20 TWh increase in biofuel production.     

GIS辅助城市用地结构分析与用地调整的应用初探

面对复杂的城市问题,单一学科的理论和方法往往束手无策,交叉学科的研究是近年来城市问题研究的主要趋势之一,特别是随着GIS的发展,借助GIS及相关学科的研究方法和手段进行城市现状分析和预测将是城市学领域发展的重要方向之一。本文以湖北省崇阳县白霓镇为例,借用经济学供需基本概蓬和分析方法,结合社会学的调查研究方法,利用系统工程方法和GIS技术,在深入调查的基础上,开创性地提出城市用地供需度的概念,并从它们与区位之间关系的角度出发分析用地结构,探讨了GIS在城市用地结构分析与辅助用地调整方面的应用,旨在抛砖引玉,引起同行们对新技术条件下传统研究方法革新的重视。     

Optimal Facility Location in a One-Dimensional Spatial Market

This paper analyzes properties of the optimal spatial arrangement of what may be interpreted as a class of public facilities. Optimality is defined as cost minimization. Three different optimality criteria are considered, and for each, the necessary and, sufficient conditions, market area size, and production levels, are derived. The relationship between optimal production levels and number of facilities needed is also considered. Next the results of implementing various pricing strategies are analyzed with emphasis given to marginal and uniform pricing. It is shown that, given certain conditions, all facilities incur operating deficits, given marginal pricing. Estimates on the level of the deficits are derived in terms of location rents. Finally, in the appendix, several important results from other studies are derived as special cases of the basic model.     

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.     

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.     

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.     

On the Finite Optimality Set of the Vector Assignment p‐Median Problem

The vector assignment p‐median problem (VAPMP) is one of the first discrete location problems to account for the service of a demand by multiple facilities, and has been used to model a variety of location problems in addressing issues such as system vulnerability and reliability. Specifically, it involves the location of a fixed number of facilities when the assumption is that each demand point is served a certain fraction of the time by its closest facility, a certain fraction of the time by its second closest facility, and so on. The assignment vector represents the fraction of the time a facility of a given closeness order serves a specific demand point. Weaver and Church showed that when the fractions of assignment to closer facilities are greater than more distant facilities, an optimal all‐node solution always exists. However, the general form of the VAPMP does not have this property. Hooker and Garfinkel provided a counterexample of this property for the nonmonotonic VAPMP. However, they do not conjecture as to what a finite set may be in general. The question of whether there exists a finite set of locations that contains an optimal solution has remained open to conjecture. In this article, we prove that a finite optimality set for the VAPMP consisting of “equidistant points” does exist. We also show a stronger result when the underlying network is a tree graph.     

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.     

On the cultural blessings of fixed book prices

The system of fixed book prices whereby publishers set the price customers pay at the bookstore is very common in Europe and, according to the European Parliament, it is a means of unique cultural importance. For this reason, it is considered to more than outweigh any negative effects on the economic efficiency of such regulations. The main conclusion of this article, however, is that it is quite hard to find convincing evidence, either theoretical or empirical, that fixed book pricing is better, even as a cultural means, than free book pricing.     

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.     

A SIMPLIFICATION AND GENERALIZATION OF THE EXCLUSION THEOREM: A TECHNICAL NOTE

Several researchers have proven that for the integrated production-location problem on the Weberian triangle, intermediate points on the edge of the triangle can never be optimal locations. Authors of previous proofs of this result have used cumbersome trigonometric arguments. We present a much simpler algebraic proof of the result, and present it in terms of the more general n -input model, where the feasible location space is a convex polygon rather than a triangle. In addition, the result generalizes immediately to other cases, such as (1) multifacility production-location problems, (2) stochastic versions of one-facility and multifacility production-location problems, and (3) comparable pure location problems (e.g., the Weber problem).     

The Spatial Structuring of Central Places

The spatial structuring of “classical” central place systems is the primary concern of this research. Emphasizing the development of such systems from basic spatial relations between centers and hinterland locations (rather than as a result of an underlying geometry of regions), this paper takes an optimization approach to the siting of central places in a single-good system. The objective function is shown to be one that maximizes both market coverage of demand and market overlap. Access to this objective is given through the natural slack covering model.     

International activity in Antarctica 1955–56

Small farmers in the Crofting Counties receive relatively low prices for their store stock partly because most of them are bought by dealers. Dealers rather than farmers purchase the stores because they are marketed in small diverse lots and because many of them are sold at centres far removed from the main areas of demand. Suggested improvements in the marketing system include grouping stock prior to sale and selling them at large accessible markets rather than at small remote ones.     

Lights and Shadows of Urban Water Demand Management: The Case of the Metropolitan Region of Barcelona

The economic, social, and environmental limits of supplying water to metropolitan areas through conventional means (reservoirs, water transfers, etc.) have resulted in growing consideration of demand management actions as well as in the use of non-conventional sources of supply. In terms of demand management, economic instruments (pricing and taxes), domestic water-saving technologies, and educational campaigns to encourage water saving during periods of drought have received special attention. While demand management policies have an effect on conserving water and therefore should be welcome, they present problems and uncertainties as well. Using the example of the metropolitan region of Barcelona, in this article I argue that water demand management policies may be insufficient for reaching their ultimate goal of controlled water consumption when confronted with structural changes in urban development such as the expansion of low-density growth, the multiplication of the number of households, or gains in income, all of which lead to a potentially greater demand for water. This calls for more integration of water policies with land use and urban development policies.     

辽宁省城市基本公共服务质量差异的时空分析

基于基本公共服务的内涵,从教育服务、文化服务、卫生服务、基础设施服务、社会保障服务、生态环境服务和信息服务7个方面构建了基本公共服务质量评价指标体系,运用熵值法对2003-2011年辽宁省城市基本公共服务质量进行综合测度,并以此为变量,利用差异系数和基尼系数对辽宁省各市基本公共服务质量差异的演变过程与空间格局进行定量分析。结果发现:辽宁省各市基本公共服务质量整体为上升的趋势,表现出较为明显的规模特征,沈阳市和大连市两极突出;2003-2011辽宁省城市基本公共服务质量区域差异总体扩大的基础上,呈现先扩大后缩小的演变趋势,且以文化服务、卫生服务和基础设施服务的差异为主;空间上,公共服务质量空间提升极化作用不断增强,表现为不断向"沈阳-大连、盘锦-本溪"的"十字"轴线紧靠。     

Spatial Pricing Policies Reconsidered: Monopoly Performance and Location

This paper reexamines the welfare implications of three pricing regimes (mill, uniform, and discriminatory) for a monopoly. Assuming linear demand and constant marginal costs, I show that with the introduction of endogenous location choice, uniform delivered pricing may provide the highest social welfare when demands in different markets are sufficiently heterogeneous; whereas discriminatory pricing always dominates uniform pricing when demands in different markets are similar.     

The Expected Maximum Distance Objective in Facility Location

Abstract In this paper we introduce a new objective function for the minimax location problem. Every demand point generates demand for service with a given probability (during a given period of time) and the objective is to minimize the expected maximum distance. The planar problem is proven to be convex and thus standard solution techniques such as using the Solver in Excel can be applied for its solution. Properties for the problem on the network are proven and an efficient algorithm proposed for its solution.