Dutt1992

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Dutt1992

  1. 1. A Kaldorian Model of Growth and Development Revisited: A Comment on Thirlwall Author(s): Amitava Krishna Dutt Source: Oxford Economic Papers, New Series, Vol. 44, No. 1 (Jan., 1992), pp. 156-168 Published by: Oxford University Press Stable URL: http://www.jstor.org/stable/2663430 Accessed: 26/10/2010 16:48 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=oup. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to Oxford Economic Papers. http://www.jstor.org
  2. 2. OxfordEconomicPapers44 (1992), 156-168 A KALDORIAN MODEL OF GROWTH AND DEVELOPMENT REVISITED: A COMMENT ON THIRLWALL By AMITAVA KRISHNA DUTT* 1. Introduction THIRLWALL (1986, 1987) has recentlydeveloped a formalpresentationof Kaldor's (1975, 1979) model of theworldeconomyexaminingthedynamic interactionbetweenprimaryand secondarysectors,and therebycontributed to our understandingof Kaldorian growthand developmenteconomics.On thebasisofhismodel,ThirlwallhasclaimedthattheKaldorianmodelcaptures theessenceoftheinteractionoftheagriculturaland industrialsectorswithin dual,less developedeconomies,thatis,thecomplementaritybetweenoutputs ofthetwosectorswithintheframeworkofreciprocaldemand,andinparticular, theroleoftheagriculturalsectorinprovidinga marketfortheindustrialsector. By so doing,Thirlwallclaimsthatthemodelis superiorto earliermodelsof agriculture-industryinteractionforlessdevelopedeconomies. ThepurposeofthispaperistoarguethatthereareproblemswithThirlwall's specificationof the structureof the Kaldorian model,' withits underlying dynamics,and withhis claimthatthemodelmakesan advance overearlier dual economymodelswithregardto analysisofthecontributionofagriculture to themarketforindustry.To do so, Section2 developstheformalKaldorian model,2Section3 analyzesitsunderlyingdynamics,and Section4 comments on theroleofdemandin themodel. 2. A Kaldorianmodel Considera closedeconomywithtwosectors,an agriculturalandan industrial sector,each producingone good.The agriculturalgood is a pureconsumption good,whiletheindustrialgoodcan bebothconsumedandinvested.Bothgoods are sold in perfectlycompetitivegoods markets.3 In theagriculturalsectorlabour,land and capitalare used forproduction. Labour is in unlimitedsupplyand has zero marginalproductso thatitslevel * I am gratefulto two anonymousrefereesofthisjournal fortheirperceptivecommentsand usefulsuggestions.I wouldliketo thanktheparticipantsofa workshopon DynamicModels at Clare Hall, Cambridge,and BillGibsonand Michael Landesmann,fortheircomments. 1 A similarKaldorian model has also been developedby Targetti(1985), and manyof our criticismsapplyto thatmodelas well. 2 We willdevelopa modelwhichusesan internally-consistentsetofassumptionswhichproduces a modelidenticaltotheonedevelopedbyKaldor,and useourversionofthemodelforourcritical analysis.Thisshouldnotbe takentoimplythatitisnotpossibletodevelopmodelswithalternative assumptionswhichalso produceKaldor's model,butourcriticalanalysisremainsvalidunlessthis alternativeanalysis,whichnegatesour criticaldiscussion,is actuallydeveloped. 3This mayappearto contradictKaldor (1975, 1979).Butsee below. E! OxfordUniversityPress 1992
  3. 3. A. K. DUTT 157 does not affectoutput.Land is given.Outputmayincreaseovertimedue to land-savingtechnicalchange,but thisrequirescapitalinvestment.Assuming strictcomplementaritybetweencapitaland thistypeoftechnicalchange,we have Qa = aaKa (1) whereQjdenotesoutput,a' thecapital-outputratio,and Ki thecapitalstock, all insectori,and wherethesubscripta refersto theagriculturalsector.Note thattheassumptionofperfectcompetitionensuresthatproductionfullyutilizes capacity.It is assumedthata fixedfractionSa oftotalagriculturaloutputis saved,and all agriculturalsavingis investedwithintheagriculturalsector,so that SaPaQa = PnIa (2) wherePi denotes(money)price,and Ii investment,insectori,and thesubscript