PRICE AND LOCATION CONJECTURES IN MEDIUM- AND LONG-RUN SPATIAL COMPETITION MODELS*

ABSTRACT. This paper examines medium-run and long-run equilibria in unbounded (circular) and bounded (linear) one-dimensional multifirm markets. A price-location adjustment model is outlined that dows simulation of the spatial equilibrium when these firms anticipate reactions from their nearest spatial rivals. Thus, the market equilibrium is derived from the interdependent but atomistic decisions of the competing firms and is not imposed by some outside observer or agency. Ail conjectures are exogenous; the three well-known price conjectures (Greenhut-Ohta, Hotelling-Smithies, and Losch) are highlighted; and the relevant comparative statics are provided.     

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.     

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.     

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.     

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.     

SPATIAL ENTRY DETERRENCE UNDER OLIGOPOLY*

ABSTRACT. This paper examines colluding, oligopolistic firms in a linear market. By assuming that rivals do not compete for consumers at their market boundaries, it is shown that an equilibrium exists without adopting a convex transportation cost function. Two price profiles are derived. The first describes firm prices in the absence of threatened entry. The second details profit-maximizing prices which forestall entrants. Given infinite relocation costs, threatened entry leads to price adjustments by the incumbent firms.     

Optimizing the Spatial Structure of the Agricultural Production Function

Important characteristics of spatial agricultural production functions are derived by introducing a non‐negative curvilinear spatial demand function for production input intensities. Given the usual neoclassical rationale assumptions of spatial demand for capital and labor inputs under competitive environment of farming in developing agricultural economies, the optimal production levels are determined by optimizing spatial demand for production inputs. Decreasing price‐to‐transport costs ratio (that is, decrease in the prices of capital goods or increase in freight rates) and increasing wage‐to‐travel costs ratio (that is, increase in labor wages or decrease in the travel rate) expand the limits of the (spatial) optimal boundary of the demand for agricultural capital goods and labor input respectively. These effects occur on account of the operation of (positive) spatial price gradient and (negative) wage‐gradient in the market region. It may be noted that elasticities of demand for production factors are spatially variant and have significant effects on the alterations in the structure of agricultural production. However, the spatial optimal solution of production has a complicated relationship with them. The price elasticity has negative and wage elasticity has positive spatial gradients in the market region. Farmers located in the periphery of the market region are not much affected by the proportionate changes occurring in the prices of agricultural capital goods but are more sensitive to the proportional changes in labor wages. Because of a decreasing trend in capital input demand and increase in labor input with distance from the market, capital‐product diminishes with a decreasing rate and labor‐product increases with an increasing rate in the spatial structure of agricultural production. As a result, capital‐labor ratio falls toward zero, which raises profit rate per unit of capital investment especially in the outer part of the market region. The equilibria of optimal production with price elasticity as well as of capital intensity with labor employment (that is, capital‐labor ratio as unity) determine spatial limits of the optimal production zone which is shifted outward subject to the provision of cheap transportation, stabilizing market prices and/or increasing wage rate at the market center. It will help in extending outwardly the optimal spatial limits of capital investment and will mobilize capital resources of farmers in the periphery for efficient and competitive capital‐dominated farming.     

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.     

Clustering and Dispersion of Duopolists in a Linear Market

The locations that two sellers will choose in a linear market has long been of interest. It is well accepted that firms will tend to cluster in the center of the market as long as demand for the product is inelastic and the market area is bounded. It has also been stated that clustering is less strong as demand becomes more elastic, but questions of when this dispersion occurs and what affects it remain to be addressed. This paper further explores clustering in spatial duopoly as elastic demand is allowed. Results indicate that the clustering behavior of sellers is related to the price of the product they sell, the cost to the consumer of acquiring the product, and the elasticity of demand. Locations of sellers in a linear market will lie between the median location and the quartiles as these parameters vary.     

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.     

