JournalofDevelopmentEconomics8(1981)1499161.North-HollandPubhshingCompany TRADE,ACCUMULATION,ANDUNEVENDkVELOPMENT* PaulKRIEMAN SloanSchoolL$Management,Cambridge,MA0213Y. USA ReceivedAprii1980,finalversionJuly1980 Thispaperdevelopsatwo-countrymodelofcapitalaccumulationandgrowthwherethe industrialsectorexhibitsincreasingreturnstoscale.ItshowsthatunevendevelopmentISa necessaryoutcomeinsuchamodel:aninitialdiscrepancyincapital-!aborratiosbetweenthe twocountrieswillcumulateovertime,leadingtothedivisionoftheworldintoacapital-rich. industrialregionandcapital-poor,agriculturalregion.Whichregiontake?;onwhichrole dependsonprimitiveaccumulation;thatis,onwhichregionstartswithmorecapital.Ifcapital ismobileinternattonally.themodelcangivenrisetoatwo-stagepatternofdevelopment a firststagewheretradeistheengineofgrowthintheleadingcountry.andasecondinwhich foreigninvestmenttakesonthatrole--w;:i~hisreminiscentoftheHohsonLenintheoryof imperialism. 1.Introduction1 Whyistheworlddividedintorichandpoornations?Mostcriticsofthy internationaleconomicorderwouldarguethatthereissmefundamental unequalizingprocessatwork.Theargumentthatthereisaninherent tendencyfcrinternationalinequalitytoincreaseisoftenreferredtoasthe doctrineofunevendevelopment.Thisdoctrineisusuallyassooiatcdwith radicalssuchasBaran(1957),Frank(1967),andWallerstein(1974),but similarargumentshavealsobeenmadebysuchlessradicalauthorsas Myrdai(1957)andLewis(1977). Thispapersetsoutamodelwhichattemptstopresenttheessentialsofthe doctrineofunevendevelopmentinschematicform.Themodelportraysa two-regionworldinwhichtheindustrialsectorsofregionsgrowthroughthe accumulationofcapital.Givenonecrucialassumption----thatthereare externaleconomiesintheindustrialsector-asmallheadstartforone regionwillcumulateovertime,withexportsofmanufacturesfromthe lead@regioncrowdingouttheindustrialsectorofthelaggingregion.This process,Iwouldargue,capturestheessenceoftheargumentthatt;radewith deveiS3pednationspreventsindustrializationinless-developedcountries. Inadditiontohelpingsynthesizeandclarifytheargumentsoftileoristsof unevendevelopment,themodelsetforthinthi,paperisofsometechnical *ThispaperwasstimulatedbydiscussionswithLanceTaylor. 0304-3878/81/0000-0000/$02.50ic!North-HollandPublishingCompany 150Y.K rugman.nude,nccumularion,andWICWF dmhqwn Pnl interest,Conventionaltradetheoryhasoftenbeencritici&ft>r beingstatic andforassumingconstantreturnstoscale.Themodeldnvelol3edheremeets theseobjections,Mhilecontinuingtomakeuseofthetoolsoforthodox theory.Oneofthesurprisingthingsthatemergesfromthe~lsratysisir; that thetheoryofunevendevelopmentfitsinverywellwiththe~~k~l~~r-~~~;~ theoryoftrade. Thepaperisorganizedinfoursections,Section2laysoutthestructureof themodel.Thebasicanalysisofthemodelsdynamicsis~rriedoutin section3.Section4considerstheroleofinternationalinvestment,andshow: thatthemodelnaturallygivesusetoatwo-stagepatternotdevelopment whichbearsastrikingresemblavxtoaHobson-Leninviewofimperialism, Finally,section5 extendstheanAysistoathreeregionworld. 2.Theyasic model Consideraworldconsistingoftworegiolls,NorthandSouth.These regionswillbeassumedtobeidenticalinthesensethatte&nologi~land behavior4relationshipsarethesame.Tosharpentheanalysis,Iwillalso assumethattheregionshaveequallaborforces,andthattheselaborforces doragrowovertime.Thuswehave L,=L:: = L. Eachregionwillbeableloproducetwogoods,amnnufacturedgoodM andanagriculturalplod!lctA,andtotradeatzerotransportationcosts, Therewillthusbe&Isingleikorldpriceofmanufaeturdgoodsmtermsaf agriculturalproducts,P,,.Agriculturalproductswillbeproducmlbylabor alone;wewillchooseunitssethatoneunitoflaborprcdduce~oneunitof agricultu.ralgoods. Thegrowthsector,however,ismanufacturing.Manufacturingwillrequire bothcapitalandlabor.Itwillbeassumedthat,@rnrkrpointofC&W ~j arr ia&oiidutrl firn~,theunitcapitalandlaborre@remenrsarefixed,Inthe aggregate,however,unitcapitalandlaborrequirementswillnotbeecrnstant; instead,ineachregiontheywillbedecreusinpfunctionsoftheregi~~ns aggregatecapitalstock.Lettingr N,c~. tN. ts betheunitcapitalandlabor requirementsinNorthandSouthrespectively.WChave 152P. Krupnan,Trudeaccrcmufarion,rindune~endevefnpmenr outofagriculture.WecandefineK,,,bynotingthatY(K,,,).K,,,/c(K,,,) -L. .