ndenotestheindustrialsector.DividingthroughbyKa, and denotingtherate ofgrowthof capitalin agriculture(which,in theabsence ofdepreciation,is la/Ka) byga,we get ga= SaaalP (3) wherep = Pn/Pa,theindustrialtermsoftrade. In theindustrialsectoroutputis producedwithlabour and capital using fixed-coefficientstechnology.The labour-outputratio is bnand the output- capitalratioisas. Perfectcompetitionensuresfullcapacityutilization,so that Qnl= anKn (4) Labour, as assumedabove, is abundant,and thisis formalizedby assuming thatitis available to theindustrialsectorat a constantwage in termsofthe agriculturalgood,4so that Wn4/Pa= T (5) whereris thefixedlevel,and Wnis theindustrial(money)wage;firmshireall theworkerstheyneedat thiswage.The workersconsumeall theirincomeand capitalists,who earn theprofits,save a fixedfractionsnof theirincome.All savingintheindustrialsectorisinvestedinthatsector.Our assumptionsimply, usingequation(5), that PnIr= sn[P-n (TbnPa)]Qn (6) DividingthroughbyPnKnand using(4) givestheequationforthegrowth-rate ofindustrialcapital, gn= snI1 (Tbn/p)]an (7) whereindustrialcapitalis assumedto be non-depreciating. 4Kaldor(1979) tookthisto be fixedbycustom.FollowingLewis(1954),wecouldfixitinterms ofaverageworker(or peasant)incomeintheagriculturalsector,makingappropriateassumptions regardingtheinstitutionalstructureofagriculture.
  4. 4. 158 A KALDORIAN MODEL REVISITED Regardingconsumptionspendingwe assume,forsimplicity,that a fixed fractiono oftotalconsumptionexpenditureis spenton theindustrialgood, and thereston theagriculturalgood. To examinethe determinationof the equilibriumgrowthrate of capital and the termsof trade in the economy,we bringequations (3) and (7) togetherintheright-handsideofFig. 1,whichis Kaldor's diagram.Equation (3) yieldsthe gq curve,and equation (7) yieldsthe g, curve which has a p-interceptof zbnand a g-asymptoteofs,,as.Definingequilibriumto be a stateat whichcapital(and withfixedoutput-capitalratios,output)in thetwo sectorsgrowsat the same rate,equilibriumis seen to be establishedat the intersectionof thega and gncurvesand theequilibriumtermsof tradeand growthratesare,respectively, P* =(saaa/sna,) + zb, (8) g = snansaaa/(saaa + zbsnan). (9) IncreasesintheparametersSaand aa shiftthegacurvetotherightand increase q* and p*, and increasesin s,,and anand reductionsin z and bnshiftthegq curve to rightand increaseg* and reduce p*. Note that the patternof consumptionexpenditure,givenby or,has no effectat all on theequilibrium valuesofg and p. So farthemodel appears to be thesame as Thirlwall's,apartfromsome minordifferenceshavingto do withthefactthathe assumesthatall industrial savingisinvested,anddoesnotmakespecificassumptionsabouttheagricultural savingsrate.5The significantdifferencebetweenour model and Thirlwall's concernsthenatureofindustrialpricing.Whilehetakestheagriculturalmarket to be competitive,so thatthepriceoftheagriculturalgood variesto clearthe market,Thirlwallassumestheindustrialmarketto be non-competitive,and firmssetthepriceas a markupon unitlabourcosts.Here he followsKaldor (1975, 1979),who usesKalecki's (1971) pricingformula, PI, = (1 + z)Wnbn (10) wherez is thefixedmarkuprate,determinedby thedegreeofmonopolyin industry.DividingbyPa thisimplies p = (1 + z)ubn (11) whichis exactlyKaldor's equation in our notation.Instead of makingthis 5For example,Thirlwallconductstheanalysisin termsofa rateofagriculturalsurplusinstead ofa savingsrate,andthenassumesawaytheconsumptionofmanufacturedgoodsintheagricultural sector,suggestingthatsuchconsumptionwillshiftthega curve(our notation)downwards.This analysisis incompletesinceitis notexplainedhow thiscurvecan be derivedwhenmanufactured goods are consumedin the agriculturalsector.Moreover,thisanalysisconceals an interesting propertyofthemodel,thatis,thattheequilibriumrateofgrowthofthemodeldependson the savingrateinagriculture,and noton themarketedsurplusratewhichdependson boththesaving rateand a.
