经济增长理论

Chapter3TheoryofEconomicGrowth主讲：陈忠斌（博士）武汉大学经济发展研究中心武汉大学经济与管理学院ChapterHighlightsEconomicgrowthisduetogrowthininputs,suchaslaborandcapital,andtoimprovementsintechnology.Capitalaccumulatesthroughsavingandinvestment.Thelong-runlevelofoutputperpersondependspositivelyonthesavingsrateandnegativelyintherateofpopulationgrowth.Theneoclassicalgrowthmodelsuggeststhatthestandardoflivinginpoorcountrieswilleventuallyconvergetothelevelinwealthycountries.ChapterHighlightsRatesofeconomicgrowthvarywidelyacrosscountriesandacrosstime.Endogenousgrowththeoryattemptstoexplaingrowthratesasfunctionsofsocietaldecisions,inparticularsavingsrates.Incomeinpoorcountriesappearstobeconvergingtowardincomelevelsofrichcountries,butatextraordinarilyslowrates.1.LongTermGrowthinChina仍然属于中低收入国家.发展不平衡：2003年，深圳市的人均GDP为6510美元，是全国平均值的6倍总量大，人均量低。总量排名第4，人均量排名第136。生活水准与美国相差100年（反映了中国经济增长质量的欠缺）。粗放式经济增长为主：主要依靠增加物质资源消耗和劳动力投入带动GDP增长。加快转变经济发展方式,推动产业结构优化升级.坚持扩大国内需求特别是消费需求的方针,促进经济增长由主要依靠投资、出口拉动向依靠消费、投资、出口协调拉动转变；由主要依靠第二产业带动向依靠第一、第二、第三产业协同带动转变；由主要依靠增加物质资源消耗向主要依靠科技进步、劳动者素质提高、管理创新转变。发展现代产业体系,大力推进信息化与工业化融合,促进工业由大变强,振兴装备制造业,淘汰落后生产能力；提升高新技术产业,发展信息、生物、新材料、航空航天、海洋等产业；发展现代服务业，提高服务业比重和水平；加强基础产业基础设施建设，加快发展现代能源产业和综合运输体系。(资源来源：中国共产党第17大报告，2007年10月15日)TheVarietyofGrowthExperiencesCopyright©2004South-Westernreturn亚当•斯密常常被认为是现代经济学之父。其《国民财富的性质和原因的研究》于1776年出版。为什么各国的发展速度不同这一问题从那时起一直是经济探索的最重要问题。AdamSmithandincreasingreturns斯密最重要的贡献之一是把以劳动分工为基础的报酬递增概念引入了经济学。他把劳动分工看作是社会经济的基础，否则每个人都变成了RobinsonCrusoe,生产自己所需要的一切。正是以劳动分工为基础的报酬递增概念，成为了对作为自行产生过程的经济进步抱有乐观主义观点的核心。报酬递增意味着劳动生产率和人均收入随着产出和就业扩张而上升；而报酬递减意味着劳动生产率和人均收入下降，劳动就业限制在某一点上－－在这一点之后，劳动的边际产品下降到生存工资的水平。报酬递增在大多数工业活动中普遍存在，而报酬递则是农业和采矿业等以土地为基础的活动的特点，因为土地是一个固定的生产要素。(A.P.Thirlwall,GrowthandDevelopment(1999),p83-86.)Appendix:ClassicalgrowththeoryTheclassicalpessimists斯密以后对经济发展过程的古典主义观点基本上悲观主义的。它集中讨论迅速的人口增长与由农业报酬递减和成本上升所造成的粮价上升对工业利润率施加的影响。最大的悲观主义者之一是托马斯•马尔萨斯(ThomasMalthus)。马尔萨斯的著作分为两部分：他的人口论和他的维持有效需求(effectivedemand)对发展的重要性的论述－－“有效需求”这个概念后来被凯恩斯所借用。事实上，马尔萨斯是强调需求对决定产出的重要性的唯一的古典经济学家－－所有其他古典经济学家都信奉萨伊定律Say’sLaw:supplycreatesitsowndemand,sothatthelevelandgrowthofoutputisafunctionofthesupplyofphysicalinputsalone.(A.P.Thirlwall,GrowthandDevelopment(1999),p86.)Appendix:ClassicalgrowththeoryTheclassicalpessimistsMalthusisbestknown,however,forhisEssayonthePrincipleofPopulation(1798),inwhichheclaimedthatthereisa‘constanttendencyinallanimatedlifetoincreasebeyondthenourishmentpreparedforit’.(A.P.Thirlwall,GrowthandDevelopment(1999),p86-87.)Thatfoodproductiononlygrowsatanarithmeticrateimplies,ofcourse,diminishingreturnstoagriculture.Theimbalancebetweenpopulationgrowthandgrowthofthefoodsupplywouldleadtothepercapitaincomeofcountriesoscillating摆动aroundthesubsistencelevel,orbeingcaughtinwhatisnowsometimescalleda‘low-levelequilibriumtrap’.Anyincreasesinpercapitaincomebroughtaboutbytechnicalprogressleadtomorebirths,whichthenreducespercapitaincomebacktosubsistencelevel.Earlydevelopmentmodelsofthe‘bigpush’weredesignedtolifteconomiesfromthistrap.

