expanding demand through price advertisement abstract retail stores frequently advertise prices when consumer search is costly advertising low prices expands the number of consumers who visit and buy we show that this demand enhancement may offset a retailer s loss in margins from the low price making advertisement desirable we further show that a multi product monopolist may choose to advertise low prices only for select products even when advertised and non advertised products are substitutes for duopolist retailers at a common location an equilibrium exists in which for some range of advertising costs one store advertises and the other free rides on its competitor

equilibrium in hotelling s model of spatial competition we study hotelling s two stage model of spatial competition in which two firms first simultaneously choose locations in the unit interval then simultaneously choose prices under hotelling s assumptions uniform distribution of consumers travel cost proportional to distance inelastic demand of one unit by each consumer the price setting subgames possess equilibria in pure strategies for only a limited set of location pairs because of this problem pointed out independently by vickrey 1964 and d aspremont et al 1979 hotelling s claim that there is an equilibrium of the two stage game in which the firms locate close to each other is incorrect a result of dasgupta and maskin 1986 guarantees that each price setting subgame has an equilibrium in mixed strategies we first study these mixed strategy equilibria we are unable to provide a complete characterization of them although we show that for a subset of location pairs all equilibria are of a certain type we reduce the problem of finding an equilibrium of this type to that of solving three or fewer highly nonlinear equations at each of a large number of location pairs we have computed approximate solutions to the system of equations next we use our analytical results and computations to study the equilibrium location choices of the firms there is a unique up to symmetry subgame perfect equilibrium in which the location choices of the firms are pure in it the firms locate 0 27 from the ends of the market at this equilibrium the support of the subgame equilibrium price strategy is the union of two short intervals most of the probability weight is in the upper interval so that this strategy is reminiscent of occasional sales by the firms we also find a subgame perfect equilibrium in which each firm uses a mixed strategy in locations in fact in the class of strategy pairs in which the firms use the same mixed strategy over locations and this strategy is symmetric about 0 5 there is a single equilibrium in this equilibrium most of the probability weight of the common strategy is between 0 2 and 0 4 and between 0 6 and 0 8 there is a wide range of pure nash as opposed to subgame perfect equilibrium location pairs the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close

large market asymptotics for differentiated product demand estimators with economic models of supply io economists often estimate demand for differentiated products using data sets with a small number of large markets by modeling demand as depending on a small number of product characteristics one might hope to obtain increasingly precise estimates of demand parameters as the number of products in a single market grows large in this paper i address the question of consistency and asymptotic distributions of iv estimates of demand in a small number of markets as the number of products increases in some commonly used demand models under conditions on economic primitives i show that under the common assumption of a bertrand nash equilibrium in prices product characteristics lose their identifying power as price instruments in the limit in many of these models giving inconsistent estimates in these cases i find that consistent estimates can still be obtained for many of the cases i consider but care must be taken in modeling demand and choosing instruments for cases where consistent estimates can be obtained i provide sufficient conditions for consistency and asymptotic normality of estimates of parameters and counterfactual outcomes a monte carlo study confirms that the asymptotic results provide an accurate description

technical note existence and uniqueness of price equilibria in defender this note provides a formal proof that for the defender model with uniformly distributed tastes the nash price equilibria exist and for a given set of positions that they are unique we also show that the profit function is well behaved continuous and quasi concave and that the maximum occurs on the concave portion of the curve

social networks and new product choice to successfully market new products in a social network it is essential to identify influential individuals whose product recommendations influence the consumption choices of their peers in this study we use spatial econometric methods to determine how individuals revise their preferences for product attributes when exposed to product recommendations from peers and how different individuals who vary in their degree of network connectedness exert influence on the product choices of others we find evidence that consumers look to others for guidance from peers in their preference for subjective taste specific parameters but tend not to respond to peer price choices our spatial methods allow us to empirically determine the influence exerted by individual members on the consumption choices of other members of the social network we find that connected members of the social network are not always the most influential in revising the consumption choices of others our estimates reveal that network proximity explains only 8 8 of influence

