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C A H I E R S

D’ÉCONOMIE POLITIQ

PAPERS

IN POLITICAL ECONO

Histoire de la pensée et théories

63

History of T hought and Theories

On perfect competition:

definitions, usages and foundations

De la concurrence parfaite :

définitions, usages et fondements

2012

Publié avec le soutien du CNRS, de l’université de Paris Ouest

et de l’Institut d’études politiques de Lille

C A H I E R S

D’ÉCONOMIE POLITIQUE

PAPERS

IN POLITICAL ECONOMY

63

On perfect competition:

definitions, usages and foundations

De la concurrence parfaite :

définitions, usages et fondements

2012

© L'HARMATTAN, 2012

5-7, rue de l'École-Polytechnique, 75005 Paris

http://www.librairieharmattan.com

diffusion.harmattan@wanadoo.fr

harmattan1@wanadoo.fr

ISBN : 978-2-336-00256-9

EAN : 9782336002569

Nathalie BERTA

Ludovic A. JULIEN

Fabrice TRICOU

LouisMAKOWSKI

Joseph M. OSTROY

AndrésÁLVAREZ

Franco DONZELLI

Antoine REBEYROL

Franco DONZELLI

RobertR. ROUTLEDGE

SOMMAIRE

On perfectcompetition:

deﬁnitions,usagesand foundations.........7

Appropriation in a competitive

theoryofvalue.......................................5

Pricetakers vs. greatnumbers:

a critique ofthe Edgeworth-Walras

convergence à la Debreu-Scarf...............77

Negishi on Edgeworth on Jevon’slawof

indiﬀerence, Walra’sequilibrium, andthe

role of large numbers:

a critical assessment............................. 109

Edgeworth on competition:

a note on Franco Donzelli ................... 155

Edgeworth on competition:

areply to Antoine Rebeyrol....................163

On price-making contractsand

economictheory:rethinking

Bertrand and Edgeworth .........................171

LeonidasPC. KOUTSOUGERAS ricetaking asan asymptotic limit

ofstrategic behavior............................ 189

Rodolphe DOS SANTOS

FERREIRA

Marco DARDI

Competition:theways to perfection....05

e perfection competition paradigm:

evolving from itsambiguities.................19

Nathalie BERTA

Ludovic A. JULIEN

Fabrice TRICOU

LouisMAKOWSKI

Joseph M. OSTROY

AndrésÁLVAREZ

Franco DONZELLI

Antoine REBEYROL

Franco DONZELLI

RobertR. ROUTLEDGE

CONTENTS

De la concurrence parfaite :

déﬁnitions,usagesetfondements.............7

Appropriation et théorie concurrentielle

de lavaleur............................................5

Price takingversusgrand nombre d’agents:

une critique de la convergence

entre WalrasetEdgeworth.....................77

Une critique de l’objection de Negishi à

Edgeworth : loi d’indiﬀérence

de Jevons, équilibre de Walras

etgrand nombre d’agents.................... 109

Edgeworth à proposde la concurrence :

une notesurFranco Donzelli............... 155

Edgeworth à proposde la concurrence :

uneréponse à Antoine Rebeyrol ............163

Contratetprice making:unréexamen

de Bertrand etd’Edgeworth ..................171

LeonidasC. KOUTSOUGERAS Leprice takingcomme limite asymptotique

de comportements stratégiques............ 189

Rodolphe DOS SANTOS

FERREIRA

Marco DARDI

Concurrence : leschemins

de la perfection....................................05

Lesoriginesambiguësduparadigme

de la concurrence parfaite .......................19

On perfect competition: deﬁnitions, usages and foundations

ON PERFECT COMPETITION:

DEFINITIONS, USAGES AND FOUNDATIONS

1 3

Nathalie Berta , Ludovic A. Julien , Fabrice Tricou

1. Introducon

Accordingto Stigler, expressingsome commonsense,“competition isa

rivalrybetween individuals…and itarises whenever two ormore parties

strive for somethingthatall cannotobtain”[Stigler1987: 531]. Market

competition isindeed arivalry, among producerson oneside and among

consumersonthe other, butalso among producersand consumersfor the

exchange gains theymust share. In other words, competition can more

widelyinduce distribution conﬂicts. Inthislatter sense,two isolatedtraders

4

negotiating in an Edgeworthian contextcan besaidto be in competition.

