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1、Chapter1Overview1.1.WarningThischapterprovidesanontechnicalsummaryofsomethemesofthisbook.Wedebatedwhethertoputthischapterfirstorlast.Awaytousethischapteristoreadittwice,oncebeforereadinganythingelseinthebook,thenagainafterhavingmasteredthetechniquespre
2、sentedintherestofthebook.Thatsecondtime,thischapterwillbeeasyandenjoyablereading,anditwillremindyouofconnectionsthattranscendavarietyofapparentlydisparatetopics.Butonfirstreading,thischapterwillbedifficult,partlybecausethediscussionismainlyliteraryandthe
3、reforeincomplete.Measurewhatyouhavelearnedbycomparingyourunderstandingsafterthosefirstandsecondreadings.Orjustskipthischapterandreaditaftertheothers.1.2.AcommonancestorCluesinourmitochondrialDNAtellbiologiststhatwehumansshareacom-monancestorcalledEvewh
4、olived200,000yearsago.Allofmacroeconomicstooseemstohavedescendedfromacommonsource,IrvingFisher’sandMil-tonFriedman’sconsumptionEulerequation,thecornerstoneofthepermanentincometheoryofconsumption.Modernmacroeconomicsrecordsthefruitandfrustrationofalong
5、love-hateaffairwiththepermanentincomemechanism.Asawayofsummarizingsomeimportantthemesinourbook,webrieflychroniclesomeofthehighandlowpointsofthislongaffair.–3–4Overview1.3.ThesavingsproblemAconsumerwantstomaximize∞Eβtu(c)(1.3.1)0tt=0whereβ∈(0,1),uisatwic
6、econtinuouslydifferentiable,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.Afirst-ordernecessaryconditionforthisproblemisu(c)t+1βEtRt+1≤1,=ifAt+1>A.(1.3.3)u(ct)ThisEulerinequalityrecursaseitherthecornerstoneorthestrawmaninmanytheoriescontainedinthisbook.Differentmodelingchoicesput(1.3.3)
