經(jīng)濟(jì)增長(zhǎng)理論

Chapter3TheoryofEconomicGrowth主講：陳忠斌（博士）武漢大學(xué)經(jīng)濟(jì)發(fā)展研究中心武漢大學(xué)經(jīng)濟(jì)與管理學(xué)院ChapterHighlightsEconomicgrowthisduetogrowthininputs,suchaslaborandcapital,andtoimprovementsintechnology.Capitalaccumulatesthroughsavingandinvestment.Thelong-runlevelofoutputperpersondependspositivelyonthesavingsrateandnegativelyintherateofpopulationgrowth.Theneoclassicalgrowthmodelsuggeststhatthestandardoflivinginpoorcountrieswilleventuallyconvergetothelevelinwealthycountries.ChapterHighlightsRatesofeconomicgrowthvarywidelyacrosscountriesandacrosstime.Endogenousgrowththeoryattemptstoexplaingrowthratesasfunctionsofsocietaldecisions,inparticularsavingsrates.Incomeinpoorcountriesappearstobeconvergingtowardincomelevelsofrichcountries,butatextraordinarilyslowrates.1.LongTermGrowthinChina仍然屬于中低收入國(guó)家.發(fā)展不平衡：2003年，深圳市的人均GDP為6510美元，是全國(guó)平均值的6倍總量大，人均量低。總量排名第4，人均量排名第136。生活水準(zhǔn)與美國(guó)相差100年（反映了中國(guó)經(jīng)濟(jì)增長(zhǎng)質(zhì)量的欠缺）。粗放式經(jīng)濟(jì)增長(zhǎng)為主：主要依靠增加物質(zhì)資源消耗和勞動(dòng)力投入帶動(dòng)GDP增長(zhǎng)。加快轉(zhuǎn)變經(jīng)濟(jì)發(fā)展方式,推動(dòng)產(chǎn)業(yè)結(jié)構(gòu)優(yōu)化升級(jí).堅(jiān)持?jǐn)U大國(guó)內(nèi)需求特別是消費(fèi)需求的方針,促進(jìn)經(jīng)濟(jì)增長(zhǎng)由主要依靠投資、出口拉動(dòng)向依靠消費(fèi)、投資、出口協(xié)調(diào)拉動(dòng)轉(zhuǎn)變；由主要依靠第二產(chǎn)業(yè)帶動(dòng)向依靠第一、第二、第三產(chǎn)業(yè)協(xié)同帶動(dòng)轉(zhuǎn)變；由主要依靠增加物質(zhì)資源消耗向主要依靠科技進(jìn)步、勞動(dòng)者素質(zhì)提高、管理創(chuàng)新轉(zhuǎn)變。發(fā)展現(xiàn)代產(chǎn)業(yè)體系,大力推進(jìn)信息化與工業(yè)化融合,促進(jìn)工業(yè)由大變強(qiáng),振興裝備制造業(yè),淘汰落后生產(chǎn)能力；提升高新技術(shù)產(chǎn)業(yè),發(fā)展信息、生物、新材料、航空航天、海洋等產(chǎn)業(yè)；發(fā)展現(xiàn)代服務(wù)業(yè)，提高服務(wù)業(yè)比重和水平；加強(qiáng)基礎(chǔ)產(chǎn)業(yè)基礎(chǔ)設(shè)施建設(shè)，加快發(fā)展現(xiàn)代能源產(chǎn)業(yè)和綜合運(yùn)輸體系。(資源來源：中國(guó)共產(chǎn)黨第17大報(bào)告，2007年10月15日)TheVarietyofGrowthExperiencesCopyright?2004South-Westernreturn亞當(dāng)?斯密常常被認(rèn)為是現(xiàn)代經(jīng)濟(jì)學(xué)之父。其《國(guó)民財(cái)富的性質(zhì)和原因的研究》于1776年出版。為什么各國(guó)的發(fā)展速度不同這一問題從那時(shí)起一直是經(jīng)濟(jì)探索的最重要問題。AdamSmithandincreasingreturns斯密最重要的貢獻(xiàn)之一是把以勞動(dòng)分工為基礎(chǔ)的報(bào)酬遞增概念引入了經(jīng)濟(jì)學(xué)。他把勞動(dòng)分工看作是社會(huì)經(jīng)濟(jì)的基礎(chǔ)，否則每個(gè)人都變成了RobinsonCrusoe,生產(chǎn)自己所需要的一切。正是以勞動(dòng)分工為基礎(chǔ)的報(bào)酬遞增概念，成為了對(duì)作為自行產(chǎn)生過程的經(jīng)濟(jì)進(jìn)步抱有樂觀主義觀點(diǎn)的核心。報(bào)酬遞增意味著勞動(dòng)生產(chǎn)率和人均收入隨著產(chǎn)出和就業(yè)擴(kuò)張而上升；而報(bào)酬遞減意味著勞動(dòng)生產(chǎn)率和人均收入下降，勞動(dòng)就業(yè)限制在某一點(diǎn)上－－在這一點(diǎn)之后，勞動(dòng)的邊際產(chǎn)品下降到生存工資的水平。報(bào)酬遞增在大多數(shù)工業(yè)活動(dòng)中普遍存在，而報(bào)酬遞則是農(nóng)業(yè)和采礦業(yè)等以土地為基礎(chǔ)的活動(dòng)的特點(diǎn)，因?yàn)橥恋厥且粋€(gè)固定的生產(chǎn)要素。(A.P.Thirlwall,GrowthandDevelopment(1999),p83-86.)Appendix:ClassicalgrowththeoryTheclassicalpessimists斯密以后對(duì)經(jīng)濟(jì)發(fā)展過程的古典主義觀點(diǎn)基本上悲觀主義的。它集中討論迅速的人口增長(zhǎng)與由農(nóng)業(yè)報(bào)酬遞減和成本上升所造成的糧價(jià)上升對(duì)工業(yè)利潤(rùn)率施加的影響。最大的悲觀主義者之一是托馬斯?馬爾薩斯(ThomasMalthus)。馬爾薩斯的著作分為兩部分：他的人口論和他的維持有效需求(effectivedemand)對(duì)發(fā)展的重要性的論述－－“有效需求”這個(gè)概念后來被凱恩斯所借用。事實(shí)上，馬爾薩斯是強(qiáng)調(diào)需求對(duì)決定產(chǎn)出的重要性的唯一的古典經(jīng)濟(jì)學(xué)家－－所有其他古典經(jīng)濟(jì)學(xué)家都信奉薩伊定律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擺動(dòng)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.增長(zhǎng)理論的模型分析

