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1、ASUPPLYANDDEMANDFRAMEWORKFORTWO-SIDEDMATCHINGMARKETSEDUARDOM.AZEVEDOANDJACOBD.LESHNOAbstract.Weproposeanewmodeloftwo-sidedmatchingmarkets,whichallowsforcomplexheterogeneouspreferences,butismoretractablethanthestandardmodel,yieldingrichcomparativestaticsandnewresultsonlargematchingmark
2、ets.WesimplifythestandardGaleandShapley(1962)modelintwoways.First,followingAumann(1964)weconsiderasettingwherea?nitenumberofagentsononeside(collegesor?rms)arematchedtoacontinuummassofagentsontheotherside(studentsorworkers).Second,weshowthat,inboththediscreteandcontinuummodel,stablemat
3、chingshaveaverysimplestructure,withcollegesacceptingstudentsrankedaboveathreshold,andstudentsdemandingtheirfavoritecollegethatwillacceptthem.Moreover,stablematchingsmaybefoundbysolvingforthresholdsthatbalancesupplyanddemandforcolleges.Wegivegeneralconditionsunderwhichthecontinuummodel
4、admitsauniquestablematching,incontrasttothestandarddiscretemodel.Thisstablematchingvariescontinuouslywiththeparametersofthemodel,andcomparativestaticsmaybederivedasincompetitiveequilibriumtheory,throughthemarketclearingequations.Moreover,givenasequenceoflargediscreteeconomiesconvergin
5、gtoalimiteconomy,thesetofstablematchingsofthediscreteeconomiesconvergestothestablematchingofthelimiteconomy.Weboundtherateofconvergenceofthesetofstablematchingsoflargediscreteeconomiestothecontinuumapproximation,andshowthatcomparativestaticsregard-ingtheuniquestablematchingofthecontin
6、uummodelextendtostrongsetorderingofthesetsofstablematchingsofapproximatingdiscreteeconomies.Wemodelthetransferrableutilitycase,asinBecker(1973).Wecharacterizethelimitofschoolchoicemechanismsusedinpractice,generalizingpreviousresultsofCheandKojima(2010).Finally,weillustratethemodel’sap
7、plicabilitybyquantifyinghowcompeti-tioninducedbyschoolchoicegivesschoolsincentivestoinvestinquality.Speci?cally,weshowthatschoolshavemuted,andpossiblyevennegativeincentivestoinvestinqualitydimensionsthatbene?tlowerrankedstudents.Date:February24,2012.Azevedo:Correspondingauthor,Harvard
8、Unive
