中级宏观经济管理学及财务知识分析规划.pptx
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中级宏观经济管理学及财务知识分析规划.pptx
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Chapter6EconomicGrowth:
MalthusandSolowTheMalthusianModelofEconomicGrowthMalthusargued:
advancesinthetechnologyforproducingfoodincreasedpopulationgrowthnoincreaseinthestandardoflivingunlessthereweresomelimitsonpopulationgrowthAdynamicmodelwithmanyperiodsConfineattentiontowhathappensinthecurrentperiodandthefutureperiodAggregateproductionfunctionwithconstantreturnstoscale:
(1)whereiscurrentaggregateoutputiscurrentfixedsupplyoflandiscurrentlaborThereisnoinvestmentandnogovernmentspendingAssumeeachpersoniswillingtoworkatanywageandhasoneunitoflabortosupply(anormalization),sothatinEquation
(1),isboththepopulationandthelaborinputY),(NLzFYLNNSupposepopulationgrowthdependsonthequantityofconsumptionperworker
(2)whereisthepopulationinthefuture(next)periodisanincreasingfunctionisaggregateconsumptionsothatiscurrentconsumptionperworker,mainlyduetothefactthathigherfoodconsumptionperworkerreducesdeathratesthroughbetternutrition)(NCgNNNgCNC0)/(/NCddgAllgoodsproducedareconsumed,soC=Y.Hence,(3)ThenuseEquation(3)tosubstituteforCinEquation
(2):
(4)Theconstant-returns-to-scalepropertyoftheproductionfunctionimpliesthatAftermultiplyingeachsidebyN,Equation(4)canberewrittenas(5),(NLzFYC),(NNLzFgNN)1,(),(NLzFNNLzFNYNNLzFgN)1,(PopulationgrowthdependsonconsumptionperworkerintheMalthusianmodelisthesteadystateforthepopulationIfthenpopulationincreasesIfthenpopulationdecreases*N*NNNN*NNNNSteadyStateAnalysisoftheMalthusianModelRecallLetting,andThenfromEquation
(2):
Inthesteadystate,sothencanbedetermined)1,(NLzFNY)(lzfyc)(/cgNNNYyNLlNCc*NNN1NN*cInpanel(b),isdeterminedInpanel(a),isdeterminedfromtheper-workerproductionfunctionSteadystatepopulationisgivenby*c*l*lLNTheSteadyStateEffectsofanIncreaseinzSupposetheeconomyisinitiallyinasteadystate,with,whichthenincreasesonceandforalltimetounchangedfallsSteadystatepopulationincreases1z2z*c*l*NPopulationincreasesovertimetoitssteadystatevalueincreasesattimeTconsumptionperworkerincreasesthendeclinetoitssteadystatevalueAnotherexample:
populationcontrolbothc*andl*increase.zHowUsefulistheMalthusianModelofEconomicGrowth?
BeforetheIndustrialRevolutioninabout1800:
economicgrowthconsistentwiththeMalthusianModelFromtheperspectiveoftheearly21stcentury:
MalthuswaswrongWhy?
-Didnotallowfortheeffectofincreasesinthecapitalstockonproduction,and-DidnotaccountforalltheeffectsofeconomicforcesonpopulationgrowthTheSolowModel:
ExogenousGrowthConsumers:
Thepopulationgrowsovertime:
whereisthepopulationinthefutureperiodistherateofgrowthinthepopulationAssumethatconsumersconsumeaconstantfractionofincomeineachperiod:
whereiscurrentconsumptionistheaggregatesavingsrateNnN)1(YsC)1(NnCsTheRepresentativeFirm:
Constantreturnsproductionfunctionwithcapitalandlaborinputs:
whereisoutputperworkeriscapitalperworkerwhereisconstantdepreciationrateand)(kzfyykd10dIKdK)1(CompetitiveEquilibrium:
Equilibriumcondition:
ICYKdNKszFK)1(),(nkdnkszfk1)1
(1)(),(NKszFIQuantityofcapitalperworkerconvergestoaconstant,quantityofoutputperworkerconvergestoaconstant,Ifs,nandzareconstant,realincomeperworkercannotgrownobettermentinlivingstandardsSteadyStateAnalysisInthelongrun,whentheeconomyconvergestothesteadystatequantityofcapitalperworker,k*,allaggregatequantities(K,Y,IandC)growattheraten.*k)(*kzfyAnalysisoftheSteadyStateInthesteadystate,byrearranging,nkdnkszfk1)1
(1)(*)()(kdnkszfComparativeStatics:
