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Spatial competition under uniform delivered pricing
Abstract
A Hotelling-type model of spatial competition is considered, in which two firms compete in uniform delivered prices. First, it is shown that there exists no uniform delivered price–location equilibrium when the product sold by the firms is perfectly homogeneous andwhen consumers buy from the firm quoting the lower delivered price. Second, when the product is heterogeneous and when preferences are identically, independently Weibull-distributed with standard deviation μ, we prove that there exists a single uniform delivered price–location equilibrium iff μ≧1/8 times the transportation rate times the size of the market. In equilibrium, firms are located at the center of the market and charge the same uniform delivered price, which equals their average transportation cost, plus a mark-up of 2μ. Finally, we discuss how our result extends to the case of n firms and proceed to a comparison of equilibria under uniform mill and delivered pricing.
... When the reservation price is below a certain threshold, the upper bound denoted by p h m is obtained by solving for the price that would be charged if there was only a single …rm acting like a monopolist in the market. 13 At this price some consumers in the market will not wish to purchase from …rm B. When the reservation price is high, …rm B sells to all consumers to maximize pro…ts. At that point the losses of …rm B from forgoing any market share outweigh the gains from increased price. ...
... Hence we conjecture that a mixed strategy equilibrium with a support described above should exist. 13 The precise value of the threshold resrevation price is not relevant to the argument here. The threshold value for V is found by taking the derivative of …rm B's pro…t function at the price when the furthest consumer refuses to purchase from …rm B. Precise computations are shown in the next result. ...
... In the long run all the possible advancements are going to be made. 13 In other words, any agent will move as far as it can, until it is stopped by an even higher type agent occupying its best desired location (and no empty locations around), and that agent who stopped it is itself stopped by another, even higher type agent, and so on, up to the location on the center or closest to the center which is occupied by the highest type agent. So in the late stages of the simulation the agent will not be able to purchase its best desirable location since in the long run that location will inevitably be occupied by an even higher type agent. ...
Chapter 2 deals with a linear city model ̉la Hotelling where the two firms share linear transport costs with their customers. Mill pricing and uniform delivery pricing are special limiting cases. We characterize the conditions for the existence of a pure strategy equilibrium in the two-stage location-price game. These enable us to identify the causes for non-existence in the two limiting cases. Chapter 3 provides simulations as well as theoretical analysis of potential spatial separation of heterogeneous agents operating on a two-dimensional grid space that represents a city. Heterogeneity refers to a characteristic which is also a determinant of individual valuation of land. We study spatial separation with respect to the distinguishing characteristic and investigate the details of emerging spatial patterns. Simulations suggest that the process of interaction with little trade friction goes through stages which resemble its end-state with high trade friction. Chapter 4 simulations, in addition to some theory, are used to investigate certain aspects of a city formation process. The model assumes two types of economic agents, workers and employers, operating on a two-dimensional grid. The agents have simple preferences, positive for the opposite type and negative for the own type in the own location. In addition, they have positive or negative preference for agglomeration in the own location. The model helps build intuition about a potentially important factor for agglomeration formation, namely, the disparity between entrepreneurial and technical skills in localities. We also determine the minimum level of positive preference for agglomeration that leads to agglomeration formation. System requirements: PC, World Wide Web browser and PDF reader. Available electronically via Internet. Title from electronic submission form. Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 2000. Vita. Abstract. Includes bibliographical references.
... Some author have assumed that the products sold by the different firms are heterogeneous, although different approaches to product heterogeneity have been taken in the literature. (see e.g. de Palma et al., 1987, Anderson et al., 1992band De Fraja and Norman, 1993 1 . Others have 1 Some authors assume that consumers' demand is given by a logit function, with consumers buying some fraction of the goods from either firms (see e.g. ...
... Others have 1 Some authors assume that consumers' demand is given by a logit function, with consumers buying some fraction of the goods from either firms (see e.g. De Palma et al., 1987, andAnderson et al., 1992b). Other assume that consumers view the goods supplied by the studied the price equilibrium in mixed strategies (Kats and Thisse, 1993). ...