Stressingthestruggle inthesharing of exchange gains, Makowski and

Ostroy[001], [01], inthisissue,relate competitivevaluationto

individual appropriation. Increasingreturnsnotablygenerate exchange gains

comparableto a collective goodwhose appropriation is subject to a costly

andthusineﬃcientnegotiation among agents.

Surprisingly,the established benchmark of competition,theso-called

perfectcompetition, neutralizes thesestrategic behaviorsand conﬂictual

5

interactions,resulting inthe elimination ofthese distribution conﬂicts.

As shown byMakowski and Ostroy, perfectcompetition (associatedwith

constant returns) dissolves these conﬂictsof appropriationsince every

individual can be paid accordingto hismarginal contribution. Inthe perfectly

competitive framework, competition isa paciﬁed interaction grounded on a

1. Universityof ReimsChampagne-Ardenne. E-mail: nathalie.berta@univ-reims.fr

. Universityof Burgondy. E-mail: ludovic.julien@u-paris10.fr

3. Universityof ParisOuestNanterre la Défense. E-mail: fabrice.tricou@u-paris10.fr

4. See Edgeworth [1881].

5. Howcanthe benchmark of competition preludestrategic behaviorsand distribution conﬂicts?Some

advancethe heuristic necessityof asimpliﬁed model prior to complexmodelsof competition. Others

detect the persistence of a Walrasianutopia (a projectof justice) ordenouncethe ideological denial of

distribution issues.

7

Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

strictorganization;itisnota conﬂicting interaction operated by resourceful

opportunistic individuals.

Exposed byMakowski and Ostroy,thisdivergence between passive

“market takers”and creative marketmakers sharpens thewell-known

diﬀerence between gentle pricetakersandstrategic price makers thatattempt

to exploit theirmarketpowers. In other words, Makowski and Ostroydeepen

the gap between perfectcompetition (or the Walrasianrule) and imperfect

competition (or the Cournotianrevival).

More generally,these linksbetween perfectand imperfectcompetitions

are not straightforward, both competitionsbeingrelated intworeversalways.

Firstly, perfectcompetitionremains the benchmark fromwhichtheoriesof

imperfectcompetition are built: inthisﬁrst way,the deﬁnition of perfect

competition is taken forgranted—mainly the lawof one price andthe price

taking behavior—and each model of imperfectcompetitionthentries to

amendsome assumption(s)usuallyassociatedwith it. isis theway—

from perfect to imperfectcompetition—adopted in applied orindustrial

economics(section3). Secondlyand conversely, asperfectcompetition

ratherpostulates whatitis supposedto explain, gametheoretic imperfect

competition isalsousedto provide foundations to perfectcompetition,

to derive competitive behaviorsfromstrategic behaviors. Inthat second

way, from imperfectcompetitionto perfectcompetition,the deﬁnition of

perfectcompetition isno moreused asanunquestionedstarting pointbut

as the limitcase of imperfectcompetition. From perfectcompetition as the

standard deﬁnition of competition, oneswitches to perfectcompetition asa

degenerate case of competition (section 4).

Before developingthesetwo kindsofrelations,we consider(without

being exhaustive)some notionsof competition developed inthe historyof

economics, includingthe marginalistnotion of competition (section).

2. The general noon of compeon

Asa phenomenon ofrivalry, competition maybe comparedto arace between

conﬂicting individualsand also be connectedwith Darwinianselection, a

process thatdisplays thesurvival ofthe ﬁttest(andthe elimination ofthe

others). Inthisline ofthought, competition isqualiﬁed asan eﬃcient

mode ofselection,the“bestones”beingthe former winnersandthe present

survivors. Unleashed competition may thusappearasaself-defeating

process:whenthe mosteﬃcientcompetitorhasprevailed, a monopolyarises

8

On perfect competition: deﬁnitions, usages and foundations

and competitionvanishes. To ensuretherobustnessof competition, many

industrial economists recommend a public interventionto protectandto

organizethe competitive interaction:some“rulesofthe game” should be

deﬁned and enforcedto eliminate abusesof dominantposition (anti-trust

laws) andto ensurethe independence of behaviors(anti-collusion laws) in

markets. Austrian economistslike Kirzner[1979] defend an oppositeview.

For them, dominantﬁrms willstaydominantaslong as theymaintaintheir

competitive advantage. Competition isa neverendingrace andtemporary

winnerscan’t stopstruggling. So monopolymaybe legitimized, beyondthe

justiﬁcation given bySchumpeter[194] intermsof innovation, aslong as

6

theydon’tbuild barriers to entry. ForHayek [1973], competition policy

shouldwisely staymodestand notdisrupt the precious “spontaneousorder.”

