The Pricing of Delivery Services*

Abstract. Due to spatial separation between points of distribution and consumption, a vital feature of retailing is the provision of delivery services by customers, retailers, or transport intermediaries. Some store retailers, many Internet retailers, and most transport intermediaries use a multizone pricing plan or a generalized N‐zone menu plan. We extend spatial pricing theory to encompass multizone plans. We prove that the optimal number of zones varies with the level of demand relative to the spatial dispersion of customers, and with the cost of implementing a zonal plan. We show that a small number of zones capture almost all the profit attainable with a spatially discriminatory plan.     

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.     

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.     

Spatial Price Discrimination in Two-Dimensional Competitive Markets

Intuition suggests that firms that can apply price discrimination make higher profits than firms that are restricted in their pricing policy. In this paper, we show that, in general, this is not the case. In the framework of a two-dimensional spatial model with elastic demand à la Lösch, we further investigate the interplay of transport costs, competition, and price policy. One of our results is that under realistic specifications of parameters each firm gains a monopolistic area in the center of its market that has the same shape as the entire market, but with a convexly or concavely distorted separating line, depending on the extension of the market.     

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.     

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.     

ACCOUNTING FOR LOCAL SPATIAL HETEROGENEITIES IN HOUSING MARKET STUDIES

We adopt a novel method to deal with omitted spatial heterogeneities in hedonic house price analysis. A Gaussian variant of the conditional autoregressive (CAR) model is used to study the impact of spatial effects. In a general linear modeling framework, we include zone‐specific random effects that are allowed to interact spatially with neighboring zones. The results demonstrate that this estimator accounts for missing spatial information, producing more reliable results on estimated spatially related coefficients. The CAR model is benchmarked against a fixed effects model. Socioeconomic neighborhood characteristics are found to have only modest impact on spatial variation in housing prices.     

THE WELFARE ASPECTS OF SPATIAL PRICING POLICIES RECONSIDERED FOR A MONOPOLY CASE*

ABSTRACT. We reexamine the price structures and their welfare implications in three pricing regimes (mill, uniform and discriminatory) for a monopoly. We show that spatial price discrimination could provide the highest social welfare and, when consumers tastes are heterogeneous enough, also the highest consumer surplus. The superiority of spatial price discrimination is partially due to the larger output produced and partially due to differential treatment for consumers with heterogeneous tastes.     

旅游景区一票制及其效率——基于产品捆绑定价模型的经济学分析

旅游景区一票制的理论基础是产品捆绑定价模型,但因为景区产品区别于其它一般产品,对景区进行捆绑定价时,不仅要考虑游客对景区的保留价格,还要考虑游客对景区时间消费量的预期（即保留时间）。本文通过只包含两个景区的保留价格一保留时间模型,对游客闲暇时间约束下的景区一票制定价及其绩效进行了分析,并推出了以下结论：（1）除了游客保留价格和保留时间,套票有效期的长短、参与一票制的景区数量的多少等也会影响一票制效率;（2）混合票制会增加效益,而纯一票制的效益不如非一票制的效益好。笔者在此基础上提出了一些建议。     

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.     

PRICING POLICY REACTIONS TO AGGLOMERATION IN A MARKET WITH SPATIAL SEARCH*

ABSTRACT. Price dispersion (variation) and agglomeration are common characteristics of spatial markets, in particular, markets with imperfect consumer information and search. However, pricing and location strategies in these markets are not well analyzed since spatial search is difficult to model without restricting the spatial dimension of the problem. This paper analyzes pricing and location strategies in a market with spatid search using a probabilistic modeling strategy that does not restrict search patterns in the plane. Specifically, the analysis considers the pricing strategy of an isolated firm in response to the agglomeration of competing firms. Results indicate that spatial and temporal price dispersion are effective responses to competitors'agglomeration. However, the relative effectiveness of these strategies varies with market conditions. In addition, agglomeration can have some counterintuitive effects. This paper also provides insights into existing theories of spatial search and spatial competition in spatially-restricted (linear and circular) markets.     

Basic Principles of a Zonal Differentiation of Farm Procurement Prices

The zonal differentiation of farm procurement prices must be placed on a more scientific footing to help eliminate present inequities in farm incomes and labor payments throughout the country. This requires a review of price zones to insure that the natural and economic conditions of production in each zone are fairly uniform, with additional price differentiation within zones if required by differences in the natural environment (mountains compared with plains). A proper relationship between prices for different farm products within a given zone must also be observed).     