This paper analyses a spatial duopoly model where firms produce homogeneous goods and set a uniform delivered price. In contrast with the existing literature, the paper shows that an equilibrium always exists. The crucial assumption in restoring the possibility of equilibrium is that firms cannot ration the supply of the good they produce. The market equilibrium is characterised for two different tie-breaking rules. When consumers buy from the nearest firm in case of equal prices, it is found that any symmetric price pair within a given range is a Nash equilibrium. If demand in each local market is equally split between the two firms charging the same price, there is only one equilibrium price pair, at which both firms make zero profits. Some welfare comparisons between the equilibria under the different tie-breaking rules are also provided.
... Some author have assumed that the products sold by the different firms are heterogeneous, although different approaches to product heterogeneity have been taken in the literature. (see e.g. de Palma et al., 1987, Anderson et al., 1992b and De Fraja and Norman, 1993) 1 . Others have 1 ...
... Some authors assume that consumers' demand is given by a logit function, with consumers buying some fraction of the goods from either firms (see e.g. De Palma et al., 1987, and Anderson et al., 1992b). Other assume that consumers view the goods supplied by the studied the price equilibrium in mixed strategies (Kats and Thisse, 1993). ...
This paper studies a spatial duopoly under uniform delivered pricing when firms do not ration the supply of the good, thus extending to a spatial context the analysis of oligopolistic markets with no rationing. The paper shows the existence of the equilibrium in prices under different tie-breaking rules (TBR) and compare the features of the equilibria found under these rules, thereby allowing to highlight the importance of the choice of the TBR in studying these models. When consumers buy from the nearest firm in case of equal prices (efficient TBR), any symmetric price pair within a given range is a Nash equilibrium, with each firm serving exactly half of the market line. If demand in each local market is equally split between the firms charging the same price (random TBR), the only equilibrium price is the one that gives zero profits to each firm. The degree of competitiveness of the market crucially depends on the TBR. Under the efficient TBR, all (but one) price equilibria deliver positive profits to both firms. Under the random TBR, the market outcome is very competitive in that firms make zero profits. None of the equilibria found under any tie-breaking rule are allocatively efficient. Copyright Springer-Verlag 2004
... Braid (1988) locates n firms on a line segment, on which the demand occurs at five even spaced the facilities. de Palma et al. (1987b) discuss a duopoly under delivered pricing in their model with linear transportation costs with parameter t. Under sufficient heterogeneity (i.e., µ > t/8), a centrally agglomerated location-price equilibrium exists. ...
This chapter first provides a review of the foundations of competitive location models. It then traces subsequent developments through time under special consideration of customer behavior. After developing a general framework for customers’ decision making, the main results are cast within this framework. The conclusion outlines a number of areas, in which existing models can be refined and made more realistic.
... This can, for instance, be observed in the automobile market, though to a much lesser extent today than ten or twenty years ago. DePalma et al. (1987a) considered a competitive location model on a linear market that uses uniform delivered pricing. Apart from this feature, the usual Hotelling assumptions apply. ...
Whereas the usual location models locate facilities based on the wishes and objectives of a single decision maker, competitive location models consider the location of facilities that are under the jurisdiction of more than one decision maker. The economist Hotelling (1929) was the first to introduce competition into location models. His results stood unchallenged for fifty years, until d’Aspremont et al. (1979) corrected an inconsistency that invalidated Hotelling’s main result. Nonetheless, this has not diminished the originality and importance of the original contribution, and it is also the reason why the present paper reviews Hotelling’s contribution and its impact on location models with multiple decision makers.
... Lee et al. (2002) believe that simulation has the capability of finding a local optimum value within each component throughout the entire supply chain. Lowering unit costs of export transportation is a top priority for today's executives of the forest products industry (Hölsä, 2005), but this supply chain has not been extensively studied with a holistic approach (De Palma et al., 1987 andKoskinen, 2009). ...