Andthe market system notonlydisplayscompetition: itemergedthrough a

historical competitive processas the mosteﬀectivesystem (and asasystem

of individual freedom). So Austrian economistsgeneralizethe principle of

competition and praise itforits virtues. eyalsounderline itsoperation

asa dynamicalprocesswhile classical and neoclassical economists tendto

7

emphasizetheeﬀectsof competition.

eviewson competition bySmith [1776], Ricardo [1817] and Marx

8

[1867] are prettyclose, even iftheymaydisagree on other topics. Inthe

classical framework, competition isessentiallyconnectedtothe logic of

capital and itsgeneral eﬀectsare balancing, butalsounbalancing. Firstly,

each capitalistcompares therate ofreturn he getsin hiscurrentallocation

totherateshewould getin alternative activities. Capitalsare moved from

lowproﬁtability sectors to high proﬁtabilityones. So production decreasesin

the former sectors,where pricesand proﬁtsareraised (as the commodityis

scarcer);andsupplyincreasesinthe latterones,where pricesand proﬁtsare

reduced (as the commodityismore abundant). Such a competitive process,

called gravitation, isequilibrating andtends to make allratesofreturn

9

equal. e leveling oftheratesof proﬁtamongsectorsis thusexplained

byfree competition, a mechanismthatdeterminesnotonly the formation

6. Accordingtothe Austrianschool,“free competition”means “free entryon markets”above all.

7. See Mc Nulty[1987].

8. See Duménil and Lévy[1990],who also mentionthat the classical ﬁeld of competition

isnothomogeneous: nonreproducibleresources(whose appropriation generates rents) are distinguished from

reproducible commodities(for whichthetheoryof production price applies).

9. See Eatwell [1987] and Semmler[1987].

9

Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

10

of pricesbutalsothe distributSecondlion of income. y, manyclassical

economistspredicted a longrun decrease ofthe generalrate of proﬁt: Ricardo

feared a gloomyfuture and Marxannounced a global crisisforcapitalism.

Competition playsa majorpartinthis systemictrend, pushing capitalists to

keep on investing in order tosurvivethe competitiverace. ForMarx,this

processleads to arise inthe organic composition of capital and eventually to

a fall ofthe generalrate of proﬁt.

Marginalisteconomistschangedthe economic conceptual framework,

shifting from a conception ofsocietymade ofsocio-economic groups(or

evenstruggling classes)to a conception ofsocietymade of homogeneous

individuals. Andtosolvethe general problem of economic coordination,

11

neoclassical political economists such asWalras relied on competition.

Marketcompetition isnot simplerivalryand opens the possibilityof a general

settlement, aunanimousagreementon asituationthatcan be determined

intwo logicalsteps. First,to putJevons’lawof indiﬀerence in Mill’s terms:

“there cannotbetwo pricesinthesame market,”becausethe poorlypaid

supplierandthe heavilycharged demander wouldwant to changetheirdeals

1

and could do it(simply recontractingtogether). Second,to put the lawof

supplyand demand in Mill’s terms:“Demand andsupply…will be made

equal. Ifunequal atanymoment, competition equalizes them.”ere cannot

be a disequilibrium price onthe market, becausetherationed demanders/

suppliers would consent to a price change allthesuppliers/demanders would

13

agreewith. So, marketcoordination is successful iftransactionsare all done

at thesame price,the price equatingsupplyand demand,which determines

marketequilibrium.

3. From perfect compeon to imperfect compeon:

deﬁnions

Stigler[1957]recalledtheway the informal notion of perfectcompetition

emerged inrelationwiththe developmentof imperfectcompetition inthe

1930’s. More precisely, heshowed how these features today usuallyassociated

to perfectcompetitionwere adopted afterWorld WarII. ese features

10. See Arena [1979], pages133 to 137.

11. Andtheydistinguished perfectcompetition foritsjust virtues(Walras) orforitseﬃcientproperties

(Pareto).

1. e notion ofrecontracting isdueto Edgeworth [1881].