TheclassicalpessimistsDavidRicardowasanotherofthegreatclassicalpessimists.In1817hepublishedhisPrinciplesofPoliticalEconomyandTaxation,inwhichhepredictedthatcapitalisteconomieswouldendupinanastationarystate,withnogrowth,alsoduetodiminishingreturnsinagriculture.(A.P.Thirlwall,GrowthandDevelopment(1999),p87-89.)FinallyweturntoKarlMarx,famousforhisbookDasKapital(1867),andhispredictionofthecollapseofcapitalism.LetusbrieflyconsiderMarx’smodelandhispredictionofcrisis.Grossoutputconsistsofthreeelements:Variablecapitalorthewagebill(v)Constantcapital(c),thatis,plantandmachinery.Surplusvalueorprofit(s)Thewageoflabouraredeterminedbytheminimumsubsistencelevel,andsurplusvalueisthedifferencebetweenoutputperworkerandminimumwageperworker.Therateofsurplusvalue,orwhatMarxcalledthe‘degreeofexploitation’,isgivenbys/v.Therateofprofitisgivenbytheratioofsurplusvaluetototalcapital,thatisWheretheratioofconstanttovariablecapital(c/v)isdefinedasthe‘organiccompositionofcapital’.Astechniquesofproductionbecomemorecapital-intensive,the‘organiccompositionofcapital’risesthroughtime,andasitdoessotherateofprofitfallsunlesssurplusvaluerises.Whilethereisnolimittotheriseinc/v,however,thereisalimittos/v.Marxforesawnomajorproblemaslongassurpluslabourexiststokeepwagesdown,buthepredictedthatascapitalaccumulationtakesplace,the‘reservearmyoflabour’,ashecalledit,woulddisappear,drivingwagesupandprofitsdown.Thecapitalist’sresponseistheneithertoattempttokeepwagesdown,leadingtothe‘immiseratinofworkers’andsocialconflict,ortosubstitutemorecapitalforlabour,whichwouldworsentheproblembyraisingc/v.

(A.P.Thirlwall,GrowthandDevelopment(1999),p88-89.)3.1.1.TheHarrod-DomargrowthmodelHarrod’soriginalmodelisadynamicextensionofKeynes’staticequilibriumanalysis.InKeynes’GeneralTheory,heconditionforincomeandoutputtobeinequilibrium(intheclosedeconomy)isthatplanstoinvestequalplanstosave.3.1.增长理论的模型分析