... Price P approaches to 2 / tu c + as price-competing increases. This implies that the equilibrium with overlapping markets lie between point C and D in Figure 3. 5 The equilibrium will occur at point C as the firms collude. Therefore, unless the firms collude, the equilibrium 4 By simulating, the numerical solution to equilibrium is that ...
The uniform delivered price is the price contains mill price and transportation cost. Although the firms bear the transportation cost, practically the firms would pass all or part of transportation cost through to consumers. The research finds that, as the demand curve slopes downward or there exists competitors or potential competitors, the U.D.P. firms neither can pass all of transportation cost through to consumers, and nor bear all of it. Furthermore, the Löschian firms are able to pass larger portion of transportation cost through to consumers than the Hotelling-Smithies competition firms do. Therefore, the U.D.P. is essentially Freight Absorption Pricing which is another spatial pricing policy used by the firms.
... Without loss of generality, consider a realization of the mixed strategy where Þrm A charges a low price and Þrm B sets a high price. 9 We obtain p u by computing the monopoly price that takes V into account. Consequently, there are two possible upper bounds on price. ...
We consider a linear city model where both firms and consumers have to incur transport costs. Following a standard Hotelling (1929) type framework we analyze a duopoly where firms facing a continuum of consumers choose locations and prices, with the transportation rate being linear in distance. From a theoretical point of view such a model is interesting since mill pricing and uniform delivery pricing arise as special cases. Given the complex nature of the profit function for the two-stage transport cost sharing game, we invoke simplifying assumptions and solve for two different games. We provide a complete characterization for the equilibrium of the location game between the duopolists by removing the price choice from the strategy space. We then find that if the two firms are constrained to locate at the same spot, the resulting price competition leads to a mixed strategy equilibrium with discriminatory rationing. In equilibrium both firms always have positive expected profits. Finally, we derive a pure strategy equilibrium for the two-stage game. Results are then compared with the mill pricing and uniform delivery pricing models.
... Without loss of generality, consider a realization of the mixed strategy where Þrm A charges a low price and Þrm B sets a high price. 9 We obtain p u by computing the monopoly price that takes V into account. Consequently, there are two possible upper bounds on price. ...
Chapter 2 deals with a linear city model la Hotelling where the two firms share linear transport costs with their customers. Mill pricing and uniform delivery pricing are special limiting cases. We characterize the conditions for the existence of a pure strategy equilibrium in the two-stage location-price game. These enable us to identify the causes for non-existence in the two limiting cases. We solve for the equilibrium of a location game between the duopolists with an exogenously given price. When the two firms are constrained to locate at the same central spot, we show the nonexistence of pure strategy equilibria, conjecture the existence of mixed strategy equilibria, and show that any such possible equilibria will always yield positive expected profits.
This paper uses the basic properties of a general model of spatial pricing and distribution to establish an operational model that is free of many standard restrictive assumptions. In particular, the landscape viewed is not subject to the usual homogeneity assumptions of (1) an even distribution of identical buyers and (2) constant freight rates. Rather, heterogeneous distributions and demands of varying forms are assumed. The operational form that is constructed herein would enable empirical testing and application over a broad range of industries and countries. A few case examples are included in the paper to help characterize the data that empirical studies could discover in a world of heterogeneities among buyers and landscapes.
This paper is the first to model consistent location conjectures under spatial price discrimination. With linear production cost, the well-known association of spatial price discrimination with efficiency vanishes as duopolists with consistent conjectures collocate at the center. With convex production cost, the duopolists do not collocate but continue to locate closer to the center than under Nash conjectures. Yet, with sufficient cost convexity, this movement to the center can actually increase welfare relative to Nash. We extend the results with linear costs to multiple private firms.
This chapter first provides a review of the foundations of competitive location models. It then traces subsequent developments through the decades under special consideration of customer behavior. After developing a general framework for customers’ decision making, the main results are put into this framework. The conclusion outlines a number of areas, in which existing models can be refined and made more realistic.