13. Orjust some ofthem, depending onthe prevailingrationingscheme.

10

On perfect competition: deﬁnitions, usages and foundations

coverlargethemes: large numberof agents(alsorelatedtothe absence of

collusion orcoalition), perfectinformation, free entryand homogeneityof

14

commodities(sometimesalso associatedwith divisibility).

ese intuitive featuresorconditionsareusedto justify whatcompetition

asa processis supposedto achieve: ﬁrst,the homogenization of price

embodied inthe‘lawof one price’andsecond,the absence ofstrategic

behaviorembodied inthe pricetaking behavior. Indeed, perfectinformation

is supposedto guaranteethat the price is unique,while homogeneityis

supposedto ensurethat thisprice is the only signalrequired forindividual

choices. Besides,the large numberof agentsis usedto justify the pricetaking

behavior,whilethe large numberof agentsisjustiﬁed byfree entry. is

deﬁnition of perfectcompetition ismainly used in applied orindustrial

economics. Modelsof imperfectcompetition arethen built uponthe

amendmentof atleastone ofthese features. esetheories—dealingwith

monopoly, duopoly, information asymmetry, productdiﬀerentiation and

so on—then constitute a non-uniﬁed myriad of partial equilibrium models

displayingsome kind ofstrategic behaviorandraisingsomesocialwelfare

issue.

Debreu[1959] brokewiththese previousintuitive featuresof perfect

competition—large number, free entryandso on—, providingthe formal

andrigorousdeﬁnitionthathad became canonical in general equilibrium

theory: each good isassociatedwith asingle price expressed in anuméraire

and eachrational agent(eithera producerora consumer) isa quantitymaker

15

who behavesasa price-taker.

Debreuand morewidely the axiomatization of general equilibrium

hadthe advantageto precisethe assumptionsformally required byperfect

competition. Andthese precisionsbrought two consequences. First, itclearly

set the conditions required for the existence andthe Paretian optimalityof

the general equilibrium andthus strictlydrew the normativescope ofthe

competitive framework:“General competitive equilibrium above allteaches

the extent towhich asocial allocation ofresourcescan be achieved by

14. ese featuresare notnormalized. Stigler[1957] doesnotevoke

homogeneitybutintroducesmobilityof factors. atis whyone can also ﬁnd ﬁve featuresinthe literature. In contrast, Roberts[1987] does

notevoke mobilitybuthomogeneityand divisibility, and alsothe absence of externalityand increasing

returns. eway these featuresﬂuctuate among authors revealslooserelations withthe general

equilibrium framework.

15. One mustaddtothe deﬁnition of perfectcompetitionthe condition of“universalityof

markets”[Arrow, 1969] foritavoids the presence of externalitiesand morewidelyof all missing markets.

11

Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

independentprivate decisionscoordinatedthrough market.”[Arrow197:

18]

Second, axiomatization provided a clariﬁcation ofthestatusof

competitivetraits. Indeed,therelation betweenthese intuitive featuresand

‘Arrow-Debreu’sformal deﬁnition is sometimesambiguous. Assumptions

of homogeneityand divisibilityare perfectlyembodied inthetheory,

tosuch a point that theymay seemredundant:thestrictdeﬁnition of

goods—asphysically speciﬁed, dated and localized commodities—includes

homogeneity sincetwo commodities whichwould notbe perfectlyidentical

would necessarilyconstitutetwo diﬀerentcommodities;andthe deﬁnition

ofthe commodity space asIRn also allows to avoid indivisibility.“Strikingly

however, free entryand large numberplayno explicit role inthis theory: all

thetheorems would hold iftherewere butasingle potential buyerandseller

of anycommodity.”[Roberts1987: 838] First,the numberof agentsisﬁxed

in ArrowDebreu’sframework; second, again from a formal pointofview,

the large numberassumption isnotnecessary, even if itis usuallyclosely

relatedto perfectcompetition. eway the pricetaking behaviorcan be

based onthe large numberof agentsisasubjectof intense discussions since

Edgeworth [1881]’sconjecture and Debreu-Scarf [1963]’sproof.

So perfectcompetition—embodied inthe lawof one price andthe price

taking behavior—can beseen asa frameworkthat “canreallyprevail onlyat

equilibrium”[Arrow1959: 41] foritis ratherpostulatedthan endogenously

setand doesnotallowany satisfactory theoryof price and equilibrium

16

formation. Despitethesewell-known critics(about thesetting ofthe price

and beyond about thestabilityofthetâtonnement), perfectcompetition

remains the benchmark fromwhich neoclassical imperfectcompetitive

theoriesare built, probablybecause of its strong normative contentand its

uniﬁedtheoretical framework.

Imperfectcompetition has since experienced arebirth: one doesnot start

fromthe given perfectcompetition assumptions,tryingto amendthem;

butconverselyone grounds these assumptions thanks to a gametheoretic

rationale. In particular, imperfectcompetition is usedto found competitive

behaviorsfromstrategic behaviors, in order to endogenizethe previous

postulated competitive framework.