Whatifthepopulationisgrowingaswell?Inthiscasewemustmassage(3.16)alittlebittogetitintopercapitaterms.Letsy(t)=[Y(t)]/[P(t)]denotepercapitaincome.Thensimplybydividingbothsidesof(3.16)byP(t),weseethatSource:DebrajRay(1998),DevelopmentEconomics,PrincetonUniversityPress,Appendix3.A.1,pp90-91.AlsoRay:“What’sNewinDevelopmentEconomics?”–availableat/user/debraj/Papers/AmerEcon.pdf.AndRay:IntroductiontoAReaderinDevelopmentEconomics–availableat/user/debraj/Papers/DevReaderIntro.pdf.此式就是哈罗德-多马增长模型的基本公式。g表示国民收入增长率或经济增长率，它等于储蓄倾向除以增量资本-产出比。该模型表明，经济增长率是由储蓄倾向和资本-产出比共同决定的，它与储蓄倾向成正比关系，与资本-产出比成反比关系。如果资本-产出不变，经济增长率就决定于储蓄倾向或储蓄率，储蓄倾向越高，则经济增长率越高。如果储蓄倾向不变，资本-产出比越低，则经济增长率越高。哈罗德-多马增长模型的批评:批评主要是针对它的假定前提：这个模型是建立在储蓄能全部转化为投资的假定之上的。这对发展中国家是特别不现实的。实际上储蓄转化为投资需要具备很多条件：(1)发展中国家往往存在着制度缺陷；(2)缺少投资所需的机器设备等物质资本品、原材料以及关键的技术、而且由于外汇短缺也不可能都靠进口来解决；(3)社会基础设施(交通通讯,电力等)十分落后，对投资造成了重大的障碍。这个模型是建立在资本-产出比不变的假定上的。实际上，随着经济发展，资本-产出比不可能不变。发展中国家为了加速工业化和实行进口替代发展战略，常常把大量的资金投入资本密集度很高的工业上，如汽车、钢铁等部门。因此。增量资本—产出比一般是趋于上升的。3.这个模型只有资本（储蓄）一个变量，这实际上暗含地假定资本—劳动比例是不变的，即资本与劳动同比例地增加，资本增加百分之一，劳动也必须增加百分之一。这也是不现实的。的确，发展中国家的劳动力资源是丰富的，但是，丰富的是无技术的、非熟练的劳动者，而受过良好教育和训练的技术人员和称职的管理者却是非常稀缺的。因此，即使投资所需的资本品能够得到满足，因缺乏有技能的劳动力和合格的管理者而不能形成实际投资，或者形成了实际投资，投资效率也是十分低下的。此外，假定资本－劳动比不变还意味着不能用劳动来代替资本，这不仅不符合实际，而且是十分有害的。因为发展中国家劳动力丰富，充分利用剩余劳动力资源是能创造出资本和增加产出的。Exercises(seechapter3,DebrajRay,)(1):Afirmissetuptoproduceandsellcottonshirts.Itbuysplantandmachineryfor$2millionandlandfor$1million,andconstructawarehouseforanother$1million.Eachyear,ithires100workersandpayseachofthem$2,000peryear.Itbuys$600,000worthofcottonfabrictobeusedinmakingtheshirts.Thefirmsells100,000shirtsayear,whichitpricesat$10pershirt.(a)Howmuchprofitdoesthefirmmakeonayearlybasis,ifyoudonotcountitssetupinvestment?(b)Howmuchincomedoesthefirmgenerateeveryyear?(c)Whatisthecapital-outputratioofthefirm?Explain,usingthisexample,whyacapital-outputratiothatexceeds1isperfectlycompatiblewithprofitmaking.Answers:(1)(a)Therunningcostsareforlabor($2000times100)andforcottonfabric,whichis$600,000.Thustotalcostsare$800,000peryear.Totalrevenuesare$1million.Thusprofits,notcountingsetupinvestment,are$200,000peryear.(b)Tofigureoutincomegenerated,wemustcountthewagepaymentstoworkersaswell,whichare$200,000.Thusincomegeneratediswagesplusprofits(therearenorentshere),whichis$400,000peryear.(c)Theoutputofthefirmis$1millionperyear.Thefirm’sinstalledcapitalis$4million.Thereforethecapital-outputratiois4.Noticethatthecapitalequipmentcanbeusedoverandoveragain(thoughitmightdepreciateovertime).Thereforeacapital-outputratiolargerthanoneisperfectlycompatiblewiththenotionofprofitability.3.1.2.TheNeoclassicalProductionFunctionY=F(K,L)Wesaythattheproductionfunctionisneoclassicalifthefollowingthreepropertiesaresatisfied.First,forallK>0andL>0,F(•)exhibitspositiveanddiminishingmarginalproductswithrespecttoeachinput:Second,F(•)exhibitsconstantreturnstoscale:Third,themarginalproductofcapital(orlabor)approachesinfinityascapital(orlabor)goesto0andapproaches0ascapital(orlabor)goestoinfinityTheselastpropertiesarecalledInadaconditions稻田条件,followingInada(1963).TheconditionofconstantreturnstoscaleimpliesthatoutputcanbewrittenasWherek=K/Listhecapital-laborratio,y=Y/Lispercapitaoutput,andthefunctionf(k)isdefinedtoequalF(k,1).Thisresultmeansthattheproductionfunctioncanbeexpressedinintensiveform集约形式