For decades the principle mathematical modeling approach to the manufacturing facility location problem has consisted of models which assume fixed demand and fixed prices. These models generally seek to minimize the firm’s costs (or maximize its profits) subject to meeting the predetermined demand constraints. More recently, efforts have begun to incorporate explicitly into mathematical models the impact that new facilities’ production will have on market prices; and therefore, upon the firm’s profit maximizing location decision. Explicit recognition of market forces in these models requires that one formulate the firm’s demand in a price elastic manner. There are a number of techniques for developing locational models which recognize the impact of price elasticity on a firm’s production decisions. One approach to developing such formulations consists of integrating or linking an economic equilibrium model with a fixed demand facility location model to create an equilibrium facility location problem or model. An equilibrium facility location model represents a locational decision-making technique which, in determining optimal location choices, takes into account the interactions between a location decision and market forces.
We consider a standard linear city model with two firms, where firms and consumers both incur transport costs. This is done by assuming that the total transport cost is shared by the buyers and sellers according to an exogenously given rule. In the model, firms choose locations and prices, with the transportation cost being linear in distance. We first derive the profit function for the two-stage transport cost sharing game and find that it has a complex form. We then invoke simplifying assumptions and solve for two different games. We provide a complete characterization for the equilibrium of the location game between the two firms by assuming fixed prices. We then examine the price game when the two firms are constrained to locate at the same spot. The equilibria of these two games provide insights about the complex two-stage game.
Given the popular misconceptions about minimum differentiation the recent and dramatic revival of interest in the concept among economists, and the fact that 60 years have elapsed since the publication of the original paper, the author believes it is time to examine this regularly referenced but rarely read contribution to geographical thought. The paper introduces the principle of minimum differentiation, explores the extent to which it has stood the test of time, and attempts to assess both Hotelling's contribution to location theory and the likely direction of future research activity. -after Author
Uniform spatial pricing is a pricing policy by which a firm delivers its product to any customer at a fixed price, independent of the customer’s location. For example, it is the method often, but not always used by mail-order and internet firms. Less well-recognized is that uniform pricing is the standard pricing method for processed food and consumer goods manufacturers for sales to supermarkets and wholesalers. This paper contributes to the literature by extending the seminal work of Smithies (1941) that explained the profit maximizing choice between uniform and mill pricing by the convexity or concavity of the consumers demand curve. To date, this result stands as the primary economic explanation of choice between these pricing policies, and I extend it in two ways. The first generalizes results for the case where customers’ demand functions are not identical. I show that profit under uniform pricing exceeds that of mill pricing when demand price elasticity and transportation cost are positively correlated. The second result applies to firms with many shipping facilities. I show that Smithies’ results hold only if the firm sets mill prices from all facilities. I present necessary and sufficient conditions for a firm to maximize mill pricing profit by pricing from all shipping facilities for the linear demand case, and sufficient conditions for the non-linear case. When mill pricing from a subset, Smithies’ results are invalid and result in increased preference for mill pricing over uniform.
Market area models determine the optimal size of market for a facility. These models are grounded in classical location theory, and express the fundamental tradeoff between economies-of-scale from larger facilities and the higher costs of transport to more distant markets. The simpler market area models have been discovered and rediscovered, and applied and reapplied, in a number of different settings. We review the development and use of market area models, and formulate a General Optimal Market Area model that accommodates both economies-of-scale in facilities costs and economies-of-distance in transport costs as well as different market shapes and distance norms. Simple expressions are derived for both optimal market size and optimal average cost, and also the sensitivity of average cost to a non-optimal choice of size. The market area model is used to explore the implications of some recently proposed distance measures and to approximate a large discrete location model, and an extension to price-sensitive demands is provided.
