资源描述：
《lecture 3 technique preparation discrete time dynamic system(宏观经济学(南开大学,龚刚)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、Lecture3DiscreteTimeDynamicSystem:aTechnicalPreparationMacroeconomicsWhyDynamicAnalysisis Important?Wehaveknownthatmacroeconomicsisabouthowmacroeconomicvariablesaredetermined.Inmacroeconomics,suchadeterminationcanoftenbedescribedbyadynamicsystemintermsofeitherdiscretetimeorcontinuoustime.
2、II.TheDiscreteTime DynamicSystemLetXt,Yt,…,Ztarerespectivelythedifferentvariablesatperiodt.Thentheirdeterminationmightbedescribedbythefollowingdynamicsystem,whichisindiscretetime:II.TheDiscreteTime DynamicSystemIffunctionf(·),g(·),…,h(·)arealllinear,theabovesystemmaybewrittenaswhereaijand
3、bi(i,j=1,2,…,n)arealltheparameters.II.TheDiscreteTime DynamicSystemThestandardformofdynamicsystemNotethat(3.1)and(3.2)canberegardedasastandardformofdiscretedynamicsystem.Otherformsofdynamicsystemcanbetransformedintothestandardform(examplesareprovidedinthetextbook)Manytheorems(propositions
4、)toresolvethedynamicsystemisbasedonthestandardform.III.TheSolutionPathand theSteadyStateThesolutionpathThesolutionofasystemdescribehowthevariableschangeovertimegiventheinitialcondition(X0,Y0,…,Z0).III.TheSolutionPathandtheSteadyStateThesolutionpath(continued)Thegraphicrepresentationofsolu
5、tionpathstXXYIII.TheSolutionPathand theSteadyStateThesteadystateThesteadystateofsystem(3.1)or(3.2),denotedas(X*,Y*,…,Z*),canbeobtainedbyposingtherestriction:III.TheSolutionPathand theSteadyStateThesteadystate(continued)Thesteadystatehasthepropertythatifthesolutionpathofthesystemisconverge
6、nt,itmustbeconvergetothesteadystate(seethefollowinggraph)III.TheSolutionPathandtheSteadyStateConvergingtotheSteadyStatetXXYX*X*Y*III.TheSolutionPathandtheSteadyStateThesteadystate(continued)However,thereisnowarrantythatallsolutionwillconvergetothesteadystate(seethefollowinggraph)III.TheSo
7、lutionPathandtheSteadyStateNoConvergingtotheSteadyStatetXXYX*X*Y*III.TheSolutionPathandtheSteadyStateThesteadystate(continued)Thereisnowarrantythatthesteadystateisunique(multiplesteadystatescouldoccur)Thereisalsonowarrantythatthesteadystateevenexists(itcouldbecomple