16. As stressed inthe famousquotation from Arrow,“each individual participantis supposedtotake price

asgiven and determine hischoicesas to purchasesandsalesaccordingly. ere isno one leftover whose

job itis to make a decision on price.”[Arrow1959: 43]

12

On perfect competition: deﬁnitions, usages and foundations

4. From imperfect to perfect compeon: foundaons

ree diﬀerentlinesofresearchwere developed in a general equilibrium

frameworkto give arational foundationto perfectcompetition, or rather to

competitive equilibrium. In addition,theyallsharethe common perspective

to provide gametheoretic foundationsforperfectcompetition by the

construction of a gamewhose equilibrium coincides withthe competitive

17

equilibrium inspeciﬁc conditions(typicallyforlarge economies). Without

being exhaustive, let’s sketchthesethree linesofresearch.

e Edgeworthian linestudies therelation betweenthe core andthe

competitive allocations[Hildenbrand, 1974]. e core providesa foundation

ofthe competitive equilibrium. Two kindsof approachesmaybe invoked:

18

the asymptotic approach andthe atomlessapproach. Both approaches

are based on cooperative gametheory. e asymptotic approachwas

performedthroughreplication procedure forﬁnite economiesbyDebreu

and Scarf [1963]. eynotably show, providedthat the initial endowments

areuniformlybounded,that the core of an economy replicated an inﬁnite

numberoftimesconverges towardthesetof competitive equilibria. e

otherone is the atomlessapproach,wherethesetof agentsisindexed by

19

a continuumwith an atomlessmeasurespace. Aumann [1964] considers

a market with a continuum oftraders. Accordingto him:“oughwriters

on economic equilibrium havetraditionallyassumed perfectcompetition,

theyhave, paradoxically, adopted a mathematical modelthatdoesnotﬁt

thisassumption. Indeed,the inﬂuence of an individual participanton

the economycannotbe mathematicallynegligible, aslong as there are

onlyﬁnitelymanyparticipants.us a mathematical model appropriate

to the intuition notion of perfect competition must contain inﬁnitelymany

participants. Wesubmit that the mostnatural model for thispurpose

containsa continuum of participants,similar tothe continuum of points

on a line or the continuum of particlesin a ﬂuid.”[Aumann 1964:39] In

thisEdgeworthian perspective,the price-taking andthe coalitionalstrategic

17. e“no-surplus”characterization of perfectcompetition

intermsof“valuationwithoutappropriation”[Ostroy1980;Makowski and Ostroy,001] can beseen asan alternativeway to found perfect

competition.

18. Khan [010]reviews several methodsformodelling perfectcompetition intermsof core equivalence

and existencetheorems. eseminaltheoreticalreference isEdgeworth [1881].

19. Shitovitz[1973] assumesan economyinwhich atomsface an atomless sector. He notablyobtains the

counterintuitiveresult that when atomshavethesame endowmentsand preferences the core coincides

withthe competitive allocations.

13

Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

behaviorscan be identiﬁedunderindividual negligibility. e cooperative

approach hasbeen criticized by the non cooperative one, especiallybecause

itdid notexplainthe formation of coalitions,which notablyquestionshow

a core allocation is reached.

esecond line ofresearch introducesnon cooperative behaviors

underCournotian competition [Mas-Colell, 198]. e allocationsare

implementedthrough interrelated markets, and competitive behaviorsin

marketscan be obtained from an environmentinwhichstrategic interactions

0

occur. Twoways were followed. e ﬁrstone is thestrategic marketgames

whichwere developedto circumvent the auctioneer[Shubik, 1973;Shapley

and Shubik, 1977;Dubeyand Shubik, 1978;Postlewaite and Roberts, 1976;

Postlewaite and Schmeidler, 1978;Sahi and Yao, 1989;Amiretal., 1991]

1

among others. Someresultsof convergence intermsof limit theorems

are obtained. esecondway, opened byGabszewiczand Vial [197] in

an exchange economy with production, and pursued byCodognato and

Gabszewicz[1991], [1993], d’Aspremont, DosSantosFerreira and

GérardVaret[1997] forpure exchange economies, features theworking andthe

consequencesof marketpowerin interrelated markets.