Mail-order and internet sellers must decide how customers pay shipping charges. Typically, these sellers choose between two
pricing policies: either “uniform pricing,” where the firm delivers to any customer at a fixed delivery charge (that may be
volume dependent), or “mill pricing,” where the firm bills the customer a distance-related shipping charge. This paper studies
price competition between a mail-order (or internet) seller and local retailers, and the mail-order firm’s choice of pricing
policy. The price policy choice is studied when retailers do not change price in reaction to the mail-order firm’s policy
choice, and when they do. In the second case, a two-stage non-cooperative game is used and it is found that for low customer
willingness to pay, mill pricing is favored but as willingness to pay rises, uniform pricing becomes more attractive. These
results are generalized showing that larger markets, higher transportation rates, higher unit production cost, and greater
competition between retailers all increase profit under mill pricing relative to uniform pricing (and vice versa). On the
other hand, cost asymmetries that favor the mail-order firm will tend to induce uniform rather than mill pricing. Some empirical
data on retail and mail-order sales that confirm these results are presented.
KeywordsSpatial competition–Internet retailing–Mail-order–Pricing policies
This paper reexamines the welfare implications of three pricing regimes (mill, uniform and discriminatory) for a monopoly in a stochastic environment. It con-siders a risk-averse monopolist faces two markets with stochastic and linear demands. The monopolist is assumed to commit to an irreversible price in each market before the uncertainty is resolved. Several unconventional results are shown to be triggered by the presence of demand uncertainty. The reason for the reversal of orthodox intuition is the asymmetry in the risk chacteristics of the markets and the willingness of the monopolist to trade increased level of expected pro ts for reduced risk.
In spatial markets firms typically use either FOB (mill) or uniform delivered (UD) pricing. What competitive factors motivate this choice and what are the welfare implications of the choice? We study these questions in a duopsony market, where farmers with unit elastic supply curves sell to processing firms. In results that differ considerably from prior work, we show that the equilibrium price policy depends upon the extent of competition in the market, with FOB pricing emerging under very competitive structures and UD pricing emerging under less competition. Mixed FOB-UD pricing may also emerge in equilibrium. In most cases welfare is higher under UD than FOB pricing. Copyright 2001 by Blackwell Publishing Ltd
The strategic incentives, with respect to the choice of price policy in spatial competition, are analyzed in a duopoly model. Price discrimination emerges as the unique equilibriu m outcome in games with either simultaneous choice of policy and pric e or sequential choice where firms may commit first to uniform mill p ricing before the actual market stage. Nevertheless, profits may be h igher with uniform pricing. The authors' models are applied to analyz e some common business practices that arise in geographical pricing, like the basing point system, and in the pricing of varieties or opti ons from a base product in a product-differentiation context. Copyright 1988 by American Economic Association.
The so-called Principle of Minimum Differentiation, stated by Hotelling, has been challenged by many authors. This paper restores the Principle by showing that n firms locate at the center of the market and charge prices higher than the marginal cost of production when heterogeneity in consumers’ tastes is ”large enough”.
Under imperfect information but otherwise competitive assumptions, spatial market equilibria are examined for two pricing structures. Under f.o.b. pricing, buyers face a price that reflects exactly the transportation cost between sellers and themselves. Under uniform delivered pricing (u.d.p.), the seller charges the same price to all buyers, inclusive of delivery. Under both, buyers know only of sellers from whom they received ads, sent randomly by sellers. It is found that u.d.p. equilibria may exist when f.o.b. equilibria do not, but not conversely. Also, f.o.b. equilibria are not always welfare superior to u.d.p. ones. These equilibria are not robust: a new firm often succeeds in penetrating a market using a different pricing structure.
This paper reexamines the theory of spatial price polices under more general conditions to compare mill pricing, uniform delivered pricing, and discriminatory local pricing and to interpret their implications when market regions are given. The analysis assumes that demand functions are linear and identical in all locations, that marginal production cost is constant, and that transportation cost is proportional to distance. The results go beyond previous findings, but do not seriously contradict them.