efficiency and surplus bounds in cournot competition we derive bounds on the ratios of deadweight loss and consumer surplus to producer surplus under cournot competition to do so we introduce a parameterization of the degree of curvature of market demand using the parallel concepts of concavity and convexity the more concave is demand the larger the share of producer surplus in overall surplus the smaller is consumer surplus relative to producer surplus and the lower the ratio of deadweight loss to producer surplus deadweight loss over total potential surplus is at rst increasing with demand concavity then eventually

the principle of minimum differentiation holds under sufficient heterogeneity 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

a definition of more systematic risk with some welfare implications producers are subject to similar production risks and so their outputs are likely correlated using the entire data set rather than summary statistics we study an ordinal definition of systematic risk for risk neutral producers in perfect competition we trace the effects of an increase in systematic risk through to impacts on welfare measures and production decisions expected welfare falls under more systematic risk but either of expected producer surplus or expected consumer surplus may rise our definition of systematic risk also has relevance for the incentive to incur r d expenditures the benefits of diversity and the gains from risksharing

market segmentation strategies of multiproduct firms we analyze a multiproduct duopoly and ask whether firms should offer general purpose products or tailor their offerings to fit specific consumer needs offering a targeted product has two effects utility increases for some consumers due to increased fit whereas utility decreases for others due to increased misfit previous work has not considered these two effects jointly and has therefore not been able to capture the tradeoff inherent in market segmentation we show that in addition to the degree of fit and misfit the intensity of competition and the fixed cost of offering an additional product determine firms market segmentation strategies extending product lines to target more narrowly defined consumer segments has been a favorite strategy of brand managers for years popular buzzwords like one on one marketing and niche marketing underline its importance in practice in this context we ask to what extent market segmentation is justified from a profitability point of view consider a competitive environment in which each firm can either offer a general purpose product or segment the market by offering products that are tailored to consumers needs while a consumer ceteris paribus prefers a product that is targeted at her own segment she would rather buy a general purpose product than a product that is targeted at another segment segmenting the market therefore has two effects first if a consumer s preferred product is offered she is better off because she is able to buy a product that exactly fits her needs we call this positive aspect of market segmentation fit second if the consumer s preferred product is not offered she is worse off because she ends up with a product that does not satisfy her needs at all this negative aspect of market segmentation is denoted as misfit

a note on fiscal policy under flexible exchange rates abstract the paper studies the effects of fiscal policy under flexible exchange rates the demand for real money balances in terms of the expenditure basket of goods is a function of income in terms of the same basket it turns out that fiscal expansion is expansionary neutral or contractionary in the money wage model depending on whether the income elasticity of the demand for money is smaller than equal to or greater than one the price of domestic goods rises is unchanged or declines in this model depending on whether the income elasticity is smaller than equal to or greater than one

testing models with multiple equilibria by quantile methods this paper proposes a method for testing complementarities between explanatory and dependent variables in a large class of economic models the proposed test is based on the monotone comparative statics mcs property of equilibria our main result is that mcs produces testable implications on the small and large quantiles of the dependent variable despite the presence of multiple equilibria the key features of our approach are that i we work with a nonparametric structural model of a continuous dependent variable in which the unobservable is allowed to be correlated with the explanatory variable in a reasonably general way ii we do not require the structural function to be known or estimable iii we remain fairly agnostic on how an equilibrium is selected we illustrate the usefulness of our result for policy evaluation within berry levinsohn and pakes s 1999 model

additional information for comments on alternative models of demand for automobiles by charlotte wojcik abstract in a recent paper in this journal econ lett 68 2000 113 wojcik argues that the nested logit is likely to be superior to demand specifications we and others have used in recent empirical work we review the relevant models and their uses consider her application and find that her conclusions are incorrect

