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1、NOTESONDYNAMICANALYSISKeithBlackburnIntroductionThesenotesareintendedtoprovideabroad,butselective,reviewofthemaintechniquesusedindynamiceconomicanalysis.Theypresumethatthereaderisalreadyfamiliarwithcertainbasicconceptsandhasalreadyattainedacertainleveloftechnica
2、lcompetence.Thematerialisdividedintotwomaintopics-theanalysisoflineardynamicsystems(includingrationalexpectationsmodels)andthesolutionofdynamicoptimisationproblems.Eachtopicisaddressedbothindiscretetimeandcontinuoustime,andanAppendixgivesafewexamplesofthetechniq
3、uesinaction.Whilethematerialmayseemdauntingatfirst,thereadershouldsoonrealisethatmanyofthetechniquesrelyonexactlythesameprinciplesandarejustdifferentwaysofsolvingthesameproblem.Themorethatoneusesthesetechniques,themorethatonebecomesfamiliarwiththeirrelativeadvan
4、tagesanddisadvantages,andthemorethatonebecomesskilledinjudgingwhichmethodismostappropriateforperformingaparticulartask.Asusual,expertisewillbegainedthroughlearning-by-doingonthebasisthatpractisemakesperfect.Othersourcesofreferencewhichthereadermayfindusefulinclu
5、dethefollowing.TheminimumlevelofknowledgepresumedtobeginwithisequivalenttothatfoundinA.C.Chiang,FundamentalMethodsofMathematicalEconomics,orC.PSimonandL.Blume,MathematicsforEconomists.Thematerial,itself,iscoveredinvaryingdegreesofdetailinA.K.Dixit,Optimisationin
6、EconomicTheory,M.I.KamienandN.L.Schwartz,DynamicOptimisation:TheCalculusofVariationsandOptimalControlinEconomicsandManagement,P.J.Lambert,AdvancedMathematicsforEconomists:StaticandDynamicOptimisation,andM.D.Intrilligator,MathematicalOptimisationandEconomicTheory
7、ApplicationsofthemethodsandtechniquescanbeobservedinR.J.BarroandX.Sala-i-1Martin,EconomicGrowth,O.J.BlanchardandS.Fischer,LecturesonMacroeconomics,D.Romer,AdvancedMacroeconomics,andT.J.Sargent,DynamicMacroeconomicTheory2PARTONEDYNAMICMODELSManyeconomicmodelsdesc
8、ribesituationsinwhichthereareimportantconnectionsbetweenthepast,presentandfuturestatesoftheenvironment.Theseintertemporallinkagesaresummarisedintheformofdynamicequati