Re-investing in the Built Environment: A Spatial Network Approach

Before launching ambitious and expensive development programmes to induce new regional technology corridors and clusters, it is critical to appreciate existing spatial economic patterns in a region. Initial economic conditions drive location decisions of firms and a labour force such that any changes must intercede onto an existing landscape built for current economic conditions. This work adopts a simple regional economic model to integrate and review traditional and modern urban location theories in order to illustrate the power of initial conditions to determine a final result. A simple spatial dynamic simulation model captures many of the pertinent effects of real estate pricing patterns to frame both opportunities and constraints to re-shape an urban landscape. Attention to 'ground up' spatially correlated location patterns revealed in price data that suggests close attention to strategic zoning can have profound impacts on the success or failure of economic development. Relatively modest policy interventions that carefully utilize existing preferences for urban amenities and concurrent real property investments involve fewer policy risks with potentially more powerful stimulative economic consequences than promised in more ambitious programmes.     

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.     

基于TOD策略的旅游新区公共交通系统规划方法——以阳宗海风景区为例

公共交通系统是旅游新区建设与发展的重要交通保障,科学的公共交通系统规划能够充分满足游客与内部居民的出行需求,并引导旅游新区空间布局的良性发展。为实现旅游新区交通的可持续发展与区域景点间的和谐互动,分析了旅游新区公共交通系统的发展需求。将TOD理念引入旅游新区公共交通系统规划,从现状调查、需求分析、方案设计、方案评价与方案实施等具体层面,设计了基于TOD策略的旅游新区公共交通系统规划流程。以昆明阳宗海风景名胜区为实例,在区域公共交通现状与公共交通需求分析的基础上,结合区域发展目标详细探讨了公交系统的规划模式,并对公交规划方案进行了评估。结果表明:基于TOD策略的旅游新区公共交通系统规划方法能够支持旅游新区用地布局和旅游业发展,并提高旅游新区公共交通系统出行的便捷性、舒适性和满意度。     

Competitive Location and Pricing on Networks

In this paper we consider a location and pricing model for a retail firm that wants to enter a spatial market tvhere a competitor firm is already operating as a monopoly with several outlets. The entering firm seeks to determine the optimal uniform mill price and its servers' locations that maximize profits given the reaction in price of the competitor firm to its entrance. A tabu search procedure is presented to solve the model together with computational experience and an example.     

Competitive Location and Pricing on Networks

In this paper we consider a location and pricing model for a retail firm that wants to enter a spatial market where a competitor firm is already operating as a monopoly with several outlets. The entering firm seeks to determine the optimal uniform mill price and its servers' locations that maximize profits given the reaction in price of the competitor firm to its entrance. A tabu search procedure is presented to solve the model together with computational experience and an example.     

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.     

THE SPATIAL MONOPSONY: A THEORETICAL ANALYSIS*

ABSTRACT. In this paper some of the most important properties of the behavior of a spatial monopsonist are derived. Many results are mirror images of corresponding results for the spatial monopolist. A few results are, however, genuinely new. A lot of effort is spent in comparing the properties of the profit function under three different pricing policies, f.o.b. (mill)-pricing, uniform delivered pricing, and spatial price discrimination. It is shown, for example, how the profitability and welfare consequences of the different policies are related to the shapes of the supply and demand functions. It is argued that the theory may have important applications in economic analyses of renewable natural resources such as forests, where total transportation costs are nonnegligible.     

MILL PRICING AND SPATIAL PRICE DISCRIMINATION MONOPOLY PERFORMANCE AND LOCATION WITH SPATIAL RETAIL MARKETS*

ABSTRACT. Most of the monopoly spatial price discrimination literature explicitly assumes uniform population density over space. It also implicitly assumes that firms (plants) are spatially isolated from each other with production and retail points that coincide in location. While departures from these assumptions have been explored separately in the literature, it remains to examine performance and location when these assumptions are relaxed simultaneously. What emerges in this paper is a model where density functions approximate a pair of cities isolated from other cities. Each city has its own retail market, while the location of a single production or wholesale point is determined by characteristics of the two markets. Comparisons of mill pricing and spatial price discrimination found in the spatial monopoly literature can be interpreted as special cases of the more general framework provided here.