on the analysis of asymmetric first price auctions we provide a new set of tools for studying asymmetric rst price auctions connecting their equilibria to the concavity of the underlying type distributions and showing how one can use surplus expressions related to symmetric auctions to bound equilibrium behavior in asymmetric auctions we apply these tools to studying procurement auctions in which as is common in practice one seller is given an advantage re ecting for example better reliability or quality we show conditions under which for any given rst price handicap auction there is a second price auction with bonuses that outperforms it with most of our results involving ex post dominance

two stage perfect equilibrium in hotelling s model hotelling i 929 suggests that his spatial competition model can be used to describe a wide range of differentiation problems he points to the selection of product variety within an industry as a potential application most of the subsequent work in his tradition has taken the equivalence of the two problems for granted in this note we look more closely at this equivalence we distinguish between two types of differentiated products according to the variety of preferences assumed with respect to those products building on this distinction we recognize that the demand faced by a firm locating on hotelling s line is analogous to the demand faced by a firm selecting a horizontally differentiated product it should be emphasized thus that the equivalence between the geographical and the product selection problem is by no means general and relies on specific assumptions about consumers preferences next we formulate a small model close to hotelling s one in which firms select a horizontally differentiated product within this model it will be shown that a pure strategy price equilibrium exists for every pair of products this statement is to be contrasted with the results of d aspremont et al i979 who have shown that in the original hotelling s setting an equilibrium fails to exist when firms are too close together 1 in addition we will examine the product selection problem faced by firms in a two stage game in the first stage each firm selects a product in the second stage the firm defines a price for its product we will seek the existence of a perfect equilibrium in this game a perfect equilibrium in this context can be viewed as a nash equilibrium in a game in which firms select a product aware of the non cooperative price equilibrium that will occur for each of their choices it will be shown that contrary to hotelling s principle the two firms will maximise their differentiation i e firms will locate at opposite ends of the market

a location model with preference for variety we propose a new location model where consumers are allowed to make multiple purchases i e one unit from each firm this model may fit many markets e g newspapers credit cards better than existing models a common feature of these markets is that some consumers are loyal to one brand while others consume more than one product our model yields predictions consistent with this observation if firms are allowed to choose their locations on the interval then spatial differentiation may not be maximal and in some cases it may even be minimal thus under certain conditions we restore hotelling s principle of minimum differentiation

asymmetric equilibria in spatial competition abstract the main purpose of this paper is to study the impact of consumer concentration around the market center on the equilibrium locations of location price games in the case of symmetric triangular density it is shown that no symmetric equilibrium exists however we demonstrate the existence of asymmetric equilibria in pure strategies these equilibria are also characterized our secondary purpose is to study the sequential entry of two firms when the location space is not restricted to the market space this leads us to uncover a substantial first mover advantage which has been neglected in the literature

equilibrium with product differentiation tive consumer formulations is used to examine the properties of single and multiple price equilibria conditions under which decreases in the intensity of consumer preferences reduce price are given it is shown that with certain types of demand curves entry can eliminate price cost markups even given product differentiation if competition is localized it is demonstrated that entry does not affect the markup finally the effect of spurious product differentiation on price is examined

note competitive price and positioning strategies brand positioning and brand pricing are important strategic decisions for marketing managers such decisions are interrelated and depend upon competitive brand positions and prices however any unilateral decisions may encourage repositioning and price adjustment by competitors thus leading to either new market equilibria or a price positioning war this paper examines such price and positioning decisions in a competitive environment by extending the defender consumer model to more complex equilibria we assume that the brands are already in the market and that positions are sticky in the sense that brands cannot leapfrog one another among the insights for such incumbent brands are if prices are symmetric and held constant firms seek to reposition toward the center of the market but price advantages by central firms can mediate that central tendency such that an equilibrium exists with positive profits if brand positions are held constant the nash equilibria for prices exist and are unique and category profits the sum of brand profits are maximized for maximum brand differentiation for two and three brand markets the subgame perfect nash equilibrium where positioning decisions are made with foresight on the price equilibria causes firms to unilaterally seek maximum brand differentiation but for four or more brands greater foresight and or cooperation appears necessary to reach the point of maximum brand differentiation these results apply where the defender consumer model is an exact description of consumer response and where the competitive reaction assumptions hold in any empirical situation such forces might be softened resulting in differentiated but not maximally differentiated brands