  5. 5. A. K. DUTT 159 ga /gn 0 k* k 0 g g FIG. 1. price-makingassumption,we have assumedprice-takingbehaviourforboth sectors. We partcompanywithKaldor and Thirlwallbecause themarkup-pricing assumptionis inconsistentwiththerestofthemodel.6First,ifz, z and b,,are exogenouslyfixed,as markuppricingand therestoftheassumptionsimply, (11) fixesthetermsoftrade:thustheyare not freeto vary,and thereis no reasonforit to be consistentwiththeequilibriumlevelgivenby(8). Second, Kalecki's (1971) markup-pricingtheoryassumesthatfirmsadjust quantities and not prices,and this requiresthat theyoperate with excess capacity (assumingfixedcoefficientsas is assumedin all our models).7Yet,ourmodel assumesfullcapacityutilization,whichis implicitlyassumedalso byThirlwall whenheassumesa constantcapital-outputratioinindustrywhichis necessary forderivingequation(7) and drawingthegq,curve;italso seemsto be implicit in Kaldor's owndiagram.8 Thirlwall'serrordoes not interferewith his formalmodel because the markup-pricingassumptionplaysno partinit.He does notuseitindiscussing the model,exceptformentioningin an unnecessaryfootnote(p. 209) that quantities(and notprices)are assumedto adjustin theindustrialsector.This does notmean,however,thattheerroris harmless:itwillbe arguedlaterthat 6 Our criticismsalso applyto Targetti(1985) who also assumesmarkuppricingin industry. Markup-pricingand full-capacityutilizationcan be made consistentwitheach other,butonly ifthereis someothermechanismwhichclearsthemarket.FitzGerald(1990), in hisformalization ofone ofKalecki's (1972) models,assumesthatthegovernmentchangesthetaxrateto clearthe industrialmarket. 8 Imperfectcompetitionanda variablemarkupratearenotnecessarilyinconsistent.Forexample, theactualmarketratecan varyto clearthemarketand thedegreeofmonopolycan seta lower bound to the markup.However,this makes the model formallyequivalentto the perfectly competitivemodelas longas themarkupis above theminimumsetbymonopolypower.
  6. 6. 160 A KALDORIAN MODEL REVISITED it is relatedto Thirlwall'sincorrectemphasison the role of agriculturein providinga marketfortheindustrialsector. 3. DynamicsandstabilityintheKaldorianmodel Whilewe have so fardefinedequilibriumin our Kaldorianmodelto refer to a statein whichthegrowth-ratesofthetwosectorsare equal,we nowturn to a discussionofdynamicsbehindequilibriumand thequestionofstability. This issue is brieflydiscussedby Thirlwall,who postulatesan adjustment equation whichmakes the discrete-timechangein the agriculturaltermsof trade,q( = l/p),dependlinearlyon thedifferencebetweenthesectoralgrowth rates(g, - ga,inournotation),andshowsthatequilibriumwillbe stableunless thecoefficientshowingthespeedofadjustmentis 'too great'.Thirlwallappears to believethat'quantitiesare assumedto adjustin theindustrialsectorand pricesintheagriculturalsector,inresponseto a disequilibriumbetweensupply and demand' (p. 209n),but thisanalysisis not pursuedcorrectly.He argues thatfora disequilibriumtermsoftrade,g and gnare unequal,whichimplies a gap betweenthecapacityoftheindustrialsectorto growand thegrowth warrantedbythedemandforitsproductfromtheagriculturalsector,but he failsto pointout whythesemagnitudesshouldbe interpretedas demandsand supplies,and whysuch a gap shouldlead to priceadjustmentsexceptfora vague referenceto the 'behaviourof food dealersand merchants'(p. 209). Given the competitivemarketassumptionfor the agriculturalgood, the adjustmentequationis ratherstrange,foritimpliesthatifthetwosectorsgrow at thesamerate,therewillbe no changein thetermsoftrade,evenifthereis an excess supplyand demand in the agriculturalmarket.The alternative Thirlwallsuggestsina footnote,'to consideradjustmentsofthetermsoftradeto differencesin the levelsof demand and supply',would seem to be clearly preferable. To follow this route, however,we need an explicitstatementof the characteristicsofdisequilibriumstates,and ofthedynamicswhentheeconomy is indisequilibrium.We considertwosimpleand plausiblecharacterizationsof suchdisequilibriaand dynamics. Thefirstdistinguishesbetweentheshortruninwhichsectorallevelsofcapital stockare givenand therelativepricevariesto clearthegoods markets,and thelong runin whichthestocksofcapitalgrowdue to investment.Market clearingin agricultureand industry,respectively,imply: Qa = (1 - Y){[zb, + (1 - s,)(p - rbn)]Qn+ (1 - Sa)Qa} (12) pQI = o{[zbn + (1 - sn)(p - zbJ)]Qn + (1 - Sa)Qa} + P(In + Ia). (13) Equations(2), (6) and (12) implyequation(13), whichshowsthattheclearing oftheagriculturalmarketimpliestheclearingoftheindustrialone,so thatwe mayconfineattentionto onlytheformer.We assumethatin theshortrunp respondspositivelyto excess supplyin the agriculturalmarket(or excess
