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When Consumers and Firms Share Transportation Costs
Abstract
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.
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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 important study shows that an understanding of product differentiation is crucial to understanding how modern market economies function and that differentiated markets can be analyzed using discrete choice models of consumer behavior.
Product differentiation - in quality, packaging, design, color, and style - has an important impact on consumer choice. It also provides a rich source of data that has been largely unexplored because there has been no generally accepted way to model the information available. This important study shows that an understanding of product differentiation is crucial to understanding how modern market economies function and that differentiated markets can be analyzed using discrete choice models of consumer behavior. It provides a valuable synthesis of existing, often highly technical work in both differentiated markets and discrete choice models and extends this work to establish a coherent theoretical underpinning for research in imperfect competition.The discrete choice approach provides an ideal framework for describing the demands for differentiated products and can be used for studying most product differentiation models in the literature. By introducing extra dimensions of product heterogeneity, the framework also provides richer models of firm location. Discrete Choice Theory of Product Differentiation introduces students and researchers to the field, starting at the beginning and moving through to frontier research. The first four chapters detail the consumer-theoretic foundations underlying choice probability systems (including an overview of the main models used in the psychological theory of choice), while the next four chapters apply the probabilistic choice approach to oligopoly models of product differentiation, product selection, and location choice. The final chapter suggests various extensions of the models presented as well topics for further research.
We show how the spatial duopoly proposed by Launhardt in 1885, where firms have access to different transportation technologies, allows one to model in a simple and elegant way the two major types of product differentiation, i.e. horizontal and vertical. We consider the cases where firms are located near the market end points or near the market center. Launhardt's analysis of price determination is then extended by allowing firms to choose strategically their transportation rates. Subgame perfect Nash equilibria involve minimum (maximum) vertical product differentiation when horizontal product differentiation is large (small) enough.
It is well known that Hotelling's model of spatial competition has no location-price equilibrium in pure strategies. The present paper studies that model where the linear space is replaced by a one-dimensional bounded space without a boundary, i.e. a circle. It is shown that the modified model does have a subgame perfect equilibrium in pure strategies and that the ‘equal distance’ location pattern is an equilibrium.
The equilibrium locations of two firms are partially centralized to the socially optimal extent if there is spatial price discrimination, and if each firm has two out of three products, or else one variety of a differentiated product with some consumers indifferent between varieties.
A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.
Space allows firms to implement a large variety of price policies, depending on the way transportation costs are passed on to customers. Somewhat surprisingly, the bulk of the work on spatial price theory has been focused on the study of mill pricing (see Gabszewicz and Thisse, 1986, for a recent survey). It is probable that the main reason for this emphasis lies in the close connection between spatial competition with mill prices and the model of product differentiation à la Hotelling-Lancaster (see, for example, Eaton and Lipsey, 1989, for further details).
We introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that are characterized by persistent excess volatility in returns to capital. We explore a quantitative case for theselearning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time-series data for U.S. stock returns and per-capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can be explained by changes in investor expectations against a background of relatively small changes in fundamental factors.
The authors provide a comparison of three spatial price policies: uniform pricing, mill pricing, and spatial price discrimination. Profits, consumer surplus, and social surplus are compared in a duopoly model. Until recently, oligopoly analysis has been stalled because of nonexistence of equilibrium. Through the addition of product heterogeneity (using a logit specification), existence can be restored and price policies compared. In contrast to monopoly analysis, consumer surplus is highest under uniform pricing and lowest under mill pricing. Profit and social surplus follow the opposite ranking. Government regulation to encourage mill pricing may therefore benefit firms to the detriment of consumers. Copyright 1989 by Blackwell Publishing Ltd.
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.
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The purpose of this note is to show that the so-called Principle of Minimum Differentiation, as based on Hotelling's 1929 paper "Stability in Competition," is invalid.
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
Examines how Hotelling's result is modified by the relaxation of some of his assumptions relative to: 1) number of firms, 2) shape of the demand curve, and 3) type of space. First pure locational models are considered. Then models with price determination are discussed. Shows that, in many cases, the 'Principle of Minimum Differentiation' as based on the Hotelling paper does not hold.- from Author