as(RobertJ.Barro&XavierSal-I-Martin,EconomicGrowth,p16-17.)3.1.2.TheNeoclassicalgrowththeoryTherearethreebasicpropositionsofneoclassicalgrowththeory:Inthelong-runsteadystate,thegrowthofoutputisdeterminedbytherateofgrowthofthelabourforceinefficiencyunits,thatis,bytherateofgrowthofthelabourforceplustherateofgrowthoflabourproductivity,andisindependentoftheratioofsavingandinvestmenttoGDP.Thisissobecauseahighersavingsorinvestmentratioisoffsetbyahighercapital-outputratioorlowerproductivityofcapital,becauseoftheneoclassicalassumptionofdiminishingreturnstocapital.(A.P.Thirlwall,GrowthandDevelopment(1999),p94.)Thelevelofpercapitaincome,however,doesdependontheratioofsavingandinvestmenttoGDP.ThelevelofPCYvariespositivelywiththesavings-investmentratioandnegativelywiththerateofgrowthofthepopulation.Givenidenticaltastes(thatis,preferencesforsavingvis-à-visconsumption)andtechnology(productionfunctions)acrosscountries,therewillbeaninverserelationacrosscountriesbetweenthecapital-labourratioandtheproductivityofcapital，sothatpoorcountrieswithasmallamountofcapitalperheadshouldgrowfasterthanrichcountrieswithalotofcapitalperhead,leadingtotheconvergenceofpercapitaincomesandlivingstandardsacrosstheworld.(A.P.Thirlwall,GrowthandDevelopment(1999),p94.)Letusnowconsiderhowthesefundamentalpropositionsarearrivedat.ThebasicneoclassicalgrowthmodelwasfirstdevelopedbyRobertSolowandTrevorSwanin1956,andhasbeenveryinfluentialintheanalysisofgrowtheversince----particularlytheuseoftheaggregateproductionfunction,asweshallcometosee.Themodelisbasedonthreekeyassumptions.Thelabourforcegrowsataconstantexogenousrate,l.Outputisafunctionofcapitalandlabour:Y=F(K,L).Theproductionfunctionrelatingoutputtoinputsexhibitsconstantreturnstoscale,diminishingreturnstoindividualfactorsofproduction,andhasaunitaryelasticityofsubstitutionbetweenfactors.Allsavingisinvested:S=I=sY.Thereisnoindependentinvestmentfunction.Whatthebasicneoclassicalgrowthmodelisdesignedtoshowisthataneconomywilltendtowardsalong-runequilibriumcapital-labourratio(k*)atwhichoutput(orincome)perhead(q*)isalsoinequilibrium,sothatoutput,capitalandlabourallgrowatthesamerate,l.Themodelthereforepredictslong-rungrowthequilibriumatthenaturalrate.(A.P.Thirlwall,GrowthandDevelopment(1999),p95.)Themostcommonlyusedneoclassicalproductionfunctionwithconstantreturnstoscaleistheso-calledCobb-Douglasproductionfunction:Whereistheelasticityofoutputwithrespecttocapital,1-istheelasticityofoutputwithrespecttolabour,andobviously+(1-)=1,thatis,a1percentincreaseinKandLwillleadtoa1percentincreaseinY,whichiswhatismeantbyoutputexhibitingconstantreturnstoscale.

