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Competitive Price Discrimination Author(s): Mark Armstrong and John Vickers Source: The RAND Journal of Economics, Vol. 32, No. 4, (Winter, 2001), pp. 579-605 Published by: Blackwell Publishing on behalf of The RAND Corporation Stable URL: http://www.jstor.org/stable/2696383 Accessed: 11/08/2008 17:16
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RAND Journalof Economics Vol. 32, No. 4, Winter2001 pp. 579-605

Competitive price discrimination
Mark Armstrong* and JohnVickers**

Wemodelfirmsas supplyingutilitydirectlyto consumers.Theequilibrium outcomeof competition in utilityspace dependson the relationship7r(u) betweenprofitand average utilityper consumer Public policy constraintson the "deals"firms may offer affect equilibriumoutcomes via their effect on Tr(u). From this perspective we examine the profit, utility,and welfare implicationsof pricediscriminationpolicies in an oligopolisticframework. Wealso show that an equilibrium outcome of competitivenonlinearpricing when consumershave private informationabout their tastes isforfirms to offer efficienttwo-parttariffs.

1. Introduction
* This articlehas two main aims. First, we propose a frameworkthat we hope will be useful in analyzingsituationswhere firmscompetebyofferingvarious"deals"involvingtariffs,bundles of outputs,and so on. Models of marketswhere firms simultaneouslycompete on a numberof dimensionsare often hardto work with. In many cases, however,this analysis can be simplified by taking a dual approachand modelling firms as competing directly in utility space. Viewed from this perspective,a firm's strategyis just to choose the (scalar)level of utility, or "valueformoney,"offered to customers.A firm'smarketsharenaturallyincreasesthe more utility it offers relative to its rivals. Centralto the analysis of competitionin utility space is the function 7r(u), which gives the maximumprofitper consumera firm can extractwhen it providesutility u to its consumers.This function succinctly capturesnot just the relevantcost and demandinformation; it also reflects any publicpolicy (or other) constraintson the deals firms may offer. The second aim of the article is to illustratethe usefulness of this dual approachby examining the profit, in utility, and welfare implicationsof public policy towardvariouskinds of price discrimination
Nuffield College, Oxford;mark.armstrong@nuffield.oxford.ac.uk. All Souls College,Oxford;john.vickers@economics.oxford.ac.uk. We are gratefulfor comments from Simon Anderson,FrankFisher,Anke Kessler, PrestonMcAfee, John Moore, Babu Nahata, Barry Nalebuff, and Dick Schmalensee, and we especially thank Lars Stole and two referees for very detailedadvice that improvedthe clarityand accuracyof this article.All remainingerrorsare our own. 1 The modelling of firms as competingin utility space is also a useful way to think...
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