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1、Chapter1Overview1.1.WarningThischapterprovidesanontechnicalsummaryofsomethemesofthisbook.Wedebatedwhethertoputthischapter?rstorlast.Awaytousethischapteristoreadittwice,oncebeforereadinganythingelseinthebook,thenagainafterhavingmasteredthetechniquespre
2、sentedintherestofthebook.Thatsecondtime,thischapterwillbeeasyandenjoyablereading,anditwillremindyouofconnectionsthattranscendavarietyofapparentlydisparatetopics.Buton?rstreading,thischapterwillbedi?cult,partlybecausethediscussionismainlyliteraryandthe
3、reforeincomplete.Measurewhatyouhavelearnedbycomparingyourunderstandingsafterthose?rstandsecondreadings.Orjustskipthischapterandreaditaftertheothers.1.2.AcommonancestorCluesinourmitochondrialDNAtellbiologiststhatwehumansshareacom-monancestorcalledEvewh
4、olived200,000yearsago.Allofmacroeconomicstooseemstohavedescendedfromacommonsource,IrvingFisher’sandMil-tonFriedman’sconsumptionEulerequation,thecornerstoneofthepermanentincometheoryofconsumption.Modernmacroeconomicsrecordsthefruitandfrustrationofalong
5、love-hatea?airwiththepermanentincomemechanism.Asawayofsummarizingsomeimportantthemesinourbook,webrie?ychroniclesomeofthehighandlowpointsofthislonga?air.–3–4Overview1.3.ThesavingsproblemAconsumerwantstomaximize∞Eβtu(c)(1.3.1)0tt=0whereβ∈(0,1),uisatwic
6、econtinuouslydi?erentiable,increasing,strictlycon-caveutilityfunction,andE0denotesamathematicalexpectationconditionedontime0information.Theconsumerfacesasequenceofbudgetconstraints1At+1=Rt+1(At+yt?ct)(1.3.2)fort≥0,whereAt+1≥Aistheconsumer’sholdingsofa
7、nassetatthebeginningofperiodt+1,Aisalowerboundonassetholdings,ytisarandomendowmentsequence,ctisconsumptionofasinglegood,andRt+1isthegrossrateofreturnontheassetbetweentandt+1.Inthegeneralversionoftheproblem,bothRt+1andytcanberandom,thoughspecialcasesof
8、theproblemrestrictRt+1further.A?rst-ordernecessaryconditionforthisproblemisu(c)t+1βEtRt+1≤1,=ifAt+1>A.(1.3.3)u(ct)ThisEulerinequalityrecursaseitherthecornerstoneorthestrawmaninmanytheoriescontainedinthisbook.Di?erentmodelingchoicesput(1.3.3)