(A.P.Thirlwall,GrowthandDevelopment(1999),p95.)Equationcanalsobewrittenin‘labourintensive’formbydividingbothsidesoftheequationbyLtogiveoutputperheadasafunctionofcapitalperhead:Thisisthe‘labour-intensive’formoftheneoclassicalproductionfunction,andcanbedrawnasinFigure.Thediminishingslopeofthefunctionrepresentsthediminishingmarginalproductofcapital.(A.P.Thirlwall,GrowthandDevelopment(1999),p95.)f(k)ykoyy*kk*Capital-laborratioy=f(k)Figure3-1.PERCAPITAPRODUCTIONFUNCTION(DebrajRay,DevelopmentEconomics,PrincetonUniversitypress,1998,p64.)k(2003)k(2002)k(2004)k*k(1+n)kt+1(1-σ)kt+syFigure3.2-aThedynamicsoftheSolowmodelSource:DebrajRay,DevelopmentEconomics(1998),p66.k(2005)k(2006)y当k<k*,实际人均资本量((1-)k+sy)超过了保持资本－劳动比不变所需要的人均资本量((1+n)k),这时,人均资本和人均产出都将增加。k(2005)k(2004)k(2006)k(1+n)kt+1(1-σ)kt+syFigure3.2-bThedynamicsoftheSolowmodelSource:DebrajRay,DevelopmentEconomics(1998),p66.k*y当k>k*,实际人均资本量[(1-)k+sy]小于为保持资本-劳动比不变所需要的人均资本量(1+n)k,结果是人均资本k和人均产出y都将下降。人均资本的净变化是储蓄超过必需投资的部分：k=sy-(n+d)k稳态定义为k=0,并且在y*和k*的值满足：sy=sf(k*)=(n+d)k*Fig3-3.STEADY-STATEOUTPUTANDINVESTMENT

图3-3的稳态出现在C点.储蓄线与投资需求线相交在C点上.无论在哪里，只要储蓄线高于需求线，资本在增加,经济就在增长。例如，从A点开始，随着时间的推移，经济向右边移动。由于资本的边际产量递减，生产函数与并行的储蓄曲线逐渐变得平直。因为必需的投资线具有不变的正斜率，所以必需的投资线与储蓄线会相交。图3-4中，经济由C点的稳态均衡起步。在C点，储蓄与必需的投资恰好相等.现在人们愿意把收入中的更大部分储蓄起来.这会引起储蓄曲线向上移动到虚线的位置。图3-4中，C点是初始的一个稳态均衡。现在，相对于必需的投资，储蓄增加了，其结果是，储蓄额比保持人均资本不变所需要的投资要多。储蓄多到足以使人均资本量增加。人均资本量将持续增加，直到达到C'点。在C'点，经济已恢复到稳态增长率n。Fig3-4A.Increaseinsavingsratemovesthesteadystateyy*kk*Capitalperheady=f(k)(n+d)ksys'ysy*k**s'y**OOutputperheadFig3-4B.Decreaseintherateofpopulationgrowthincreasethesteady-staterateofgrowthofaggregateoutput.Capitalperheady*kk*y=f(k)(n+d)ksysy*k**yy**OOutputperhead(n'+d)ksy**在规模报酬不变的生产函数条件下,在长期中,储蓄率的增加只是提高人均产出水平和人均资本水平,而不是提高人均产出增长率.(Macroeconomics,8edition,byDornbusch,p57.）Figure3-5.ADJUSTMENTTONEWSTEADYSTATEFigure3-7.EXOGENOUSTECHNOLOGICALCHANGE引进了技术进步因素解决了人均收入的长期增长趋向于零的尴尬局面。但是，问题还没有结束。在新古典增长模型中，技术进步是外生的，也就是说是从外部引入的，与模型中的任何变量没有关系。新古典增长模型假定商品和要素是完全自由流动的。即使假定技术进步率最初在国家间存在很大差距，最终也应该趋于相同。然而，无论是收入水平还是增长率，趋同在全世界都没有发生。而且除了少数几个国家之外，发达国家与发展中国家之间的经济差距在近几十年反而拉大了。Appendix3.1.2..Cobb-DouglasproductionfunctionOneformthatisespeciallypopularistheCobb-Douglasproductionfunction.Thus,theCobb-Douglasformsatisfiesthepropertiesofaneoclassicalproductionfunction.

