A theory of economic growth

398 Pages·2002·3.267 MB·English

by  de Croix D.l., Michel P.

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ATheoryofEconomicGrowth
Thisbookprovidesanin-depthtreatmentoftheoverlappinggenera-
tionsmodelineconomicsincorporatingproduction.Inchapter1,the
authorsinvestigatecompetitiveequilibriaandcorrespondingdynamics:
existenceanduniquenessofequilibrium,globaldynamicsofcapital(in-
cludingpovertytraps),andvariousextensionsofthemodel.Chapter2
analyzestheoptimalityofallocationsinthisframework,usingboththe
value function and marginal approaches. Optimality with unbounded
growth is also analyzed. Policy issues, including the Second Welfare
Theorem, pensions, government spending, and optimal taxation, are
discussedinchapter3.Thenotionofpublicdebtisintroducedinchap-
ter4,andthesustainabilityofpolicieswithbudgetdeficits/surplusesis
examined.Thelastchapterpresentsextensionsofthemodelincluding
altruism,education/humancapital,andhabitformation.Methodolog-
icalemphasisisputonusinggeneralpreferencesandtechnologies,on
theglobalstudyofdynamicaspectsofthemodel,andonfurnishingad-
equatetoolstoanalyzepoliciesinvolvinginter-generationaltransfers.
David de la Croix is Professor of Economics at the Universite´
catholique de Louvain and Research Associate of the National Fund
forScientificResearchinBelgium.Hehasservedasavisitingprofes-
sorattheUniversityofCalifornia,LosAngeles.ProfessordelaCroix’s
researchinterestsinmacro-economicsincludedemographics,overlap-
ping generations and human capital, and growth and cycles. He has
published articles in leading refereed journals such as the Journal of
EconomicTheory,EuropeanEconomicReview,JournalofEconomic
DynamicsandControl,JournalofAppliedEconomics,ReviewofEco-
nomicDynamics,andJournalofPopulationEconomics.
PhilippeMichelisProfessorofEconomicsatGREQAM,Universite´de
laMe´diterrane´e(Aix-MarseilleII)andaseniormemberofInstitutUni-
versitairedeFrance.HetaughtpreviouslyattheUniversite´ deParisI.
The author or coauthor of six books, most recently Monnaie, Dette,
etCapital(1999),ProfessorMichel’sresearcharticleshaveappearedin
prominentjournalssuchasEconometrica,ReviewofEconomicStudies,
JournalofEconomicTheory,JournalofOptimizationTheoryandAp-
plications,andInternationalEconomicReview.Hisresearchandteach-
ing focus on politics and modeling in macroeconomics and dynamic
theory.
FurtherPraiseforATheoryofEconomicGrowth
“Theoverlappinggenerationsmodelandtheinfinitelylivedordynasticmodelare
thetwoworkhorsesofmodernmacroeconomics.DeLaCroixandMichelhave
writtenawonderfullyaccessiblegraduatetextbookontheoverlappinggenerations
model.Theycarefullytakestudentsthroughessentiallyeveryvariantofthemodel,
provealargenumberofknownresults,andofferafewnewonesaswell.Thisbook
isanessentialadditionasateachingtoolandaninvaluablereferenceonevery
economist’sshelf.”
–V.V.Chari,UniversityofMinnesota
“Inrecentdecadesoverlappinggenerationmodelshavebecomeacentral
frameworkofanalysisintheresearchofeconomicgrowth.Theauthorspresenta
comprehensiveandlucidexpositionofthedynamicstructureofthebasic
overlappinggenerationfeatureswithproduction.Highlyrecommendedfor
researchersandgraduatestudentsinthefieldsofgrowththeoryanddynamic
macroeconomics.”
–OdedGalor,BrownUniversity
“Someofthemosthotlydebatedgovernmentpoliciesarethosethatinvolve
redistributionacrossgenerations,suchassocialsecurityandpubliceducation.Dela
CroixandMichelprovideamanualofeconomictoolsforevaluatingthesesortsof
policiesbasedonsimpleoverlappinggenerationsmodels.Theirpresentationof
thesemodelsstrivestocombineapplicabilityforpolicyanalysiswithasolid
foundationindynamicgeneralequilibriumtheory.Theirbookshouldbeofuseto
economistsfromthelevelofadvancedundergraduatestudentstoresearchersand
teachers.”
–TimothyJ.Kehoe,UniversityofMinnesotaandFederalReserve
BankofMinneapolis
A Theory of Economic Growth
Dynamics and Policy in
Overlapping Generations
DAVIDDELACROIX
IRES,Universite´catholiquedeLouvain,Belgium
PHILIPPEMICHEL
GREQAM,Universite´delaMe´diterrane´e,France
         