DiﬀerentCournotWalrasequilibrium conceptscan be modelled, each depending ontheway

strategic behaviorisintroduced [Gabszewiczand Michel, 1997]. Inthese

Nashian perspectives,the Cournot-Walrasequilibria can coincidewiththe

competitive equilibrium inthe case of large economies[Lahmandi-Ayed,

001]. Morerecently,the Cournot-Walrasequilibrium concepthasbeen

developedwithinthestrategic marketgamesapproach in marketeconomies

with a continuum oftraders[Busetto etal.,008; 011]to endogeneizethe

type of behavioraseithercompetitive or strategic.

ethird line is recentandthrowsa diﬀerentlightonthestrategic

foundationsof perfectcompetition, in bringingtogethermatching and

bargaining games[Gale,000]. Conversely tothetwo preceding linesof

research,these dynamic modelsaim at specifyingthe economic institutions

withinwhich agentsinteract. Rubinstein and Wolinsky[1985] consideraset

0. eseminalreference isCournot[1838].

1. Onthispoint,see and Postlewaite-Schmeidler[1978]whoshow that the price-taking behaviormay

be a dominant strategy.

. Anotherapproach, based on conjecturalvariations,takesinto account the perceptionsbyagentsof

theirmarketenvironmentand concerns the agent’sbeliefsabout therivals’ responses to change in his

ownstrategy[Bowley, 194]. e degree of marketpowermaybe parameterized byconjecturalvariations

[Dixit, 1986]. Itcan also beshownthat the competitive equilibrium isa locallyconsistentconjectural

equilibrium [Julien,010],sustainingthe ideathatperfectcompetition isonlydeﬁned in equilibrium.

14

On perfect competition: deﬁnitions, usages and foundations

oftradersﬂowingthroughthe marketover time andsearching at random for

trading opportunities. Whentheymeet,thetermsoftradesare determined

bybargaining. Itcan beshownthat the dynamic matching andthe bargaining

implement the competitive equilibrium [Gale, 1986]. Some extensionsare

given byMcLennan and Sonnenschein [1991]. ese ﬁnite game models

generate limits theorems, but theyare essentiallyassessed on period length

ordiscountfactorand notonthe numberoftraders. Sothe coincidence

between perfectand imperfectcompetitionsdoesnothere depend onthe

(large)size ofthe economy, contrary tothe basic idea developed inthe

Edgeworthian and Cournotian perspectives.

5.Contribuon highlights

Compeon, appropriaon and valuaon

Neo-classical economicsessentiallyenvisions the pricesystem as “the barometer

ofvaluation”involving pricetakingreactive agents. In“Appropriation fora

competitivetheoryofvalue,”L. Makowski and J.M. Ostroycontrast this

view withthe alternative conception ofthe pricesystem as “the meansof

appropriation”moved byprice making opportunistic agents. ere isactually

nostrictmutual exclusion betweenvaluation and appropriation, buteach

paradigm or theory tendsfavoronetheme andto downgradethe otherone.

On oneside, from Walras to Debreu, neo-classical economicsfocused on

valuation, appropriation being eitheran independentconcern orasecondary

issue. Inthisline, appropriation isa propertyofvaluation:“Appropriation

is thestandard by whichthe eﬃciencyofvaluation ismeasured.”Onthe

other side, intheview studied and developed byMakowski and Ostroy,

appropriation ispromoted as the main question and as the driving force

ofvaluation. Inthatline,“appropriation isa generic description of an

individual’seﬀorts to extractgainsfrom others,” so distribution leads(and

isnotabsorbed by) price determination. e dualitybetweenvaluation and

appropriation proposed byMakowski and Ostroyisfruitful and innovative,

asitallows themto develop a modiﬁedversion of mainstream economics

onthe basisof a newlight thrown onthe historyof economicthought.

Under thisperspective, ﬁve diﬀerent themescan berevisited:rentasan

appropriation phenomenon in classical political economy; the primacyof

valuation in neoclassical political economy; valuation and appropriation

in planned ormarketeconomicsystems;property rightsas the bound for

15

Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

appropriation in institutional economicsand ﬁnally, of course, incentive and

appropriation in newmicroeconomics.

