optimal-growth-notes

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1、LECTURENOTESONECONOMICGROWTHTheOptimalGrowthProblemToddKeisterCentrodeInvestigaciónEconómica,ITAMkeister@itam.mxJanuary2005Thesenotesprovideanintroductiontothestudyofoptimalgrowthintheone-sectorneoclassicalgrowthmodelincontinuoustime.Themodelisde-velopedu

2、singtheanalogyofRobinsonCrusoelivingonadesertedisland.BoththeHamiltonianmethodandthephasediagramarepresentedandex-plainedonanintuitivelevel.Somefamiliaritywithoptimizationtheoryanddifferentialequations,aswellasathoroughunderstandingofintermediate-levelmic

3、roeconomics,isassumed.Roughdraft.Commentsandcorrectionswouldbewouldbegreatlyappreciated.Thesenotesmaybedistributedfreely,providedthattheyaredistributedintheirentirety.T.Keister:NotesonEconomicGrowthLectureOutline1A“RobinsonCrusoe”Model31.1Technology41.2In

4、tensiveForm61.3Preferences91.4Feasibleconsumptionplans121.5Theoptimalgrowthproblem132TheHamiltonianMethod:142.1A3-steprecipe142.2IntuitionfortheHamiltonianapproach162.3WorkingwiththeFOC243FindingtheSolution263.1Thephasediagram263.2Transversalityandfeasibi

5、lity303.3Drawingtimepaths364ComparativeDynamicsExercises374.1Differentlevelsofimpatience384.2Differentdepreciationrates392TheOptimalGrowthProblem1A“RobinsonCrusoe”ModelWearegoingtostartwithwhatisinmanywaysarathersimplemodel.Itisgoingtolooknothinglikeamode

6、lofamoderneconomy,forinstance.Nevertheless,wearegoingtoworkthroughthismodelcompletely,goingoverallthedetailsofhowtosolveit.Someofthismayalreadybefamiliartoyou,butIwantyoutogooveritcarefullybecauseitisthefoundationofeverythingwewilldointhiscourse.Inadditio

7、n,wewillseelaterthat,byreinterpretingthevariablesinthemodelandmakingafewminorchanges,wecaninterpretthemodelasarepresentationofamodern,market-basedeconomy.Iamgoingtosetupthemodelbytellingastoryaboutafamilyofpeoplewholivealoneinaveryprimitiveenvironment.The

8、goalofthisanalogyistohelpyouseeveryclearlywhatthevariablesandtheequationsinthemodelmean,andtogainsolidintuitionforthesolution.Onceweunderstandthemodelverywell,wewillseethatdifferentinterpretationscanbegiventothese1s