the effects of banning advertising in junk food markets we develop a structural model to analyze the eects of banning advertising on market equilibria and welfare in junk food markets we consider the impact on demand and prices and show how to quantify welfare eects when advertising might lead consumers to take decisions that are inconsistent with their underlying preferences we use transaction level data on the potato chips market and nd that banning advertising leads to a direct reduction in demand but also toughens price competition leading to lower prices and increased demand welfare increases as consumers benet from no longer making distorted

a synthesis of the macroeconomic approaches to exchange rate determination abstract the paper develops a general model with the goods money domestic and foreign bond and labor markets the special assumptions needed to generate the predictions of the different approaches from the model are found it turns out that the assumption of perfect capital mobility essentially generates the monetarist predictions and perfect monetary sterilization by the central bank at a fixed interest rate the predictions of the elasticity absorption approach the approaches turn out to be independent rather than conflicting parts of the general model each approach abstracting from what the other is analyzing this is technically done by dichotomizing the general model the monetarists making the money market equation and the keynesians the goods market and balance payments equations the independent ones while the keynesian monetarist and short term portfolio balance approaches differ in their policy regime assumptions the long run portfolio balance approach differs in its equilibrium condition by constraining the trade balance to equilibrium

learning by doing organizational forgetting and industry dynamics learning by doing and organizational forgetting have been shown to be important in a variety of industrial settings this paper provides a general model of dynamic competition that accounts for these economic fundamentals and shows how they shape industry structure and dynamics previously obtained results regarding the dominance properties of flrms pricing behavior no longer hold in this more general setting we show that forgetting does not simply negate learning rather learning and forgetting are distinct economic forces in particular a model with learning and forgetting can give rise to aggressive pricing behavior market dominance and multiple equilibria whereas a model with learning alone cannot

cheap talk games may have unique informative equilibrium outcomes abstract we demonstrate that cheap talk games can have unique informative equilibrium outcomes by providing an example of an infinite action bayesian game which absent cheap talk does not possess an equilibrium

adaptive learning models of consumer behavior abstract in a model of dynamic duopoly optimal price policies are characterized assuming consumers learn adaptively about the relative quality of the two products a contrast is made between belief based and reinforcement learning under reinforcement learning consumers can become locked into the habit of purchasing inferior goods such lock in permits the existence of multiple history dependent asymmetric steady states in which one firm dominates in contrast belief based learning rules must lead asymptotically to correct beliefs about the relative quality of the two brands and so in this case there is a unique steady state

differentiating the consumer benefits from labeling of gm food products although recurrent evidence is found that consumers have different willingness to pay for gm and non gm products there is disagreement in the scientific community about the size of consumer benefits from gm labeling in this article we use a theoretical model based on a standard constant elasticity of substitution ces to explain the importance of the quality effect it is shown that failing to consider the quality effect may yield an overestimation of benefits from gm labeling voluntary or mandatory

personalized pricing and advertising an asymmetric equilibrium analysis we study personalized price competition with costly advertising among n quality cost differentiated firms strategies involve mixing over both prices and whether to advertise in equilibrium only the top two firms advertise earning bertrand like profits welfare losses initially rise then fall with the ad cost with losses due to excessive advertising and sales by the wrong firm when firms are symmetric the symmetric equilibrium yields perverse comparative statics and is unstable our key results apply when demand is elastic when ad costs are heterogeneous and with noise in consumer tastes