- Considernextthedistributionofincome.Therearetwocases:thecasein whichatleastsomelaborisusedinagriculturalproduction,andthecaseof completespecializationinmanufacturing. Ifsomelaborisusedin agriculture,thistiesdownthewagerate,whichis1intermsofagricultural goods,1/P,intermsofmanufactures,Wecanthendeterminetherentalper unitofcapitalasaresidual.Forsimplicity,letusasume(thoughitisrjt essential)thatcapitalgoodsareproducedbylaboralone,i.e.,weinclude themaspartofagriculturaloutput.Thentherentalperunitofcapital, measuredinagricultural(orwage)units,isalsotheprofitrate,andwehave p)N =(P,, -lN).!cN.(5) wherepN,psareprofitratesNorthandSouth.SincecandD arefunctionsof thecapitalstocks,wecanalsowrite(5)asapairofreducedformequations (6) wherei~!iP,~ and?p/c?Karebothpositive. ?Shen aregioniscompletelyspecializedinmanufacturing,(6)nolonger holds.InsteadtherateofprofitisdeterminedinKaldorianfashionbythe requirementthatsavingsequalzero,ifthereisnoforeigninvestment,orby therateofprofitonforeigninvestmentifthereissuchinvestment.Inthe lattercasethewagerateisresiduallydetermined. ToclosethemodelweneedtospecifyI hedemandside.1 willmaketwo strongassumptionsforthesakeofeasyalgebra;theconclusionsofthemodel couldbederivedunderweakerbutlessconvenientassumptions.First,saving behaviorisclassical:allprofitsandonlyprofitsaresaved.Second,afixed proportionpofwageswillbespentonmanufactures,1 -ponagricultural goods. Thesavingsassumptionmeansthat,if thereisnointernationalinvestment, ther.tteofgrowthofthecapitaistockineachregionwilljustequaltherate ofprofit. K,K,= px,k,,!K, = ps. (7) Itiseasytosee!mwthiscangiverisetoanunequalizingspiral.Suppose weareatanyearlystageinthedevelopmentoftheworldeconomywhere bothregionsarenon-specialized,butNorthhasaccumulatedmorecapitai thanSouth.Thensincetheregionswillfaceacommonrelativepriceof manufactures,by(6) therateofprofi\andtherateofgrowthwillbelargerin theb*egionwhichalreadyhasmorecapital.Thisisthebasisforthe divergenceanalyzedinmoredetailbelow. P.hrugmun.Trudtz.uccumkttinn,uttdutwendtwloptttettr153 Therelativepriceofmanufacturedgoodswillbedeterminedbyworld demandilndsupply.Smceafractionpofwagesisspentonmailufactures. providedthatl;otlrcountriesproducesomeagriculturalgoodswehav: w_~4,-I- 41=A-LN+ 4.(8) whichcar!berewristenas ThisgivesusarelationshipbetweenthetwocapitalstocksandP,,,:itis apparentthatP,,isdecreasinginbothcapitalstocks.NotealsothatK,and K,et4tersymmetrically.sothatwhereK,=K,.CP,,iK,:= ;P,,iK,. Fit,&.wecancombine(6),(7),and(9)toexpresstherateofchangeeach regionscapitalstockasafunctionofthelevelsoibothcapitalstocks: I&/X.= g(K,,K,k R,K,=g(K,.K,). (10) Weknowth;lttheeffectofanincreaseinthuc!th~rregionscapitalstock mustbetoturnthetermsoftradeagainstmanufacturesandthusreduce profits:sog?O,thetraceis positive:whileif l+ -I-I$EI~~0,thedeterminantisnegative.Thusanyinterior equilibriumis unstable. References Baran,P..1957. Thepoliticaleconomyofgrowth(MonthlyReviewPress, NewYork). Chacholiadcs.M..1978, Internationaltrudctheoryandpaliev(McGraw-Hill.NewYork) Frank,A-O.,1967, CapitalismandunderdevclopmtmtinLaiinAmarica(MonthlyR~iewPrms, NewYork). H&son.J.A.,1902, Imperialism:Astudy (Nisbct,London). Lenin,V.I.,1939.Imperialism.thehigheststageofcapitalismflntcrna~itianul Dublishcrs.New York).