This paper reexamines the welfare implications of three pricing regimes (mill, uniform and discriminatory) for a monopoly in a stochastic environment. It con-siders a risk-averse monopolist faces two markets with stochastic and linear demands. The monopolist is assumed to commit to an irreversible price in each market before the uncertainty is resolved. Several unconventional results are shown to be triggered by the presence of demand uncertainty. The reason for the reversal of orthodox intuition is the asymmetry in the risk chacteristics of the markets and the willingness of the monopolist to trade increased level of expected pro ts for reduced risk.
This paper considers the ways in which pricing policies will affect location choice in both monopolistic and duopolistic markets. It is shown that the monopolist's optimal location depends crucially on the shapes of demand and delivery cost functions and the pricing policy applied. The median location is unlikely to be chosen. With spatial competition, pricing strategies also affect location choice. There will be greater production concentration under f.o.b. or uniform delivered pricing than under optimal discriminatory pricing. For certain consumer distributions, Hotelling-type concentration is to be expected whereas collusion will lead to some dispersion of production.
A comprehensive review of principles and tools developed for the prediction and analysis of the location of production activities. The authors draw especially from the microeconomics of production decisions and firm behaviour in various markets. In a short-run analysis the authors examine plant utilization, transportation, pricing and output. The medium-term problem is discussed through the Launhardt-Weber model: the price-locational model is treated for spatial monopoly and oligopoly under alternative pricing systems. Finally the long-run problems are analysed and the economic implications examined. -after Editor
This paper reexamines the welfare implications of three pricing regimes (mill, uniform and discriminatory) for a monopoly in a stochastic environment. It con-siders a risk-averse monopolist faces two markets with stochastic and linear demands. The monopolist is assumed to commit to an irreversible price in each market before the uncertainty is resolved. Several unconventional results are shown to be triggered by the presence of demand uncertainty. The reason for the reversal of orthodox intuition is the asymmetry in the risk chacteristics of the markets and the willingness of the monopolist to trade increased level of expected pro ts for reduced risk.
This paper investigates the spatial pricing policies of a sample of firms in the United States, West Germany and Japan. We begin in Section I by providing general results for the three countries. These suggest that f.o.b. pricing is the exception rather than the rule. Furthermore, there appear to be significant differences between the countries in the degree of spatial price discrimination. The remainder of the paper examines whether the inter-country differences in spatial discrimination can be explained by a theory of spatial pricing. Section II uses the theory of spatial pricing proposed in Greenhut and Greenhut (1975) to derive an operational model. In Section III the parameters of this model are estimated from the individual country data and the results are discussed. Section IV presents the conclusions. The data used in this study were obtained from a survey of firms in the three countries. In each country target regions were selected with (a) similar urban-rural proportions, as restricted by (b) existing acquaintanceships with professors in or near these urban-rural centres. Survey constraint (b) was imposed after a mailed questionnaire "pilot study" in the United States had indicated a likely need for follow-up mailings, phone calls and even interviews before a sufficient number of responses from a particular place (e.g., a particular state in the United States) could be expected. After selecting our comparable survey areas, firms were picked at random from industrial lists of business establishments in each country, and questionnaires were mailed to them. The questionnaire is reproduced in the Appendix. The firms that returned questionnaires were compared to non-responding firms. No distinction in size of firm, industry type or location was apparent for any country or sub-region studied. Among the respondents, we dropped from the sample all firms that were not subject to a significant freight cost (defined to be a 5 per cent minimum "freight cost to delivered cost ratio" on sales to at least one distant market point). Our findings on pricing strategies are summarized in Table 1. Firms in the United States tend to price discriminatorily. Of 174 sampled firms, less than one-third priced non-discriminatorily (f.o.b.). The spokesmen for the remaining firms (67 per cent) admitted that they did not add full freight cost to their mill price on all of their distant sales. These firms therefore priced discriminatorily. The tendency to price discriminatorily is even greater in West Germany and Japan, with the percentage of discriminating firms approximately
The profit equivalence of mill and uniform prices
- Beckman
Spatial competition á la Cournot
- Anderson
The principle of minimum differentiation holds under sufficient heterogeneity
- Norman