1. Introduction to Dynamics

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1、IntroductiontodynamicmodelsTwoperiodmodelIntroductiontoDynamicOptimizationMinWangNationalSchoolofDevelopment,PekingUniversityNovember13,2012IntroductiontodynamicmodelsTwoperiodmodelIntertemporaldecisionModernmacrobasesoneconomicdynamics.Astandardmicroproblem(Intratemporaldecision)MaxF(x)x2Xs.t.G(

2、x)CwhereF(x)iscontinuousandstrictlyquasiconcave,andtheconstrainedsetfx:G(x)Cgisconvex.Noticethatintratemporaldecisionisabouthowtomakeoptimalchoiceatonepointofatime.Intertemporaldecisionistointroduceanewdimension"time",whichisthemostimportantaspectofchoicetheory.IntroductiontodynamicmodelsTwoper

3、iodmodelExamplesofintertemporaldecisionDynamicmodelisaboutintertemporaldecision.E.g.Howdoyouallocatestudytimeforthiscourse?Whyareyouhere?Whydopeoplesave?Whatisyourlifecycledecision?Whatisyourjobsearchstrategy?Howtodeterminetheassetprice?Ifyouownanoil/coalreserve,howmuchandwhendoyouextractit?Inani

4、ntertemporaldecisionproblem,peoplechooseasequenceofactionsthroughtime.IntroductiontodynamicmodelsTwoperiodmodelAnexampleofdynamicmodel:optimalgrowthmodelDependingonhowtomodelthetime,wehavecontinuous-timemodel,whichrequiresthetoolofoptimalcontroltheoryandismainlyusedin…nancialeconomicsandresourcee

5、conomics,anddiscrete-timemodel,whichourcoursefocuseson.Optimalgrowthmodel(Ramsey,1928):theeconomyconsitsofonegood,whichcanbeconsumedorinvested;acontinuumofidenticalhouseholdsofsizeone;amonetaryutilityfunctionU(ct)withU0(ct)>0andU00(ct)<0,andautilitiydiscountfactorb<1;aconstant-return-to-scaleprod

6、uctionfunctionY=F(K,L),whichhastheintensiveformy=f(k)withf0(k)andf00(k)<0;IntroductiontodynamicmodelsTwoperiodmodelAnexampleofdynamicmodel:optimalgrowthmodelSupposetheeconomybeginsatdate0(withaninitialconditionk0)andlastsforTperiods(Tcouldbe¥).eachhouseholdhasoneunitoflaborineachperiod(sincehoues

7、holdshavenopreferenceonleisure,thelaborwouldbeinelasticallysupplied);householdsdiscountfutureutilitybyadiscoutfactorboradiscountrater.thentheoptimalgrowthproblem(orsocialplanner’sproblem)isTMaxbtU(cdtåt)¥fct,k+1gt=0t=0