The Edgeworth-Walras convergence

A. Álvarez’spaperisentitled“Pricetakingvsgreatnumbers: A critique ofthe

Edgeworth-Walrasconvergenceà laDebreuScarf.”islimit theorem is used

to give foundations tothe Walrasian equilibrium, arguingthatEdgeworth’s

theoryofrecontractisasuitableway toreach competitive allocations. Itis

seen asa generalization of Edgeworth’sconjecturewhichsets thatWalrasian

equilibrium isa limitcase of Edgeworthian equilibriumwhenthe number

of agentsisinﬁnite. e paperchallenges this usual interpretation ofthe

Edgeworth-Walrasconvergence. First, it shows that the Walrasian framework

avoidsquestions thatareunavoidable in an Edgeworthian framework:the

pricetaking assumptionrestson institutional assumptions—thenuméraire,

the presence ofthe auctioneerand of brokers—which alltry to neutralize

strategic behaviors,to avoid price manipulation. Second, it shows that the

strategic behaviorsbehind Edgeworth’sconception ofrecontracting are

misleading inthe cooperative game framework of DebreuScarf andthat

the core isnota goodrepresentation of Edgeworth’s ‘ﬁnalsettlements’. e

assimilation ofthe‘ﬁnalsettlements’andthe coalitionsofthe gametheoryis

based on awell-known but veryparticularexample—thereplica economy—

of Edgeworth’s writingsand involvesawrong interpretation of Edgeworth’s

notionsof coalition, combination orcooperative association.

F. Donzelli’s “critical assessment”about “Negishi on Edgeworth on Jevons’s

Lawof indiﬀerence, Walras’equilibrium, andtherole of large numbers”also

deals withthe Edgeworth-Walrasconvergencewith an inﬁnite numberof

agentsand focusesonthe Edgeworthian conceptof coalition. However,the

pointofviewadopted byF. Donzelli isdiﬀerent: he questions the objection

addressed byNegishi [198]totheso called Edgeworth’sconjecture. First,

the paper setsauniﬁedreformulation—withthe contemporary toolsof

microeconomics—of Walrasian and Edgeworthian equilibria, clarifyingthen

thestatusof Jevons’s ‘lawof indiﬀerence’and ofthe large numberassumption

forboth authors. Second,using his reformulation of Edgeworth’sprocessof

recontract, F. Donzelli addressesobjections to Negishi’s result. e latterhas

shown,usingsome open coalitions that the arbitrage mechanisms supporting

the lawof one price are at work as soonthere aretwo agents: in other words,

reaching Walrasian equilibriawould not requirethe assumption of a large

numberof agents. F. Donzelli’spapercriticizes thisposition,stressingthat

16

On perfect competition: deﬁnitions, usages and foundations

Negishiusesassumptions which are notcompatiblewith Edgeworth’s

recontracting. ese interpretationsof Edgeworth’s recontracting and

coalitionsandtherole of arbitrage mechanismshavethen beenthesubject

of a discussionwith A. Rebeyrol inthisissue.

Cournot,Bertrand and Edgeworth

e article of L. Koutsougeras, entitled“Price Taking as the Asymptotic

Limitof Strategic Behavior,”providesa generalization ofthe ideathatNash

equilibriatendto competitive equilibria as the numberof agentsincreases

withoutlimit. e authordevelopsan asymptotic approachto explainthe

emergence of pricetaking behaviorinthe framework ofstrategic market

games. isframework enables to dealwith price formation andtrade process

inthe line of Dubey-Shubik [1978], Peck-Shell [1989] and Sahi-Yao [1989]

among others. He notablyprovidesa criterion—arate of convergence—

to measurethe individual behavior’sdeparture from pricetaking,usingthe

wedge betweenthe pricevector’shyperplane andthesupporting hyperplane of

3

the indiﬀerencesurface in equilibrium. Itis shownthat,underassumptions

onthe distribution oftraders’characteristics,this wedge (the gap indicator)

becomesarbitrarily small foralltradersas the numberof agents tends toward

inﬁnity. So,strategic behaviorisapproximately thesame aspricetaking in an

economy with a large numberof agents. e approximation becomesﬁner

whenthe numberoftradersincreases.

In hisarticle, entitled“On price-making contractsand economictheory:

rethinking Bertrand and Edgeworth,”R. Routledge outlinesan alternative

approachto contractformationwhich combinesBertrand’s[1883] insight

regarding price competitionwith Edgeworth’s[1881] notion ofrecontracting.

Inthe ﬁrstpartofthe paper,the authorcriticizes the inabilityofthe

standard models(relatedtothe Bertrand paradox)to provide a convincing

price-making foundation forcompetitive equilibrium. He providesaricher

approachto contractformationwhich maygive a more credible foundation

forperfectcompetition. e mainresultis thata price-making analog of

the Debreu-Scarf [1963] approach can be providedtoshow that, in large

markets, price-making contractsare‘close’ tothe competitive equilibrium.