  7. 7. A. K. DUTT 161 demandfortheindustrialgood), and formalizethiswiththeequation dp/dt= 0{L[a + sa(1 - a)]aak -(1 - o)[(1 - s)p + szb,]an} (14) where0 > 0 is an adjustmentcoefficient,k = Ka/Kn,and the termswithin curlybracketsisexcesssupplyofagriculturalgoodsdividedbyK,. In theshort run,givenk(withgivenKa and K), p adjustsaccordingto thisequation.Since dp/dtis negativelyrelatedto p theadjustmentprocessis stable,so thatthe economyconvergesto short-runequilibrium,whendp/dt= 0, where p = {[( -/(l- )) + sa]aa/(1 - s)a,}k - -bs,,/(1- sn). (15) Thisequationcan be representedbythelineintheleft-handsideofFig. 1.For anyk,theshort-runequilibriumvalueofp can be readofffromthiscurve,and theshort-runequilibriumvaluesofgaand g, can be read offfromthegaand g, curves.9In thelongrun,k changesaccordingto dk/dt= k(ga- g) (16) whichimplies,using(3) and (7), dk/dt= k{(saaa/p) - s,[1 - (zb,/p)1a,} (17) Atlong-runequilibrium,whendk/dt= 0,theexpressionwithincurlybrackets mustvanish,whichimpliesthatga= g,. This long-runequilibriumis stable, sincea rise(fall)in k impliesa rise(fall)in p (fromequation(15)) whichin turnreduces(increases)dk/dt(byequation(17)). The convergencetolong-run equilibriumcan be shownusingFig. 1: startingfromanyk above (below) the long-runequilibriumoneitcan beseenthatg,isgreater(less)thanga,implying thatkfalls(rises)overtimeto taketheeconomyto theequilibrium,as shown bythearrows. The second characterizationassumes thatp is sticky,but thatit adjusts over time.'0 Here p and k are givenat a point in timeand over timep adjustsaccordingto (14) and k accordingto (17). The equilibriumforthis characterizationwillbe thesameas thatinthepreviousone,butthedynamics aredifferent,as shownin Fig.2. The pplineshowscombinationsofp and k at whichdp/dt= 0 and isgivenby(16). Similarly,thekklineshowscombinations ofp and k at whichdk/dt= 0, and is seenfrom(17) to be givenby (8). As illustratedin thefigure,thedynamicsmaybe cyclical,but theequilibriumis 9For meaningfulshort-runequilibriumwithpositiveratesofaccumulationin bothsectorswe requirep > rbn(see equations(3) and (7)). From(15) thiscan be shownto imply k > rbna,/[(c~/(1-o)) + Snaa Ifthisconditionis not satisfied,therelativesize oftheagriculturalsectorbecomestoo largeto allowmarketclearingata relativepricesufficienttoallowanyindustrialprofitsandhenceindustrial capitalaccumulation. 10Thereareproblemsofreconcilingfixedpricesand excesssuppliesand demandswhichwedo notgo intohere,followingthefix-pricedisequilibriummodelswhichassumeperfectcompetition.
  8. 8. 162 A KALDORIAN MODEL REVISITED P k k Pa 0 k FIG.2. necessarilystable,as can be seen by evaluatingthe Jacobianof the system aroundtheequilibrium,givenby !(1-,:(- s,,)a,,0[x+ SaO1 - X)]aaO] L(Saaa+sjbjp)2 0 whichhas a negativetraceand a positivedeterminant,whichis sufficientfor local stability. Whichevercharacterizationweadopt,forgivenp,equations(3) and (7) give us growthratesofKa and K,, and thesecan be read offfromtheright-hand side ofFig. 1. For anygivenp we findtheactualratesofgrowthofthetwo sectors,andthesegrowth-ratesmoveovertimetotaketheeconomytolong-run equilibrium. 4. The roleofdemand Asmentionedabove,Thirlwallemphasizestheroleofagricultureinproviding a marketforthe industrialgood, and claims that the Kaldorian model is superiorto Lewis's(1954,1972)becausethelatterdidnottakedemandfactors intoaccount.He stressestheimportanceofdemandby labellingtheKaldor curvesgdand g, (ourgaandg,curves,respectively),statingthattheagricultural growthrate curverepresents'the rate of growthof purchasingpower,or demand,overindustrialgoods' (p. 204). " Ifthemarketfortheagriculturaldoes notclearrapidlyenough,in practicerationingand/or parallelmarketswillemerge.We have abstractedfromsuchcomplicationshere.