exclusive dealing as a barrier to entry evidence from automobiles exclusive dealing contracts between manufacturers and retailers force new entrants to set up their own costly dealer networks to enter the market we ask whether such contracts may act as an entry barrier and provide an empirical analysis of the european car market we first estimate a demand model with product and spatial differentiation and quantify consumers valuations for dealer proximity and dealer exclusivity we then perform policy counterfactuals to assess the profit incentives and possible entry deterring effects of exclusive dealing we find that there are no unilateral incentives to maintain exclusive dealing but there is a collective incentive for the industry as a whole furthermore a ban on exclusive dealing would raise the smaller entrants market share but more importantly consumers would gain not so much because of increased price competition but rather because of the increased spatial availability which compensates for the demand inefficiency from a loss of dealer exclusivity

communication in bargaining over decision rights abstract this paper develops a model of bargaining over decision rights between an uninformed principal and an informed but self interested agent we introduce two different bargaining mechanisms tacit and explicit bargaining in tacit bargaining an uninformed principal makes a take it or leave it price offer to the agent who then decides whether to accept or reject the offer in the equilibrium of the game the principal inefficiently screens out some agent types so that the agent s private information cannot be fully utilized when the decision is made in explicit bargaining in which parties can communicate explicitly via cheap talk before tacit bargaining however an equilibrium with no such inefficient screening exists even when the conflict of interest is arbitrarily large we also follow a mechanism design approach showing that under certain conditions explicit bargaining is an optimal bargaining mechanism that maximizes the joint surplus of the parties

consumer heterogeneity and strategic quality decisions though recent studies show that quality differentiation is an equilibrium outcome products of similar qualities frequently are observed in the marketplace this inconsistency may be explained by incorporating consumer heterogeneity along unobservable attributes into a model of competition in this paper consumers not only take into account the quality and price of a product but also their heterogeneous tastes along other attributes which are unobservable to firms we investigate the effect of heterogeneity along the unobservable attributes on both quality and price equilibrium in a two stage game framework we show that when consumers are sufficiently heterogeneous along the unobservable attributes the firms offer products of identical qualities in equilibrium under low levels of heterogeneity along the unobservable attributes however our results are consistent with past research which argues for quality differentiation

near optimality of second price mechanisms in a class of asymmetric auctions consider a setting with n sellers having i i d costs with log concave density f from cumulative f and a buyer who puts a premiumi on procuring from seller i we show how for any given 1 n a sim ple second price bonus auction can be chosen which comes surprisingly close to giving the auctioneer the same surplus as an optimal mecha nism the bonuses depend only on the magnitude and monotonicity of the slope of virtual costs given f we show that these in turn depend only on fairly coarse information about f we explore how this result generalizes to asymmetrically distributed costs abstract

spatial price discrimination with heterogeneous products product heterogeneity is introduced into the context of spatial price discrimination many of the strong properties of the standard homogeneous goods case which are attained as a limit case here are shown to be no longer valid in particular the social optimum is no longer sustainable as a market equilibrium unless products are either identical or else very different

fiscal policy and the real exchange rate abstract this paper reconsiders some conventional notions about fiscal policy under flexible exchange rates using an extended version of the dornbusch overshooting model the extension allows for a long run link between output and the real exchange rate unanticipated permanent fiscal policy affects both current and long run output while the long run effect is always in the expected direction it is possible that the current effect is perverse both fiscal and monetary policy must cause either nominal exchange rate overshooting or perverse domestic interest rate effects the results suggest that real shocks are a potential source of high exchange rate variability

comparative advertising disclosing horizontal match information improved consumer information about horizontal aspects of products of similar quality leads to better consumer matching but also to higher prices so consumer surplus can go up or down while profits rise with enough quality asymmetry though the higher quality and hence larger firm s price falls with more information so both effects benefit consumers this occurs when comparative advertising is used against a large firm by a small one comparative advertising as it imparts more information therefore helps consumers although it also improves the profitability of the small firm overall welfare goes down because of the large loss to the attacked firm

