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1、EconomicsDepartmentoftheUniversityofPennsylvaniaInstituteofSocialandEconomicResearch--OsakaUniversityANoteonPriceSystemsinInfiniteDimensionalSpaceAuthor(s):EdwardC.PrescottandRobertE.Lucas,Jr.Reviewedwork(s):Source:InternationalEconomicReview,Vol.13,No.2(Jun.,1972),p
2、p.416-422Publishedby:WileyfortheEconomicsDepartmentoftheUniversityofPennsylvaniaandInstituteofSocialandEconomicResearch--OsakaUniversityStableURL:http://www.jstor.org/stable/2526035.Accessed:21/12/201222:27YouruseoftheJSTORarchiveindicatesyouracceptanceoftheTerms&Con
3、ditionsofUse,availableat.http://www.jstor.org/page/info/about/policies/terms.jsp.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuseinformationtechnologyandtoolstoincreasepro
4、ductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org..Wiley,EconomicsDepartmentoftheUniversityofPennsylvania,InstituteofSocialandEconomicResearch--OsakaUniversityarecollaboratingwithJSTORtodigitize,preserveandextenda
5、ccesstoInternationalEconomicReview.http://www.jstor.orgThiscontentdownloadedonFri,21Dec201222:27:38PMAllusesubjecttoJSTORTermsandConditionsINTERNATIONALECONOMICREVIEWVol.13,No.2,June,1972ANOTEONPRICESYSTEMSININFINITEDIMENSIONALSPACE*BYEDWARDC.PRESCOTTANDROBERTE.LUCAS
6、,JR.DEBREU[2],undercertainassumptions,provesthatanyvaluationequilibriumisaParetooptimumandconversely.Avaluationequilibriumisaresourceallocationandapricingschemesuchthatnoconsumercanbemadebetteroffwithoutspendingmoreandnoproducercanmakealargerprofit.Mathe-matically,ap
7、ricingschemeisacontinuous,linearfunctionaldefinedonthespaceofcommodities.Ifthecommodityspaceisfinitedimensional,suchafunctionalmayalwaysbewrittenasaninnerproductp'z,wherebothpandzareelementsofthecommodityspace.Inthiscase,thei-thcomponentofphasthenaturalinterpretation
8、asthepriceofthecommodityrepresentedbythei-thcomponentofz.Ifthecommodityspaceisnotfinitedimensional,however,nosuchgeneral"representa