  9. 9. A. K. DUTT 163 Whileit is truethatin theKaldorian model theagriculturalsectorsbuys productsfromtheindustrialsector,and a higherrateofagriculturalgrowth impliesa higherrateofgrowthofthedemandfortheindustrialgood (bothfor investmentand consumptionpurposes) and thisis shownbythefactthatin ourmodelan upwardshiftingawillimplya higherequilibriumrateofgrowth oftheindustrialsector-this is trueforanymodelin whichthetwo sectors tradewitheachother.In theKaldorianmodeltheindustrialgood is demanded also withinthatsector,and ifit growsmorerapidlydue to internalreasons (say due an increasein sj,)itwillcreatea marketforitsownincreasedoutput. Thisis becauseeach sectoralways(identically)investsitsentiresavingwithin thesector,and thereis thereforeno demandproblemin anysector:iftheysell theirproductto theothersectortheysimplyexchangeitforan equal value of theproductofthatsector,thegaininmarketdue tothepurchaseofitsproduct by the other sector exactlycompensatingthe loss in marketdue to its purchaseoftheproductoftheothersector.Agriculturedoes not serveas a solutionto industry'smarketproblemsimplybecause thereis no market problemforindustryin thismodel.'2 Agriculture'scontributionto industrializationin this model is fromthe supplyside,throughtheprovisionofwagegoods and labourto theindustrial sector.The wagegoodsproblemarisesfromthetermsoftrade:iftheindustrial termsoftradedeteriorates,industrywillhave to pay a higherproductwage, itsprofitswillbe squeezed,and accumulaionin industrywillbe reduced,as shownby equation (7). If the agriculturalsectorgrowsfasterat a givenp (say due to a higherSa) thiswill make the industrialsectorgrowfasterin equilibrium,butonlybecauseitrelaxesthewage-goodsconstraint,turningthe termsoftradetowardsindustry.Thelaboursupplyproblemarisesifz increases which,as we haveseenabove,willpushtheg,,curveto theleftand reducethe rateofgrowth. This discussionmakesit clearthattherole ofagriculturein thismodelis similarto its roles in the neoclassical and classical models criticizedby Thirlwall.All threemodels neoclassical,classical and Kaldorian assume awaydemandproblems.The neoclassicalone (Jorgenson(1961) forexample) is differentfromtheothersbecause it assumesthatlabour is fullyemployed, 12 The dynamicanalysisofSection3 castsfurtherdoubt on Thirlwall'sinterpretations.In our firstcharacterizationthereis no senseinwhichpositionsoutoflong-runequilibriumcan be called 'demand-constrained',pace Thirlwall:the marketsclear at any short-runequilibrium.Along a dynamicpathwhenkchanges,and giventheparametersofthemodel,ifg, risesovertimeg9must fall,whichis contraryto whatwouldhappenifa higheragriculturalgrowthincreasedthedemand forindustrialoutputand made itgrowfaster.It is truethata rightwardshiftin thegacurve(due to a parametricshift)whichincreasesequilibriumga wouldincreasetheequilibriumgrowth-rateof theindustrialsector,but thismustbe truein any dynamicequilibriumforany model witha balancedgrowthequilibriumpath(as was thecase fortheLewisand Jorgensonmodelsas well). Whilethe last two commentsapplyforour rigid-pricemodel as well,the firstdoes not,since disequilibriumstateswithexcessdemandand supplyare possible.But,as Fig. 2 makesit clear, thereis no one-to-onerelationbetweenexcessdemandor supplyforthe industrialgood, and whetherwe areabove orbelowtheequilibriump; thedirectionofexcessdemanddependson k as well.