(RobertJ.Barro&XavierSal-I-Martin,EconomicGrowth,p16-17.)(DebrajRay,DevelopmentEconomics,PrincetonUniversitypress,1998,p91-94.)Appendix3.1.2..Cobb-DouglasproductionfunctionwhereAisapositiveconstant.WhatdoestheCobb-Douglasproductionfunctioncapture?Firstofall,theparameterAisameasureofthedegreeoftechnologicalknowledgeintheeconomy.ThelargerisA,

thelargeristhemagnitudeofoutputforanyfixedcombinationofKandL.WiththeCobb-Douglasfunction,

Acanalso

beinterpretedasameasureoftheproductivityoflabor.Toseethis,notethatequationcanberewrittenasThenELisjusttheamountofeffectiveunitsoflaborusedinproduction.3.1.3.TheNew(endogenous)GrowththeoryThe‘new’growththeoryrelaxestheassumptionofdiminishingreturnstocapitalandshowsthat,withconstantorincreasingreturns,therecanbenopresumptionoftheconvergenceofpercapitaincomesacrosstheworld,orofindividualcountriesreachingalong-runsteady-stategrowthequilibriumatthenaturalrate.Iftherearenotdiminishingreturnstocapital,investmentisimportantforlong-rungrowthandgrowthisendogenousinthissense.(A.P.Thirlwall,GrowthandDevelopment(1999),p115.)3.1.3.TheNew(endogenous)GrowththeoryInthese‘new’modelsofendogenousgrowth,pioneeredbyRobertLucas(1988)andPaulRomer(1986,1990),thereareassumedtobepositiveexternalitiesassociatedwithhumancapitalformationandresearchanddevelopmentthatpreventthemarginalproductofcapitalfromfallingandthecapital-outputratiofromrising.WehaveaproductionfunctionincapitalofY=AK,where=1.Indeeditcanbeseenfromtheexpressionofthecapital-outputratio,thatis,(A.P.Thirlwall,GrowthandDevelopment(1999),p115.)3.1.3.TheNew(endogenous)GrowththeoryThatanythingthatraisestheproductivityoflabour(Y/L)inthesameproportionasK/Lwillkeepthecapital-outputratioconstant.LearningbydoingandembodiedtechnicalprogressinthespiritofArrow(1962)andKaldor(1957),aswellastechnologicalspilloversfromtrade(GrossmanandHelpman,1990,1991)anddirectforeigninvestment(deMello,1996),areadditionalpossibilitiestoeducationandresearchanddevelopment.除了教育和研究开发以外的另一些影响增长的因素.

(A.P.Thirlwall,GrowthandDevelopment(1999),p116.)3.1.3.TheNew(endogenous)GrowththeoryThefirstcrudetestofthe‘new’growththeoryistoseewhetherornotpoorcountriesdogrowfasterthanrichones,orinotherwordstoseewhetherthereisaninverserelationbetweenthegrowthofoutput(oroutputperhead)andtheinitiallevelofpercapitaincome.Ifthereis,thiswouldprovidesupportfortheneoclassicalmodel.Ifthereisnot,thiswouldsupportthenewgrowththeory’sassertionthatthemarginalproductofcapitaldoesnotdecline.Theequationtobeestimatedis

3.1.3.TheNew(endogenous)GrowththeoryWheregiistheaveragegrowthofoutputperheadofcountry-ioveranumberofyearsandPCYi

isitsinitiallevelofpercapitaincome.Asignificantlynegativeestimateofb1wouldevidenceofunconditionalconvergenceorbeta(β)convergenceasitiscalledintheliterature;thatis,poorcountriesgrowingfasterthanrichwithoutallowingfor不考虑

anyothereconomic,socialorpoliticaldifferencesbetweencountries.Aswesee,noneofthestudiestakinglargesamplesofdevelopedanddevelopingcountrieshavebeenabletofindevidenceofunconditionalconvergence.Theestimateofb1isnotsignificantlynegative;infactitisinvariablypositive,indicatingdivergence

