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.     

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.     

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.     

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.     

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.     

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.     

HOTELLING'S “MAIN STREET” WITH MORE THAN TWO COMPETITORS*

ABSTRACT. I analyze oligopolistic competition among three or more firms located on Hotelling's (1929) Main Street and show that in contrast with Hotelling's duopoly, the symmetric locational structure supports a noncooperative equilibrium in prices. However, in a two-stage game of location choice in the first stage, and price choice in the second stage, there exists no subgame-perfect equilibrium where the whole market is served. This is because, starting from any locational pattern, firms have incentives to move toward the central firm. This strong version of the Principle of Minimum Differentiation destroys the possibility of a locational equilibrium. The results are a direct consequence of the existence of boundaries in the space of location. The sharp difference between these results and those of the standard circular model (whose product space lacks boundaries) shows that the general use of the circular model as an approximation to the line interval model may be unwarranted.     

Game Theory and Institutional Entrepreneurship: Transfer Pricing and the Search for Coordination International Tax Policy

Coordination in international tax policy is extremely problematic. Economists and political scientists have explained this lack of coordination by arguing that tax competition triggers a prisoner's dilemma. In this article I argue that not all international tax policy can be reduced to the prisoner's dilemma syndrome. Transfer pricing policy, the object of this study, can be modeled as a coordination game. By drawing upon game theory and new institutional analysis, I argue that institutional entrepreneurs who decide to play their favorite option first can facilitate the emergence of international policy coordination. This idea is examined in the context of the creation of the new Organization for Economic Cooperation and Development rules on transfer pricing. The conclusion is that coordination emerges in transfer pricing policy through a process of conflictual institutionalization.     

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.     

DEREGULATING THE DISTRIBUTION OF ELECTRICITY: PRICE AND WELFARE CONSEQUENCES OF SPATIAL OLIGOPOLY WITH UNIFORM DELIVERED PRICES*

ABSTRACT. Theoretical, spatial oligopoly models are developed and calibrated to simulate the price and welfare consequences of deregulating the retail price of electricity (the distribution function), assuming competing sources of generation supply are available. Two types of distribution competition are considered, retaining the currently used uniform delivered pricing structure: competition for customers at neighboring utilities’ borders and franchise competition. Because duplicate facilities are required for borderline competition, short-run price increases ranging between 14 and 37 percent over existing regulated prices are estimated for upstate New York, largely because deregulated prices reflect replacement, not historic, costs of facilities.     

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.     

Location and Pricing Decisions of a MultiStore Monopoly in a Spatial Market

Abstract.  This article presents an analysis of location and pricing decisions of a monopolist about to open several stores in a compact geographical space. The number of stores is made endogenous by the introduction of fixed costs. A novel methodology is developed, by which the firm's location and price decisions are represented as continuous functions defined over the geographical space. This modeling artifact generates a negligible error but simplifies the solution considerably and allows the derivation of several intuitive results. Although the focus is on one‐dimensional markets, it is shown that the method can easily be adapted to two‐dimensional markets.     

基于系统动力学的我国旅游景区门票定价研究

已有景区门票定价研究大都从现实景区数据出发,建立门票价格、景区属性和社会经济指标的多元回归模型。然而这种计量研究,并没有从景区门票定价的多目标性出发,也忽视了影响门票定价各因素之间的相互影响关系。本文构建ISM模型分析影响景区门票定价的主要因素及其相互关系,根据因素相互作用关系建立景区门票定价系统因果关系图和系统流图,并设定系统动力学方程。仿真结果显示,成本票价逐年下降并于2022年降至最低,而最终票价将呈现先降低后升高的趋势。     

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。     

Product Differentiation and Location Choice in a Circular City*

Abstract. The paper analyzes spatial competition among firms that sell substitute and/or complementary products. The firms first choose locations on the perimeter of a circular city and then compete in quantities (à la Cournot). Both linear and convex (quadratic) transport costs are considered. In general, multiple location equilibria are encountered. Complete agglomeration, partial agglomeration, and complete dispersion are possible. Convex (quadratic) transport cost substantially shrinks the set of equilibria obtained under linear transport cost. In general, the results obtained for a larger number of firms selling complementary products are strikingly different from those obtained under a duopoly.     

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.     

OPENNESS TO TRADE AND INDUSTRY COST DISPERSION: EVIDENCE FROM A PANEL OF ITALIAN FIRMS*

ABSTRACT We use Italian firm‐level data to investigate the impact of trade openness on the distribution of firms across marginal cost levels. In so doing, we implement a procedure that allows us to control not only for the standard transmission bias identified in firm‐level TFP regressions but also for the omitted price bias due to imperfect competition. We find that more open industries are characterized by a smaller dispersion of costs across active firms. Moreover, in those industries the average cost is also smaller.     

Designing Markets: Why Competitive Bidding and Auctions in Government Often Fail To Deliver

Governments continue to embrace the market‐like mechanisms of auctions and bidding. This essay considers how governments (as bid‐takers) and firms and nonprofits (as bidders) strategically interact in the design and implementation of these systems. I assess with regard to the uniqueness of bidding in government four principles on the role of: credible commitments, rational collusion, the setting of reserve prices, and heterogeneity among bidders. I also address recent calls for expanding the use of dynamic pricing in government.