  10. 10. 164 A KALDORIAN MODEL REVISITED but Lewis's and Kaldor's are similar:theybothassumethatsurpluslabour exists(so thatthewagein industryin termsoftheagriculturalgood is fixed), andthatall savingsareautomaticallyinvested.Theonlyrealdifferencebetween thetwo is thatthe Kaldorian model assumesthatthereis no intersectoral capitalmobility,all savingsbeinginvestedwithinthesectoroforigin,whilethe Lewis (1954, 1972) model in whichthe two sectorsof a closed economy tradewitheach otherassumesthatthereis no investmentin agriculturewhere outputgrowsonlydue to technologicalchange,and theagriculturalsurplusis investedin theindustrialsector.13We are thusentitledto call theKaldorian modela classicalone,similarin spiritto theLewismodel.'4 If demand issues are to be adequately introducedinto the Kaldorian frameworkweneedtomodifythemodelofSection2. In thatmodelweresolved thecontradictionbetweenthemarkup-pricingequation(10) andwageequation (5) byjettisoningtheformer,butdemandissuescan be broughtinbyretaining the markupequation and forsaking(5) instead.'5 This alternativemodel appearsto be closerin spiritto someofKaldor's otherworkon thetermsof tradeand growth,whereitis assumedthatthereis markuppricinginindustry, whiletheagriculturaltermsoftradeare flexibleand demand-determined.16 Because industrypracticesmarkuppricing,it may be assumedthatfirms adjustoutputaccordingto demand,so thattheyhaveexcesscapacity;thuswe dispensealso withthefull-capacityassumptiongivenby(4). Maintainingthe full-capacityand flex-priceassumptionsfortheagriculturalsector,thesupply- demandbalanceequationsforthetwomarketscan be writtenas - [a(l - sa) + sa]aak/p+ (1 - c){[l + (1 - s)z]/(1 + z)}u = 0 (18) a(l- s)ak/p - {1 - a[1 + (1- s,)z]/(1 + z)}u + gn+ gak = 0 (19) whereu = QI/Kn,a measureofcapacityutilizationin theindustrialsector.To completethemodel we assumethatindustrialinvestmentdependspositively ontherateofcapacityutilizationinindustry,'17so that,ina simplelinearform, 13 Lewis(1954) appearsat timesto assumeaway tradebetweentwosectors,butourcomments arerelevantforhismodelinwhichthetwosectorsproducedifferentproductsand tradewitheach other(see pp. 172-3). This correspondsto thesecondofthethreemodelsin Lewis(1972). 14 See Dutt(1989) fora formalcomparisonofthealternativemodelsdiscussedhere as wellas others-in termsofa commongeneralframework. 15 We couldactuallyretainboth,determiningthetermsoftradefrom(11). In theshortrun,for givenk,wecouldthendeterminethelevelofcapacityutilizationfromthemarket-clearingequation fortheagriculturalsector seeequation(18) below.In thelongrun,withpdetermined,thesectoral growthratesare determinedby(3) and theagriculturalmarket-clearingequationsolvesfork. 16 See Kaldor's (1976) analysisoftheinteractionbetweentheprimaryproducingand industrial sectorsoftheworldeconomy.It is also consistentwithKalecki's (1971) viewsofpricing.Other 'closures'are possible,whichendogenizethe markupin industrybut introducean independent investmentfunction,or whichintroduceforeigntrade.Whiletracesofsuchalternativemodelscan be foundin Kaldor's otherwork,forthesake ofbrevitywe concentrateonjust one model. 17ThisfollowsKaldor (1940). It is also customary(see Robinson(1962)) to maketherateof profitan argumentofthedesiredaccumulatonfunctioninneo-Keynesiangrowthmodels.Butsince (10) impliesthatherateofprofitis givenby r z= ZA(1+ z)]U, and sincewe are assumingz to be givenin our analysis,thisinfluenceis also beingcapturedby thecapacityutilizationargument.