rationalizability learning and equilibrium in games with strategic complementarities we study a rich class of noncooperative games that includes models of oligopoly competition macroeconomic coordination failures arms races bank runs technology adoption and diffusion r d competition pretrial bargaining coordination in teams and many others for all these games the sets of pure strategy nash equilibria correlated equilibria and rationalizable strategies have identical bounds also for a class of models of dynamic adaptive choice behavior that encompasses both best response dynamics and bayesian learning the players choices lie eventually within the same bounds these bounds are shown to vary monotonically with certain exogenous parameters we study the class of noncooperative supermodular games introduced by topkis 1979 and further analyzed by vives 1985 1989 who also pointed out the importance of these games in industrial economics supermodular games are games in which each player s strategy set is partially ordered the marginal returns to increasing one s strategy rise with increases in the competitors strategies so that the game exhibits strategic complementarity 2 and if a player s strategies are multidimensional marginal returns to any one com ponent of the player s strategy rise with increases in the other components this class turns out to encompass many of the most important economic applications of noncooperative game theory in macroeconomics diamond s 1982 search model and bryant s 1983 1984 rational expectations models can be represented as supermodular games in each of these models more activity by some members of the economy raises the returns to increased levels of activity by others in oligopoly theory some models of bertrand oligopoly with differentiated products qualify as supermodu lar games in these games when a firm s competitors raise their prices the marginal profitability of the firm s own price increase rises a similar structure is present in games of new technology adoption such as those of dybvig and spatt 1983 farrell and saloner 1986 and katz and shapiro 1986 when more users hook into a communication system or more manufacturers adopt an interface standard the marginal return to others of doing the same often rises similarly in some specifications of the bank runs model introduced by diamond and dybvig 1983 when more depositors withdraw their funds from a bank it is more worthwhile for other depositors to do the same in the warrant exercise

aggregation and imperfect competition on the existence of equilibrium we present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products the central result provides general conditions under which there exists a pure strategy price equilibrium for any number of firms producing any set of products this includes products with multi dimen sional attributes in addition to the proof of existence we provide conditions for uniqueness our analysis covers location models the characteristics approach and probabilistic choice together in a unified framework to prove existence we employ aggregation theorems due to prekopa 1971 and borell 1975 our companion paper caplin and nalebuff 1991 introduces these theorems and develops the application to super majority voting rules we present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products the central result is that there exists a pure strategy price equilibrium for any number of firms producing any set of products in addition to the proof of existence we provide conditions for uniqueness our model both unites diverse strands of the earlier literature and opens up uncharted areas for future analysis in particular we expand the traditional one dimensional framework to allow for multi dimen sional product differentiation our approach involves twin restrictions on consumer preferences one on individuals preferences the other on the distribution of preferences across society these are generalizations of the restrictions supporting 64 majority rule presented in caplin and nalebuff 1988 to prove existence we apply a new technique of aggregation this technique is valuable in a variety of other problems in the companion paper we use the aggregation result to generalize our earlier work on 64 majority rule and to characterize the relationship between the distribution of human capital and the distribution of income caplin and nalebuff 1991 there are additional applications in statistics and in search theory we begin with a brief review of the early literature on imperfect competition describing in more detail the existence problem and previous solutions section 3 presents our twin assumptions and shows that they cover many standard cases in section 4 we introduce the aggregation theorem and use it in the analysis of demand functions the proof of existence of equilibrium is in section

product differentiation and oligopoly in international markets the case of the u s automobile industry this paper develops and estimates a model of the u s automobile industry on the demand side a discrete choice model is adopted that is estimated using micro data from the consumer expenditure survey the estimation results are used in conjunction with population weights to derive aggregate demand on the supply side the automobile industry is modelled as an oligopoly with product differentiation equilibrium is characterized by the first order conditions of the profit maximizing firms the estimation results are used in counterfactual simulations to investigate two trade policy issues the effects of the ver and exchange rate pass through

