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1、ValuationEquilibriumandParetoOptimumAuthor(s):GerardDebreuReviewedwork(s):Source:ProceedingsoftheNationalAcademyofSciencesoftheUnitedStatesofAmerica,Vol.40,No.7(Jul.15,1954),pp.588-592Publishedby:NationalAcademyofSciencesStableURL:http://www.jstor.org/stable/89325.Accessed:02/12/201204:22Yourus
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3、nologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org..NationalAcademyofSciencesiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoProceedingsoftheNationalAcademyofSciencesoftheUnitedStatesofAmerica.http://www
4、.jstor.orgThiscontentdownloadedbytheauthorizeduserfrom192.168.52.72onSun,2Dec201204:22:28AMAllusesubjecttoJSTORTermsandConditions1A.Borel,"SurlacohomologiedesespacesfibresprincipauxetdesespaceshomogBnesdes)upesdeLiecompacts,"Ann.Math.,57,No.1,115,1953;"HomologyandCohomologyofmpactConnectedLieGr
5、oups,"thesePROCEEDINGS,39,No.11,1142-1146,1953.2M.Morse,"TheCalculusofVariationsintheLarge,"Math.Colloq.Pub.,18,1934.3E.Cartan,"LaGeometriedesgroupessimples,"(Euvres,2,PartI,793;alsopapersreferredtherein.SeealsoE.Stiefel,"UbereineBeziehung..."Comm.Math.Helv.,14,350-380,12.C.Chevalley,TheoryofLi
6、eGroupsI(Princeton,N.J.:PrincetonUniversityPress,1946).R.Bott,"Non-degenerateCriticalManifolds"(toappearinAnn.Math.).VALUATIONEQUILIBRIUMANDPARETOOPTIMUM*BYGERARDDEBREUCOWLESCOMMISSIONFORRESEARCHINECONOMICSCommunicatedbyJohnvonNeumann,May6,1954Foraneconomicsystemwithgiventechnologicalandresourc
7、elimitations,indi-lualneedsandtastes,avaluationequilibriumwithrespecttoasetofpricesisaitewherenoconsumercanmakehimselfbetteroffwithoutspendingmore,andnooducercanmakealargerprofit;aParetooptimumisastatewherenoconsumernbemadebettero
