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
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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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
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