讲义分析英文1

1®CHAPTER8EconomicGrowthIIMANKIW'SMACROECONOMICSMODULESAPowerPointTutorialToAccompany

MACROECONOMICS,

6th.ed.N.GregoryMankiwByMannigJ.Simidian2TechnologicalProgressintheSolowModelTheSolowmodeldoesnotexplaintechnologicalprogressbut,instead,takesitasgivenandshowshowitinteractswithothervariablesintheprocessofeconomicgrowth.3FiveQuestionsToexaminehowanation’spublicpoliciescaninfluencethelevelandgrowthofthecitizens’standardofliving,wemustaskfivequestions.Shouldoursocietysavemoreorless?Howcanpolicyinfluencetherateofsaving?Aretheresometypesofinvestmentthatpolicyshouldencourage?Whatinstitutionsensurethattheeconomy’sresourcesareputtotheirbestuse?5)Howcanpolicyincreasetherateoftechnologicalprogress?TheSolowmodelprovidesthetheoreticalframeworkwithinwhichweconsidertheseissues.4AddingtheEfficiencyofLabor"E"Toincorporatetechnologicalprogress,theProductionFunctionisnowwrittenas:

Y=F(K,L

E)ThetermL

Emeasuresthenumberofworkers.ThistakesintoaccountthenumberofworkersL

andtheefficiencyofeachworker,E.ItstatesthattotaloutputYdependsoncapitalKandworkersLE.TheessenceofthismodelisthatincreasesinE(efficiency)areanalogoustoincreasesinL

(numberofworkers).Inotherwords,asingleworker(iftwiceasproductive)canbethoughtofastwoworkers.L

Edoublesandtheeconomybenefitsfromtheincreasedproductionofgoodsandservices.5Labor-AugmentingTechnologicalProgressCapital

perworker,kk*TheSteadyStateInvestment,sf(k)(d+n+g)k

TechnologicalprogresscausesEtogrowattherateg,andLgrowsatratensothenumberofworkersL

Eisgrowingatraten+g.Now,thechangeinthecapitalstockperworkeris:Dk=i–(d+n+g)k,whereiisequaltosf(k).Note:k=K/LEandy=Y/(L

E).So,y=f(k)isnowdifferent.Also,whenthegtermisadded,gkisneededtoprovidedcapitaltonew“effectiveworkers”createdbytechnologicalprogress.sf(k)6Labor-augmentingtechnologicalprogressatrategaffectstheSolowgrowthmodelinmuchthesamewayasdidpopulationgrowthatraten.Nowthatkisdefinedastheamountofcapitalpereffectiveworker,increasesinthenumberofeffectiveworkersbecauseoftechnologicalprogresstendtodecreasek.

Inthesteadystate,investmentsf(k)exactlyoffsetsthereductionsinkbecauseofdepreciation,populationgrowth,andtechnologicalprogress.Important…7Capitalpereffectiveworkerisconstantinthesteadystate.Becausey=f(k),outputpereffectiveworkerisalsoconstant.Buttheefficiencyofeachactualworkerisgrowingatrateg.So,outputperworker,(Y/L=yE)alsogrowsatrateg.TotaloutputY=y(EL)growsatraten+g.Onlytechnologicalprogresscanexplainsustainedgrowthandpersistantlyrisingstandardsofliving.TheEffectsofTechnologicalProgress8

Steady-stateconsumptionismaximizedif MPK=d+n+g, rearranging,MPK-d=n+g.Thatis,attheGoldenRulelevelofcapital,thenetmarginalproductofcapital,MPK-d,

equalstherateofgrowthoftotaloutput,n+g.Becauseactualeconomiesexperiencebothpopulationgrowthandtechnologicalprogress,wemustusethiscriteriontoevaluatewhethertheyhavemoreorlesscapitalthantheywouldattheGoldenRulesteadystate.TheintroductionoftechnologicalprogressalsomodifiesthecriterionfortheGoldenRule.TheGoldenRulelevelofcapitalisnowdefinedasthesteadystatethatmaximizesconsumptionpereffectiveworker.So,wecanshowthatsteady-stateconsumptionpereffectiveworkeris:

c*=f(k*)-(d+n+g)k*9Steady-stateGrowthRatesintheSolowModelWithTechnologicalProgressVariableSymbolSteady-StateGrowthRateCapitalpereffectiveworkerk=K/(EL)0Outputpereffectiveworker y=Y/(EL)=f(k)0OutputperworkerY/L=yE

gTotaloutput Y=y(EL)

n+g10FromGrowthTheorytoGrowthEmpiricsSofarwehaveintroducedtechnologicalprogressintotheSolowmodeltoexplainsustainedgrowthinstandardsofliving.Let’snowdiscusswhathappenswhentheorymeetsfacts.11BalancedGrowthAccordingtotheSolowmodel,technologicalprogresscausesthevaluesofmanyvariablestorisetogetherinthesteadystateThispropertyiscalledbalancedgrowth.Inthesteadystate,outputperworker,Y/L,andcapitalstockperworker,K/L,bothgrowatrateg,whichistherateoftechnologicalprogress.ThisisconsistentwithU.S.datainthatghasbeenabout2percentconsistentlyoverthepast50years.Technologicalprogressalsoaffectsfactorprices.Therealwagegrowsattherateoftechnologicalprogress,buttherealrentalpriceofcapitalremainsconstantovertime.Again,overthelast50years,therealwagehasincreasedby2percentandhasincreasedbyaboutthesameasrealGDP.Yet,therealrentalpriceofcapital(realcapitalincomedividedbythecapitalstock)hasbeenaboutthesame.12ConvergenceThepropertyofcatch-upiscalledconvergence.