  11. 11. A. K. DUTT 165 gn= af+ bu (20) withpositiveparameters,and thatagriculturalinvestmentdependsinversely on theindustrialtermsoftradeso that ga= /P. (21) The structureofthismodelis similarto thoseofthe'structuralist'modelsof Taylor(1982, 1983),theonlymajordifferenceshavingto do withtheprecise specificationofthesectoralinvestmentfunctions.18 In theshortrun,giventhesectoralcapitalstocksand hencek,we assume thattheagriculturaland industrialgoods marketsclear,respectively,through variationsin Pa and Q, whichimplyvariationsin p and u. Substituting(20) and (21) into(18) and (19) we solvefortheshort-runequilibriumvalues, U = 65[c(1- sa) + sa]aa/1 (22) p = Qk/{T(l -cx)[1 + (1 -S)Z]/(1 + Z)} (23) where Q = [x(l - sa) + s0]aa{sn[z/(1 + z)] - 5} + {(1 - cx)(saaa- 8)[1 + (1 - sJ)z]/(1 + z)} Short-runstabilityrequiresQ > 0, whichwe assume.19Observingthat the short-runequilibriumvalueofu is independentofk,and substitutingthisinto (20), we can obtainthegncurveofFig. 3.20 Equation (21) is representedby theg. curve,and equation(23) bylineOA. In theshortrun,givenanyk,we can determinep, gn and g.. In the long run k moves over time to a balanced-growthpathat k*. If ? increasesequation (22) shows that u will increase: a higherrate of agriculturalinvestmentincreasesthe demand for industrialgoods for investmentpurposesand raisesindustrialoutputin theshortrun.Since(20) showsthatthegncurveis pushedup as well,therateofindustrialgrowthis also increasedin thelongrun.In thismodel,clearly,fasteragriculturalgrowth 18 Taylor(1982) assumesthatg, and g9are functionsofsectoralratesofprofit.Taylor(1983) takesg9to be institutionallyfixedand g, to dependon thegap betweenindustrialand agricultural profitrates.Sincewitha non-capitalistagriculturetheagriculturalrateofprofitisdifficulttodefine, we haveassumedthatagriculturalinvestmentdependson thetermsoftrade. '9 Thisconditionwillbe satisfiedwhensnz/(1 + z) > 6 andsaaa > B.The firstoftheseconditions is the familiarconditionthatthe savingresponse(to variationsin u) in the industrialsector exceedsinvestmentresponse.The second conditionimpliesthat capital always flowsout of agriculture;Saaa = E implies,from(21) thatthereare no intersectoralcapitalflows.Capital flows into agricultureare not necessarilydestabilizing,sincethisis a sufficient,and not a necessary conditionforstability. 20 IfwesubstituteforQ from(24) into(23) wewillgetan inverserelationbetweenp and u given k,and hencean inverserelationbetweenp and gnfrom(21). However,sincethiscurvewouldtake kas givenitcouldnotbe usedto examinethedynamicpathoftheeconomy.Whatourhorizontal gnlinetakesintoaccountis thefactthatchangesin k and p are proportionaland leaveunaffected thelevelsofu and gn.
  12. 12. 166 A KALDORIAN MODEL REVISITED P P /A 0 k* k 0 g* FIG. 3. increasesindustrialgrowthbyprovidinga morerapidly-expandingmarketfor itsproduct. A comparisonofthisamendedKaldorianmodelwiththemodelofSection 2 showswhythelatter(and Thirlwall's)does notallowtheagriculturalsector toplaya roleinprovidinga marketfortheindustrialsector.Thismodeldiffers fromthepreviousones in twocrucialways.First,it departsfromthenotion that all saving is identicallyinvested;this is achieved by introducingthe independentinvestmentfunctions.The investmentfunctionfortheindustrial sectorimpliesthat the aggregatedemand forthe industrialgood will not identicallybe equal toitsaggregatesupply,so thata demandproblemforthat sectorcan arise.Second,itallowsforintersectoralcapitalmobilityand thereby ensuresthattheagriculturalsectorcan actuallysolvethedemandproblemfor theindustrialsectorbybuyingfromita differentamountthanwhatitsellsto it.Ifwe assumeawayintersectoralcapitalmobilityin thedemand-constrained modeljust discussedand assumesaaa = a, we find,using(18) and (19), that savingequals investmentin theindustrialsector,or that 1= s,1z/(1+ z)]u. (24) Equations(20) and(24) thensolvefortheequilibriumvalueofu(in bothshort and long runs),fromwhichit followsthatg,,dependsonlyon z, s, and the investmentparametersintheindustrialsector.Theindustrialsectoris demand- constrainedin thesensethatan increasein demand(forinstancean increase in a) willincreasethelevelsofcapacityutilizationand capitalaccumulation; but thereis stillno room foragricultureto solve the marketproblemfor industry:ifagriculturalincomerises(say due to a risein aa) thetermsoftrade will turnagainstagriculture,but u and g,,will be unchanged.Agricultural
