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
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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).