Ifthereisnotconvergence,countriesthatstartoffpoorarelikelytoremainpoor.TheSolowmodelmakespredictionsaboutwhenconvergenceshouldoccur.Accordingtothemodel,whethertwoeconomieswillconvergedependsonwhytheydifferinthefirstplace(i.e.,savingsrates,populationgrowthrates,andhumancapitalaccumulation).13FactorAccumulationVersusProductionEfficiencyDifferencesinincomearearesultofeither:1)Factorsofproductionsuchasthequantitiesofphysicalandhumancapital2)EfficiencywithwhicheconomiesusetheirfactorsofproductionPutsimply,workersinapoorcountryeitherdon’thavethetoolsandskills,ortheyarenotputtingtheirtoolsandskillstothebestuse.14KeyQuestionIntermsoftheSolowmodel,thecentralquestioniswhetherthelargegapbetweentherichandpoorisexplainedbydifferencesincapitalaccumulation,ordifferencesintheproductionfunction.15Thesavingsratedeterminesthesteady-statelevelsofcapitalandoutput.OneparticularsavingrateproducestheGoldenRulesteadystate,whichmaximizesconsumptionperworker.Let’susetheGoldenRuletoanalyzetheU.S.savingrate.CompareMarginalproductofcapitalnetofdepreciation(MPK–d)Growthrateoftotaloutput(n+g)RecallthatattheGoldenRulesteadystate,(MPK–d)=(n+g)

16AmountofcapitalintheGoldenRulesteadystateIftheeconomyisoperatingwithlesscapitalthanintheGoldenRulesteadystate,then(MPK–d>n+g)IftheeconomyisoperatingwithmorecapitalthanintheGoldenRulesteadystate,then(MPK–d<n+g)17U.S.EconomyMarginalproductofcapitalnetofdepreciation(MPK–d)Growthrateoftotaloutput(n+g)TomakethiscomparisonfortheU.S.economy,weneedtoestimatethegrowthrateofoutput(n+g)andanestimateofthenetmarginalproductofcapital(MPK–d).U.S.GDPgrowsatabout3percentperyear,so,n+g=0.03.Wecanestimatethenetmarginalproductofcapitalfromthefollowingfacts:18Wesolvefortherateofdepreciationdbydividingequation2byequation1:dk/k=(0.1y)/(2.5y)d=0.04Andwesolveforthemarginalproductofcapital(MPK)

bydividingequation3byequation1:(MPK

k)/k=(0.3y)/(2.5y)MPK=0.12

1)Thecapitalstockisabout2.5timesoneyear’sGDP,ork=2.5y2)Depreciationofcapitalisabout10percentofGDP,ordk=0.1y3)Capitalincomeisabout30percentofGDP,orMPK

k=0.3yThus,about4percentofthecapitalstockdepreciateseachyear,andthemarginalproductofcapitalisabout12percentperyear.Thenetmarginalproductofcapital,MPK–d,isabout8percentperyear.19Wecannowseethatthereturnstocapital(MPK–d=8percentperyear)iswellinexcessoftheeconomy’sgrowthrate(n+g=3percentperyear).ThisindicatesthatthecapitalstockintheU.S.economyiswellbelowtheGoldenRule-level.Inotherwords,iftheUnitedStatessavedandinvestedahigherfractionofitsincome,itwouldgrowfasterandeventuallyreachasteadystatewithhigherconsumption.20ChangingtheRateofSavingPublicsavingisthedifferencebetweenwhatthegovernmentreceivesintaxrevenueminuswhatitspends.Whenspending>revenue,itisabudgetdeficitWhenspending<revenue,itisabudgetsurplusPrivatesavingisthesavingdonebyhouseholdsandfirms.21EstablishingtheRightInstitutionsNationsmayhavedifferentlevelsofproductivityinpartbecausetheyhavedifferentinstitutionsthatgoverntheallocationoftheirscareresources.Forexample,anation’slegaltraditionisaninstitution.Otherexamplesarethequalityofthegovernmentitselfandthelevelofcorruptionthatexistswithinthepoliticalinfrastructure.22EncouragingTechnologicalProgressTheSolowmodelshowsthatsustainedgrowthinincomeperworkermustcomefromtechnologicalprogress.TheSolowmodel,however,takestechnologicalprogressasexogenous,andthereforedoesnotexplainit.23BeyondtheSolowModel:EndogenousGrowthTheoryTheEndogenousGrowthTheoryrejectsSolow’sbasicassumptionofexogenoustechnologicalchange.24TheBasicModelStartwithasimpleproductionfunction:Y=AK,whereYisoutput,Kisthecapitalstock,andAisaconstantmeasuringtheamountofoutputproducedforeachunitofcapital(noticingthisproductionfunctiondoesnothavediminishingreturnstocapital).OneextraunitofcapitalproducesAextraunitsofoutputregardlessofhowmuchcapitalthereis.ThisabsenceofdiminishingreturnstocapitalisthekeydifferencebetweenthisendogenousgrowthmodelandtheSolowmodel.Let’sdescribecapitalaccumulationwithanequationsimilartothosewe’vebeenusing:DK=sY-dK.Thisequationstatesthatthechangeinthe