(Thirlwall,GrowthandDevelopment(1999),p116.)3.1.3.TheNew(endogenous)Growththeory

Beforejumpingtotheconclusionthatthisisarejectionoftheneoclassicalmodel,however,itmustberememberedthattheneoclassicalpredictionofconvergenceassumesthatthesavingsorinvestmentratio,populationgrowth,technologyandallfactorsthataffecttheproductivityoflabourarethesameacrosscountries.Sincetheseassumptionsaremanifestlyfalse,therecanneverbethepresumptionofunconditionalconvergence(eveniftherearediminishingreturnstocapital),onlyconditionalconvergence,holdingconstantallotherfactorsthatinfluencegrowthofpercapitaincome,includingpopulationgrowth(p),theinvestmentratio(I/Y)andvariablesthataffectthe3.1.3.TheNew(endogenous)Growththeory

investmentratio(I/Y)andvariablesthataffecttheproductivityoflabour,forexampleeducation(ED),researchanddevelopmentexpenditure(R&D),trade(T)andevennon-economicvariablessuchaspoliticalstabilitymeasuredbythenumberofrevolutionsandcoups(PS).Theequationtobeestimatedistherefore3.1.3.TheNew(endogenous)GrowththeoryAndthequestiontobeaskediswhathappenstothesignoftheinitialpercapitaincomevariable(PCY)whentheseothervariablesareintroducedintotheequation?Ifthesignturnsnegative(b<0)whenallowanceismadefortheseotherfactors,thisissupposedtorepresentarehabilitation(n.复原)oftheneoclassicalmodel(seeBarro,1991);thatis,therewouldbeconvergenceifitwerenotfordifferencesbetweenrichandpoorcountriesinalltheseotherimportantvariablesinthegrowthprocess.‘New’growththeorywouldbesupportedbyfindingthateducation,researchanddevelopmentexpenditureandsoonmatter,anditisthesefactorsthatkeepthemarginalproductofcapitalfromfalling,producingactualdivergenceintheworldeconomy(Thirlwall,GrowthandDevelopment(1999),p116.).K.J.Arrow(1962)K.J.Arrow(1962)tookontheviewthatthelevelofthe"learning"coefficientisafunctionofcumulativeinvestment(i.e.pastgrossinvestment).UnlikeKaldor,Arrowsoughttoassociatethelearningfunctionnotwiththerateofgrowthininvestmentbutratherwiththeabsolutelevelofknowledgealreadyaccumulated.BecauseArrowclaimedthatnewmachinesareimprovedandmoreproductiveversionsofthoseinexistence,investmentdoesnotonlyinduceproductivitygrowthoflaboronexistingcapital(asKaldorwouldhaveit),butitwouldalsoimprovetheproductivityoflaboruponallsubsequentmachinesmadeintheeconomy.K.J.Arrow(1962)Thetrickistoutilizetheconceptthatwhilefirmsfaceconstantreturns,theindustryoreconomyasawholetakesincreasingreturnstoaccount.Thiscanbeeasilyformalized.TakingouroldCobb-Douglasproductionfunction,Y=AKaL1-a,thereisconstantreturnstoscaleforallinputstogether(sincea+(1-a)=1).Therefore,asnotedintheSolowmodel,itmightseemasifoutputpercapitalandconsumptionpercapitadoesnotgrowunlesstheexogenousfactor,A,growstoo.ToendogenizeA,letusfirstestablishtheCobb-Douglasproductionfunctionforeachindividualfirm:Yi=AiKiaLi1-a

where,onecannote,theoutputofanindividualfirmisrelatedwithcapital,laboraswellasthe"augmentation"oflaborbyAi.K.J.Arrow(1962)Arrow(1962)assumedthatAi,thetechnicalaugmentationfactor,mightthuswrittenlookspecifictothefirm,butitisinfactrelatedtototal"knowledge"intheeconomy.Thisknowledgeandexperience,Arrowargued,iscommontoallfirms:afreeandpublicgood(i.e.non-competitiveconsumption).Sothefirstquestionishowknowledgeisaccumulated.Arrowarguedthatitarisesfrompastcumulativeinvestmentofallfirms.LetuscallthiscumulativeinvestmentG.Thus,Arrowassumedthatthetechnicalaugmentationfactorisrelatedtoeconomy-wideaggregatecapitalinaprocessof"learning-by-doing".K.J.Arrow(1962)Inotherwords,theexperienceoftheparticularfirmisrelatedtothestockoftotalcapitalintheeconomy,G,bythefunction:Ai=Gz