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.此式就是哈羅德-多馬增長(zhǎng)模型的基本公式。g表示國(guó)民收入增長(zhǎng)率或經(jīng)濟(jì)增長(zhǎng)率，它等于儲(chǔ)蓄傾向除以增量資本-產(chǎn)出比。該模型表明，經(jīng)濟(jì)增長(zhǎng)率是由儲(chǔ)蓄傾向和資本-產(chǎn)出比共同決定的，它與儲(chǔ)蓄傾向成正比關(guān)系，與資本-產(chǎn)出比成反比關(guān)系。如果資本-產(chǎn)出不變，經(jīng)濟(jì)增長(zhǎng)率就決定于儲(chǔ)蓄傾向或儲(chǔ)蓄率，儲(chǔ)蓄傾向越高，則經(jīng)濟(jì)增長(zhǎng)率越高。如果儲(chǔ)蓄傾向不變，資本-產(chǎn)出比越低，則經(jīng)濟(jì)增長(zhǎng)率越高。哈羅德-多馬增長(zhǎng)模型的批評(píng):批評(píng)主要是針對(duì)它的假定前提：這個(gè)模型是建立在儲(chǔ)蓄能全部轉(zhuǎn)化為投資的假定之上的。這對(duì)發(fā)展中國(guó)家是特別不現(xiàn)實(shí)的。實(shí)際上儲(chǔ)蓄轉(zhuǎn)化為投資需要具備很多條件：(1)發(fā)展中國(guó)家往往存在著制度缺陷；(2)缺少投資所需的機(jī)器設(shè)備等物質(zhì)資本品、原材料以及關(guān)鍵的技術(shù)、而且由于外匯短缺也不可能都靠進(jìn)口來解決；(3)社會(huì)基礎(chǔ)設(shè)施(交通通訊,電力等)十分落后，對(duì)投資造成了重大的障礙。這個(gè)模型是建立在資本-產(chǎn)出比不變的假定上的。實(shí)際上，隨著經(jīng)濟(jì)發(fā)展，資本-產(chǎn)出比不可能不變。發(fā)展中國(guó)家為了加速工業(yè)化和實(shí)行進(jìn)口替代發(fā)展戰(zhàn)略，常常把大量的資金投入資本密集度很高的工業(yè)上，如汽車、鋼鐵等部門。因此。增量資本—產(chǎn)出比一般是趨于上升的。3.這個(gè)模型只有資本（儲(chǔ)蓄）一個(gè)變量，這實(shí)際上暗含地假定資本—?jiǎng)趧?dòng)比例是不變的，即資本與勞動(dòng)同比例地增加，資本增加百分之一，勞動(dòng)也必須增加百分之一。這也是不現(xiàn)實(shí)的。的確，發(fā)展中國(guó)家的勞動(dòng)力資源是豐富的，但是，豐富的是無技術(shù)的、非熟練的勞動(dòng)者，而受過良好教育和訓(xùn)練的技術(shù)人員和稱職的管理者卻是非常稀缺的。因此，即使投資所需的資本品能夠得到滿足，因缺乏有技能的勞動(dòng)力和合格的管理者而不能形成實(shí)際投資，或者形成了實(shí)際投資，投資效率也是十分低下的。此外，假定資本－勞動(dòng)比不變還意味著不能用勞動(dòng)來代替資本，這不僅不符合實(shí)際，而且是十分有害的。因?yàn)榘l(fā)展中國(guó)家勞動(dòng)力豐富，充分利用剩余勞動(dòng)力資源是能創(chuàng)造出資本和增加產(chǎn)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稻田條件,followingInada(1963).TheconditionofconstantreturnstoscaleimpliesthatoutputcanbewrittenasWherek=K/Listhecapital-laborratio,y=Y/Lispercapitaoutput,andthefunctionf(k)isdefinedtoequalF(k,1).Thisresultmeansthattheproductionfunctioncanbeexpressedinintensiveform集約形式