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
  
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz de Alarcón 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
http://www.cambridge.org
©David de la Croix and Philippe Michel 2004
First published in printed format 2002
ISBN 0-511-02891-1 eBook (Adobe Reader)
ISBN 0-521-80642-9 hardback
ISBN 0-521-00115-3 paperback
ToAnna,Cle´mence,Elo¨ıse,Franc¸oise,
Mathieu,The´re`se,Timothe´e,
andallfuture,yetunborn,generations.

Contents
Introduction pagexiii
OverlappingGenerationsandMacro-economics xiii
OverlappingGenerationsinOtherFields xv
OutlineoftheBook xvi
Acknowledgments xvii
1 CompetitiveEquilibria 1
1.1 TheModel 1
1.1.1 Two-period-livedIndividuals 2
1.1.2 Neo-classicalTechnology 3
1.1.3 Firms 4
1.2 MainAssumptions 4
1.2.1 TheAssumptionsontheUtilityFunction 4
1.2.2 TheAssumptionsontheProductionFunction 6
1.3 TheBehavioroftheAgentsatPeriodt 10
1.3.1 TheYoungIndividuals 10
1.3.2 TheInter-temporalElasticityofSubstitution 11
1.3.3 ThePropertiesoftheSavingsFunction 12
1.3.4 TheOldIndividuals 15
1.3.5 TheFirms 15
1.4 TheTemporaryEquilibrium 16
1.5 TheInter-temporalEquilibriumwithPerfectForesight 19
1.5.1 ExistenceofEquilibria 20
1.5.2 UniquenessoftheInter-temporalEquilibrium 22
1.6 CapitalDynamicsataRationalInter-temporalEquilibrium 27
1.6.1 SteadyStatesandStability 27
1.6.2 Dynamics 29
1.6.3 TheBehaviorNear0 34
1.6.4 AQuickLookattheEmpiricsofGrowth 37
vii
viii Contents
1.7 ComparisonofMyopicandPerfectForesight 39
1.7.1 TheSteadyStates 41
1.7.2 LocalStability 42
1.7.3 UniquenessoftheSteadyState 43
1.8 ApplicationsandExtensions 45
1.8.1 MyopicandPerfectForesightinanExample 45
1.8.2 ADemographicShock 50
1.8.3 Non-separableUtilityFunction 51
1.8.4 HomotheticPreferences 53
1.8.5 HeterogeneousAgents 54
1.8.6 TechnicalProgress 56
1.8.7 ImperfectCreditMarket 57
1.8.8 Three-period-livedHouseholds 64
1.8.9 BorrowingConstraintsintheThree-periodModel 66
1.9 Conclusion 70
2 Optimality 72
2.1 OptimalityofStationaryPaths 73
2.1.1 FeasibleLong-runCapitalStock 74
2.1.2 TheOptimalStationaryPath:TheGoldenAge 77
2.1.3 Under-andOver-accumulationofCapital 80
2.2 OptimalityoftheDynamics 82
2.2.1 DynamicEfficiency 82
2.2.2 ParetoOptimalityofDynamics 86
2.3 ThePlanningProblem 90
2.3.1 TheObjectiveFunction 91
2.3.2 PropertiesoftheValueFunction 92
2.3.3 ExistenceandMonotonicityofOptimalPaths 95
2.3.4 LimitoftheOptimalPathandOptimal
SteadyState 99
2.4 MarginalAnalysisofOptimalSolutions 101
2.4.1 TheOptimalityConditions 102
2.4.2 ThePlanner’sStationarySolution 106
2.4.3 LocalDynamics 106
2.4.4 AGraphicalExposition 108
2.5 UnboundedOptimalGrowth 112
2.5.1 ExistenceofOptimalPathsWhenσ >1 112
2.5.2 ExistenceofOptimalPathsWhenσ <1(andγ ≥1) 114
2.5.3 ExistenceofOptimalPathsWhenσ =1 115
2.5.4 GeneralResult 116
2.5.5 TheLong-runGrowthRate 116
2.6 ApplicationsandExtensions 117
2.6.1 PropertiesofthePolicyFunctionsWhen f(0)>0 118
2.6.2 Application:TheOptimalSpeedofConvergence 120