上海大都市区物联网产业集聚与空间演化

新兴技术产业的空间集聚与扩散对大都市区的空间结构有直接的影响,厘清新兴技术产业的空间分布和区位选择规律对新兴产业集群培育和大都市区空间结构调整都具有重要的政策意义。本文分析了上海市物联网企业的空间分布和集聚特征,结果发现初创期物联网企业在郊区集聚,随后向郊区其他区域扩散,并呈现出从单极向多极集聚转变的空间演化进程。通过构建负二项回归探究上海物联网企业的区位选择因素,结果表明制度因素和企业集聚效应对企业区位选择有重要影响。在产业发展初创期,企业区位选择受政府管制和市场机制双重影响,其中制度因素发挥了关键作用;而在随后的兴起期,产业集聚效应对新企业的入驻具有强大的吸引力。     

SPATIAL COMPETITION WITH CONSISTENT CONJECTURES*

ABSTRACT Equilibrium in spatial models invariably depends on firms' conjectures about how competitors will react to their price changes. This paper analyzes spatial price and location equilibrium when firms hold consistent (i.e. correct) conjectures. Most spatial models assume an exogenous conjecture. Consistent conjectures are one method, albeit a controversial one, for endogenizing the conjecture. We show that the consistent conjecture about a competitor's reaction to a price change in the simplest case is 1/3. When demand is elastic the consistent conjecture is a decreasing function of the radius. It is always below 1/3 and can be negative. In the third model, we show that the consistent conjecture declines as the number of dimensions and the number of competitors increases.     

A SPATIAL COMPETITION APPROACH TO CENTRAL PLACE THEORY: SOME BASIC PRINCIPLES*

ABSTRACT. This paper investigates the potential offered by the model of spatial competition for the study of central place theory. We consider n firms selling m substitutable or complementary goods to a continuum of consumers evenly distributed along a linear segment. Consumers have the same income and the same utility function which is quadratic in the goods supplied by the firms and linear in the numeraire. The main results are as follows. (1) In any location equilibrium in which all goods are consumed everywhere, each good supplied by a single firm is sold at the market center. In Christaller's terminology, this means that when the exhaustive principle holds in equilibrium, highest-order goods are made available at the center. (2) When all goods (excluding the numéraire) are complements to each other and each good is sold by a single firm, there always exists an equilibrium in which all the firms locate coincidentally. (3) If the stores selling a given good are under the control of a single owner then, in any equilibrium for which the exhaustive principle holds, the stores are located in a way such that the total transport cost (borne by consumers) is minimized.     

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.     

基于GWR模型的合肥居住地价影响因素研究

以合肥市主城区为例,基于2010-2014年居住用地的出让数据,运用地统计法、GWR模型等方法,对合肥市居住地价的空间异质性及其影响因素进行研究。研究表明：①合肥市居住地价的空间分布呈现出显著的多中心的空间结构,地价的峰值区分别以老城区、政务区天鹅湖及滨湖新区塘西河公园为中心呈现圈层式分布;②不同的地价影响因素表现出不同的空间分布特征,其中容积率对居住地价的贡献度空间差异最大,其次是宗地面积,主干路次之,交通站点对居住地价的贡献度最小;③厘清各影响因素对地价的作用机制,建立动态的数字地价模型,不仅能促进土地资源的集约利用,重塑城市的空间结构,而且能为城市整体价值的发挥提供重要的理论支撑。     

Cournot Retail Chains

In this paper a model of spatial Cournot competition among retail firms is devised and used to assess the effect of a variety of structural factors on retail prices and profits. The model illustrates the spatial chain of interaction that firms must anticipate to reach equilibrium when organized in chains or as independents. It shows the sensitivity of price to the location of stores, the number of stores per location, and transportation cost.     

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.     

Asymmetric Entrant Locaiton with a Discrete Consumer Distribution: Spatial Price Discrimination Versus Mill Pricing

In this paper I examine the profit-maximizing locations of entrants. Suppose that firms practice spatial price discrimination and consumer locations are discrete, such as five equally spaced towns on a roadway. With completely inelastic consumer demand an entrant between two existing firms is often indifferent between the symmetric (central) location and a continuum of asymmetric (noncentral) locations. However, downward-sloping consumer demand often causes the entrant to strictly prefer either of two asymmetric locations to any other location. These results are very different from those found in mill-pricing (free-on-board or f.o.b.-pricing) models.     

Profit-Rate Maximization in Interdependent Markets: A Research Note

In the theory of the firm it is conventional to regard firms as (total)profit-maximizing institutions. In this paper it is shown that the interdependence among firms that is characteristic of monopolistic competition makes it plausible for them also to choose to maximize the rate of profit on capital advanced. For a homogeneous product with inelastic total demand, such as gasoline retailing, firms acting as rational agents, facing fixed costs in a homogeneous spatial market, and choosing to set prices under rate of profit-maximization can achieve higher total profits than firms operating under total profit-maximizing objectives.