AnIncreaseintheSavingsRateThecurve,shiftsuplevelsofcapitalperworkerandoutputperworkerarehigherBUTthereisnoeffectonthegrowthratesofaggregatevariables)(*kszfBeforetimeT,aggregateoutputisgrowingattheconstantrate,SavingsrateincreasesattimeTAftertimeT,outputthenconvergesinthelongruntoanewhighersteadystategrowthpathnConsumptionperWorkerandGoldenRuleCapitalAccumulationConsumptionperworkerinthesteadystateis(goldenrulequantityofcapitalperworker)givesthemaximumconsumptionperworker,Propertyofthegoldenrule:
*)()(kdnkzfc*grk*cdnMPkComparativeStatics:
AnIncreaseinLaborForceGrowthAnincreaseinthelaborforcegrowthrate(n)causesadecreaseinthequantityofcapitalperworkerandoutputperworkerGrowthratesinaggregateoutput,aggregateconsumptionandaggregateinvestmentincreaseComparativeStatics:
AnIncreaseinTotalFactorProductivityTheSolowModelpredictsthatacountrysstandardoflivingcancontinuetoincreaseinthelongrunonlyiftherearecontinuingincreasesintotalfactorproductivity(z)MathematicalSolution(Appendixp.636)Inthesteadystate,Hence,Thesignisambiguous,sothatconsumptionperworkercouldincreaseordecreasewithanincreaseinthesavingsrate*)()(kdnkzfcdsdkdnkzfdsdc*)(ThegoldenrulesteadystatequantityofcapitalperworkersolvestheproblemsolvesorAs,)()(max*kdnkzfk*grk0)()(*kdnkszf)()(*grgrgrkzfkdns0)(*dnkfzgr0)()(*kkdnkzfRecallinthesteadystate,TotallydifferentiatingEquation(A.1),wegetHence,solvingfortheappropriatederivatives,0)()(*kdnkszf0)()(*dnkszfkzfdsdk0)(*dnkszfkdndk0)()(*dnkszfksfdzdk0)()()(*dzksfdnkdskzfdkdnkfszGrowthAccountingIfaggregaterealoutputistogrowovertime,itisnecessaryforafactororfactorsofproductiontobeincreasingovertime,orfortheretobeincreasesintotalfactorproductivity.GrowthAccounting:
anexercisetomeasurehowmuchofthegrowthinaggregateoutputoveraperiodoftimeisaccountedforbygrowthineachoftheinputstoproductionandbyincreasesintotalfactorproductivityGrowthAccountingGrowthaccountingstartsbyconsideringtheaggregateproductionfunctionfromtheSolowgrowthmodel,Cobb-Douglasproductionfunctionisagoodanalyticaltoolforgrowthaccounting.Theproductionfunctiontakestheformwhere),(NKzFYaaNKNKF1),(10aGrowthAccountingSupposeweset=0.36,thentheproductionfunctionisIfwehavemeasuresofaggregateoutput,thecapitalinput,andthelaborinput,thentotalfactorproductivitycanbemeasuredasaresiduala64.036.0NzKY64.036.0NKYzKNzYAGrowthAccountingExerciseThetableshowshowthegrowthinthecapitalstock,inemployment,andintotalfactorproductivitycontributetothegrowthinrealoutputIncreasesinmeasuredtotalfactorproductivitycouldbetheresultof:
-newinventories-goodweather-newmanagementtechniques-favorablechangesingovernmentregulations-decreasesintherelativepriceofenergy(anyotherfactorthatcausesmoreaggregateoutputtobeproducedgiventhesamequantitiesofaggregatefactorinputs)SolowResidualsandtheProductivitySlowdownTotalfactorproductivitywasveryhighthroughoutmostofthe1950sand1960sDramaticdecreaseintotalfactorproductivitygrowthbeginninginthelate1960sandcontinuingintothe1980s:
productivityslowdownSomeReasonsfortheProductivitySlowdown1.MeasurementProblem:
manufacturinggoodsservices2.Increasesintherelativepriceofenergy:
measurementproblemininputs3.3.Thecostsofadoptingnewtechnology:
informationrevolutionandlearningTheCyclicalPropertiesofSolowResidualsFluctuationsinSolowresidualsabouttrendarehighlypositivelycorrelatedwiththefluctuationsinGDPabouttrendFluctuationsintotalfactorproductivitycouldbeanimportantexplanationforwhyGDPfluctuates(RBCtheory)
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- 中级 宏观经济 管理学 财务 知识 分析 规划