monopolistic competition in the spirit of chamberlin special results the idea of large group monopolistic competition was first introduced by chamberlin in i 933 although a large literature has developed on this topic since that time it can be argued that few of the models which have been formulated really capture monopolistic competition in chamberlin s sense in a companion paper to this one hart i 983 a model was presented which it was claimed did satisfy the desiderata of large group monopolistic competition specifically the model had the property that i there were many firms producing differentiated commodities 2 each firm was negligible in the sense that it could ignore its impact on and hence reactions from other firms 3 free entry led to zero profit of operating firms but 4 each firm faced a downward sloping demand curve and hence equilibrium price exceeded marginal cost the model of hart i983 was quite general and only such issues as the existence and limiting properties of equilibrium were considered the purpose of the present paper is to analyse a special case of this model in greater detail and to consider in this context the old question of whether too few or too many brands are produced under monopolistic competition before embarking on the analysis however let me briefly indicate why i believe that there is a need for a new model of monopolistic competition further discussion of this may be found in hart i983 in the last few years a sizeable literature has developed on imperfect competition and product differentiation see for example dixit and stiglitz i977 lancaster i979 salop i979 and spence i976 in much of this literature see for example spence i976 markets of fixed finite size are considered where the entry of firms is limited by the existence of set up costs under these conditions only a finite number of firms can operate and hence firms will not be negligible in the sense of 2 in addition due to the integer problem operating firms will generally make strictly positive profits i e 3 is violated models of

competition of firms discriminatory pricing and location1 two costlessly mobile firms are to be located in a market region a subset of the plane the firms compete by setting locations and delivered price schedules to study this competitive stiuation an appropriate extensive form game is defined along with an appropri ate noncooperative solution concept existence and general properties of the equilibrium are demonstrated among the results are each firm increases its profit by locating so as to decrease total cost to both firms of serving the market firms will never locate coinciden tally if they have identical production costs and transport cost rates or if these are different and the firms are located in a circular market region having a uniform demand distribution this paper studies competition between two profit maximizing firms in space who are costlessly mobile and may discriminate in price we will allow the firms to set locations and delivered price schedules and we will be concerned with the existence and properties of equilibria in location and price starting with hotelling 9 the spatial competition literature has focused on location on bounded linear markets by two or more firms hotelling assumed identical firms that produced a single good with constant cost of production and considered consumers to be uniformly distributed and to have inelastic demand he also assumed that the consumers pay transport cost and purchase the good from the cheapest source hotelling claimed that a nash equilibrium in locations for the two firm market existed and yielded back to back locations at the center of the market many authors most recently d aspremont gabszewicz and thisse 2 have noted that an equilbrium in prices and location does not exist for hotelling s model however if the firms employ identical exogeneously specified prices hotelling s conclusions hold subsequent work by smithies 14 hartwick and hartwick 7 and eaton 3 claimed to show that a nash equi librium in f o b prices and locations can exist in markets with a uniform distribu tion of consumers each of whom have identical elastic demand functions for the two and three firm problems the work of d aspremont et al casts doubt on these conclusions without the adoption of restrictive conditions our work contrasts with these works and related research which has dealt with linear markets with uniform distributions of customers and with identical firms our work will involve markets that are subsets of the plane having nonuniform distributions of customers our firms will be allowed to be different that is have differences in production and transport costs however the fundamental difference in our approach is that our firms will set discriminatory prices and not price f o b in many ways our work will represent the discriminatory pricing

bertrand equilibrium in a differentiated duopoly this paper studies the stability of price competition in a horizontally differentiated duopoly the firms demand is derived from a distribution of consumer preferences this description of the consumer sector is applicable to a large class of differentiated commodity markets including spatial competition models the author shows that there is a pure price setting equilibrium when consumer tastes are sufficiently dispersed further conditions on the dispersedness of preferences guarantee uniqueness of the equilibrium in addition the author examines the relation between consumer preferences and the competitiveness and efficiency of the equilibrium outcome copyright 1992 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association