thus,asthephysicalcapitalstockGaccumulates,knowledgeusedbyaparticularfirmalsoaccumulatesbyaproportionzsuchthatYi=GzKiaLi1-a

where,note,onlyGdoesnothaveasubscripti(i.e.isnotparticulartothefirm),itisaproductiveforceexternaltothefirms(i.e.aMarshallianexternality)andassumedafreepublicgood.Thisforceisfreeandanyfirmemployingitwillnotimplicateonanotherfirm'sconsumption:itisfreely-availableknowledge.K.J.Arrow(1962)Thus,westillmaintainCRSatthefirmlevel,butintheaggregate,however,G=K----sinceitisonlytheaccumulatedstockofcapitalfortheeconomy.Therefore,the"economy-wide"aggregateproductionfunctionis:Y=Ka+zL1-a

Arrow(1962)assumedthata+z<1.Therefore,increasingonlycapital(oronlylabor)doesnotleadtoincreasingreturns.Wecanobtainincreasingreturnstoscaleasa+z+(1-a)="z">0,butcapitalandlabormustbothexpand.However,byaddingthisrestriction,Arrow'soriginalmodelexhibitsnon-increasingreturnstoscaleinaggregateiftherateofgrowthinaneconomyissteady.SummaryNeoclassicalgrowththeoryaccountsforgrowthinoutputasafunctionofgrowthininputs,particularlycapitalandlabor.Therelativeimportanceofeachinputdependsonitsfactorshare.Laboristhemostimportantinput.Long-rungrowthresultsfromimprovementsintechnology.Absenttechnologicalimprovement,outputperpersonwilleventuallyconvergetoasteady-statevalue.Steady-stateoutputperpersondependspositivelyonthesavingrateandnegativelyontherateofpopulationgrowth.Economicgrowthinthemostdevelopedcountriesdependsontherateoftechnologicalprogress.Accordingtoendogenousgrowthmodels,technologicalprogressdependsonsaving,particularlysavingdirectedtowardhumancapital.Internationalcomparisonssupportconditionalconvergence.Adjustingfordifferencesinsavingsandpopulationgrowthrates,developingcountriesadvancetowardtheincomelevelsofthemostindustrializedcountries.Thereareextraordinarilydifferentgrowthexperiencesindifferentcountries.Highsaving,lowpopulationgrowth,outward-lookingorientation,andapredictableeconomicenvironmentareallimportantprogrowthfactors.DebrajRaychapter3-(6)ConsidertheSolowmodelwithaproductionfunction,whereAisafixedtechnologicalparameter.Explicitlysolveforthesteady-statevalueofthepercapitacapitalstockandpercapitaincome.Howdothesevalueschangeinresponsetoarisein(a)thetechnologicalparameterA,(b)therateofsavings,(c)α,(d)δ,thedepreciationrate,and(e)thepopulationgrowthraten?Answer:DebrajRaychapter3-(6)

ThisisamoremathematicalexercisethatwillhelpyouunderstandhowthesteadystateintheSolowmodelisdescribed.Wehavetheequationdescribinghowtotaloutputisproducedwithcapitalandlabor.Inthefirststep,wetransformthisintoaper-capitamagnitudebydividingthroughbythelaborforceL(thereisnotechnicalprogressheresothatlaborisjustthesameaseffectivelabor).Ifwedefiney=Y/Landk=K/L,weseethatThereforetheequationdescribingtheSolowmodelisInthesteadystate,k(t)=k(t+1)=.Consequently,Answer:DebrajRaychapter3-(6)

Inthesteadystate,k(t)=k(t+1)=.Consequently,Nowwesolvethisequationtofigureoutwhatthevalueof

mustbe.Tryit:youwillseethatorthatNowusingthisequation,youshouldbeabletoeasilytellthedirectioninwhich

moves,inresponsetoallthechangesaskedaboutinthequestion.DebrajRaychapter3-(10)

Thinkof