  13. 13. A. K. DUTT 167 expansiondoes expandindustrialdemandbyraisingagriculturalincome,but sincetradeis balanceditis exactlyoffsetbya higherdemandforagricultural goods bytheindustrialsector. 5. Conclusion This paper has developeda consistent,formalKaldorian modelofgrowth and development,drawingon theworkofThirlwall(1986, 1987).It has also analyzedthedisequilibriumdynamicsbehindthemodeland demonstratedits dynamicstability,somethingnot adequatelydone before.This analysishas shown that Kaldorian model is not what Thirlwall and indeed Kaldor himself thoughtit to be, thatis, a model of an economywitha fixprice industrialsectorand a flexpriceagriculturalsector,and one whichadequately capturestheroleoftheagriculturalsectorin solvingtheproblemofdemand fortheindustrialsector.Instead,ithas shownthatthemodelis similarto that ofLewiswhich,accordingtopreviousinterpretations,didnotadequatelyfocus on thedemandissue. ThoughtheKaldorian modeldoes not liveup to Thirlwall'sexpectations, however,we stillbelieve that it is an usefulcontribution.First,although similarto theLewis model,it departsfromLewis's staticfocuson disguised unemploymentand develops a dynamicanalysisof capital investmentand technicalchangein agriculturewhichis morerelevantforunderstandingthe behaviourof dual economiesusingindustrialcapital in agriculture.Second, demandissuescan be introducedeasilyby modifyingthemodel to make it consistentwithsomeofKaldor's otherwork.Finally and thisis a direction not pursuedin thispaper themodel has laid thefoundationon whichthe analysisofseveralimportantissuescan be based: Canning(1988) demonstrates howtheroleofincreasingreturnsto scale in dual economiescan be analyzed usinga Kaldorian model and Dutt (1990) uses the model to analyze the implicationsofintersectoralcapitalflows. Universityof NotreDame,Indiana REFERENCES CANNING, D. (1988). "Increasingreturnsinindustryand theroleofagricultureingrowth",Oxford EconomicPapers,40,463-76. DUTT, A. K. (1989). "Alternativemodels of agriculture-industryinteraction",unpublished, UniversityofNotreDame. DUTT, A. K. (1990). "Intersectoralcapital mobilityin a Kaldorian model of development", unpublished,UniversityofNotreDame. FITzGERALD, E. V. K. (1990). "Kalecki on financingdevelopment:an approach to themacro- economicsofthesemi-industrialisedeconomy,CambridgeJournalof Economics,14(2), June, 183-203. JORGENSON, D. (1961). "The developmentofa dual economy",EconomicJournal,71,309-34. KALDOR, N. (1940). "A Model oftheTrade Cycle",EconomicJournal,March. KALDOR, N. (1975). "What is wrongwitheconomictheory",QuarterlyJournalof Economics, August.
  14. 14. 168 A KALDORIAN MODEL REVISITED KALDOR, N. (1976). "Inflationand Recessionin the World Economy",EconomicJournal,86, December. KALDOR, N. (1979). "EquilibriumTheoryand GrowthTheory",in M. J.Boskin(ed.), Economics andHumanWelfare.EssaysinHonorof TiborScitovsky,New York,AcademicPress. KALECKI, M. (1971). SelectedEssays on theDynamicsof the CapitalistEconomy,Cambridge, CambridgeUniversityPress. KALECKI, M. (1972). Selected Essays on the EconomicGrowthof the Socialist and Mixed Economy,Cambridge,CambridgeUniversityPress. LEWIS, W. A. (1954). "Economic DevelopmentwithUnlimitedSuppliesofLabour", Manchester Schoolof EconomicsandSocial Studies,22, 139-91. LEWIS, W. A. (1972). "Reflectionson UnlimitedLabour" in L. di Marco (ed.), International EconomicsandDevelopment,EssaysinHonorof Raul Prebisch,New York,AcademicPress. ROBINSON,J.(1962). EssaysintheTheoryof EconomicGrowth,London,Macmillan. TARGETTI,F. (1985). "Growthand thetermsof trade:a Kaldorian two sectormodel",Metro- economica,February,79-96. TAYLOR, L. (1982). "Food PriceInflation,TermsofTrade and Growth",in M. Gersovitz,C. F. Diaz-Alejandro,G. RanisandM. R. Rosenzweig(eds),TheTheoryandExperienceofEconomic Development,London,GeorgeAllenand Unwin. TAYLOR,L. (1983). StructuralistMacroeconomics,New York,Basic Books. THIRLWALL,A. P. (1986). "A GeneralModel ofGrowthand Developmenton Kaldorian Lines", OxfordEconomicPapers,38, 199-219.

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