3. e marginalrate ofsubstitution in casetheutilityfunction is twice diﬀerentiable.

17

Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

Walrasian allocationsare contained inthe Edgeworth core and price-taking

equilibria are contained inthe Bertrand core. Hence, as thesetof market

tradersbecomeslarge,the onlyprices whichremain inthe Bertrand core

are competitive prices. erefore a newprice-making foundation for the

competitive equilibrium emergesfromthe Bertrand core.

Final synthec notes

In hisanalytical note,“Competition:theways to perfection,”R. DosSantos

Ferreira distinguishes two (times two)typesof foundationsforperfect

competition. e ﬁrst way to perfection is the absence of marketpower

found in large economies. is “smallsize”argumentcan be found in a

noncooperative contextà la Cournotorin a cooperative contextà la Edgeworth.

Beyondthe monopolycase, Cournot seescompetition asa non-cooperative

game between producers. Whenthe numberof competitorsgoes up,the

marketpowerof eachregularlygoesdown.“Indeﬁnite competition”is the

limitcasewherethe marketprice hasbecome insensitiveto each producer’s

action andtends to equalthe marginal cost. Edgeworth developsasimilar

idea in a diﬀerentcontext,when heseespure exchange asa cooperative game

between contractors. Whenthe numberoftradersgoes up,the bargaining

powerof eachregularlygoesdown. In a large economy,theshrunk core

isnothing morethanthesetof Walrasian allocations. esecondway to

perfection isa given normal conduct, eitherpeaceful oraggressive. at

“standard of behavior”argumentcan be found in Walras(among others) for

the quietmode orin Bertrand for the hostile mode. Pricetaking behavior

maybeseen asa norm of conduct voluntarilyobserved by the marketagents,

whatever their sizes. Under this vision,the presence of pricetakershas to be

completed by the intervention ofsome marketmaker(s):sometâtonnement

operatorsin Walrasand a“marketparticipant”forDebreu. Bertrand

advancesanothernorm of conductforproducers: priceundercutting.

Such an“aggressive”pricesetting mayleadto a market result similar tothe

“peaceful”perfectlycompetitive equilibrium, as soon as there are only two

producers. So, perfectcompetition ishere grasped asan outcomethatcan be

obtainedthrough opposite conducts.

Tostarthisepistemological and ethical comment,“e perfectcompetition

paradigm: evolving from itsambiguities,”M. Dardistates that thisparadigm

18

On perfect competition: deﬁnitions, usages and foundations

isnotareference for theworking of competition, buta benchmark for the

alleged outcome of competition: equilibrium. isentailsissuesabout the

epistemologicalstatusofthe paradigm,which isintensiﬁed by the numerous

interpretationsofthe normative meaning at stake. euniversal construction

ofthe competitive equilibrium isfascinating, asitjoinsindividual pursuitof

happinessand eﬃcient social order;but twoshortcomingsmaybe identiﬁed.

First,there are persisting epistemological ambiguities. e assumed

competitiveresult relieson a peculiarkind of marketorganization,the

tâtonnement,which displaysneither robust stabilitynorempirical accuracy.

Debreuaccepted perfectcompetitionto bereducedto an algebraicstructure

isolated from facts, farfrom both Walras’sidealism and Pareto’spositivism.

Recently, manyformsof competitive outcomeshave beenstudiedthanks to

complexdynamicsapproachesand gametheorymodels,which challenge

the perfectcompetition paradigm as the onlybenchmark. Second,there

are deeperethical ambiguities, about thereduction ofsocial happiness to

itsindividual andtradable components. Behindthe questioning of Pareto

optimality, individual preferencesare challenged as the onlybasisfor social

good:with Sen, democraticvaluesare broughtback onthe economic ﬁeld

and economics takesback its shape of political economy, embedded in ethics

and political philosophy.

Acknowledgements

eworkshopFoundations, deﬁnitions and usages of perfect competitiontook

th

place at the Universityof ParisOuestNanterre la Défense on January13

th

and 14 ,011. We are gratefultotheresearch centerEconomiX (UMR

CNRS735),the departmentof economicsofthe Universityof ParisOuest

Nanterre la Défense (thanks to C. Bidard), andthe Region Île-de-France

forﬁnancial and organizationalsupports. We also acknowledge A. Béraud,

G. CodognatDe Vo, M roey, B. Ingrao and A. Rubinstein for their report

activities, and also N. Yannelisforhisparticipation intheroundtable.

19

Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

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