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當(dāng)k<k*,實(shí)際人均資本量((1-)k+sy)超過了保持資本－勞動(dòng)比不變所需要的人均資本量((1+n)k),這時(shí),人均資本和人均產(chǎn)出都將增加。k(2005)k(2004)k(2006)k(1+n)kt+1(1-σ)kt+syFigure3.2-bThedynamicsoftheSolowmodelSource:DebrajRay,DevelopmentEconomics(1998),p66.k*y當(dāng)k>k*,實(shí)際人均資本量[(1-)k+sy]小于為保持資本-勞動(dòng)比不變所需要的人均資本量(1+n)k,結(jié)果是人均資本k和人均產(chǎn)出y都將下降。人均資本的凈變化是儲(chǔ)蓄超過必需投資的部分：k=sy-(n+d)k穩(wěn)態(tài)定義為k=0,并且在y*和k*的值滿足：sy=sf(k*)=(n+d)k*Fig3-3.STEADY-STATEOUTPUTANDINVESTMENT

圖3-3的穩(wěn)態(tài)出現(xiàn)在C點(diǎn).儲(chǔ)蓄線與投資需求線相交在C點(diǎn)上.無論在哪里，只要儲(chǔ)蓄線高于需求線，資本在增加,經(jīng)濟(jì)就在增長(zhǎng)。例如，從A點(diǎn)開始，隨著時(shí)間的推移，經(jīng)濟(jì)向右邊移動(dòng)。由于資本的邊際產(chǎn)量遞減，生產(chǎn)函數(shù)與并行的儲(chǔ)蓄曲線逐漸變得平直。因?yàn)楸匦璧耐顿Y線具有不變的正斜率，所以必需的投資線與儲(chǔ)蓄線會(huì)相交。圖3-4中，經(jīng)濟(jì)由C點(diǎn)的穩(wěn)態(tài)均衡起步。在C點(diǎn)，儲(chǔ)蓄與必需的投資恰好相等.現(xiàn)在人們?cè)敢獍咽杖胫械母蟛糠謨?chǔ)蓄起來.這會(huì)引起儲(chǔ)蓄曲線向上移動(dòng)到虛線的位置。圖3-4中，C點(diǎn)是初始的一個(gè)穩(wěn)態(tài)均衡。現(xiàn)在，相對(duì)于必需的投資，儲(chǔ)蓄增加了，其結(jié)果是，儲(chǔ)蓄額比保持人均資本不變所需要的投資要多。儲(chǔ)蓄多到足以使人均資本量增加。人均資本量將持續(xù)增加，直到達(dá)到C'點(diǎn)。在C'點(diǎn)，經(jīng)濟(jì)已恢復(fù)到穩(wěn)態(tài)增長(zhǎng)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**在規(guī)模報(bào)酬不變的生產(chǎn)函數(shù)條件下,在長(zhǎng)期中,儲(chǔ)蓄率的增加只是提高人均產(chǎn)出水平和人均資本水平,而不是提高人均產(chǎn)出增長(zhǎng)率.(Macroeconomics,8edition,byDornbusch,p57.）Figure3-5.ADJUSTMENTTONEWSTEADYSTATEFigure3-7.EXOGENOUSTECHNOLOGICALCHANGE引進(jìn)了技術(shù)進(jìn)步因素解決了人均收入的長(zhǎng)期增長(zhǎng)趨向于零的尷尬局面。但是，問題還沒有結(jié)束。在新古典增長(zhǎng)模型中，技術(shù)進(jìn)步是外生的，也就是說是從外部引入的，與模型中的任何變量沒有關(guān)系。新古典增長(zhǎng)模型假定商品和要素是完全自由流動(dòng)的。即使假定技術(shù)進(jìn)步率最初在國(guó)家間存在很大差距，最終也應(yīng)該趨于相同。然而，無論是收入水平還是增長(zhǎng)率，趨同在全世界都沒有發(fā)生。而且除了少數(shù)幾個(gè)國(guó)家之外，發(fā)達(dá)國(guó)家與發(fā)展中國(guó)家之間的經(jīng)濟(jì)差距在近幾十年反而拉大了。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.除了教育和研究開發(fā)以外的另一些影響增長(zhǎng)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不考慮

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.復(fù)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