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Increasing Returns in Industry and the Role of Agriculture in Growth
Author(s): David Canning
Source: Oxford Economic Papers, New Series, Vol. 40, No. 3 (Sep., 1988), pp. 463-476
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/2663016
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Oxford Economic Papers 40 (1988), 463-476
INCREASING RETURNS IN INDUSTRY AND
THE ROLE OF AGRICULTURE IN GROWTH
By DAVID CANNING
THE PROBLEM of increasing demand for food coupled with diminishing
returns in agriculture was central to the classical growth theories of Malthus
(1966) and Ricardo (1951). This theory predicts that the economy must
eventually stagnate, due to agriculture using ever increasing resources with
falling productivity. This has not happened in the developed world.
The aim of this paper is to demonstrate that, with increasing returns to
scale in the industrial sector, diminishing returns in agriculture need not be
a barrier to growth. The growth of the economy may be unlimited, despite
ever increasing demand for agricultural produce and in the absence of
technical progress, if the increasing returns in the capital goods industries
are sufficient to outweigh the diminishing returns to capital in agriculture.
The engine of growth is firmly located in the industrial sector; agriculture
becomes more productive, but only by the use of ever larger amounts of
cheap capital goods.
Neoclassical growth theory, as set out by Meade (1961) and Solow (1970),
assumes constant returns to scale and the unlimited reproduction of the
factors of production, allowing a steady, positive, rate of growth in the long
run. It ignores the presence of a fixed factor (land), but seems compatible
with the experience of the developed world in the late 19th and the 20th
centuries. Kaldor (1957, 1975, 1979) emphasizes growth of manufacturing
output, capital accumulation, and the productivity gains these generate.
This leads to a theory of economic development which highlights the
transition from agriculture to manufacturing as the key to a high rate of
Thirwall (1986) investigates a model of growth and development along
Kaldorian lines. The importance of balanced growth is emphasized;
agricultural output must grow at the same rate as industrial output in
equilibrium. The results of his model are a return to the classical view; the
growth rate is regulated by increases in productivity in agriculture and the
cultivation of new lands. This constraint may be relaxed for an individual
country by international trade, but taking the world as a whole the
agricultural sector must eventually dominate.
A simple model is developed to show that increasing returns in industry,
and in particular the production of capital goods, may relax the long run
constraint agriculture places on growth. With increasing returns in some
sectors, and diminishing returns (due to a fixed factor) in others, balanced
equilibrium growth is not possible. Even if each sector's output grows at the
same rate the proportion of resources devoted to each sector changes; more
importantly, given each sector uses different factor proportions, growth will
change the relative rewards of the different factors of production and, given
differential savings rates, the future growth rate.
With increasing returns at the plant level in industry we cannot assume
perfect competition; the number of firms must be determined endogenously.
Industrial structure is very important; fewer firms will allow greater
exploitation of scale economies, but will lead to lack of competition and
may result in demand growth being siphoned off into higher prices and
profits rather than producing extra output. In order to overcome the
problem of food production increasing returns in the capital goods industry
must be large enough to overcome the decreasing returns to employing
capital in agriculture, but small enough to ensure that there are enough
firmsin the capital goods industry to prevent monopoly pricing.
Instead of concentrating on aggregate relationships I shall construct a
small general equilibrium model of the economy. While this is perhaps more
detailed than necessesary it does ensure consistency.
Three time scales are considered. In the short period the supply of each
factor, land, labour, and capital, is fixed, and equilibrium is brought about
by the price mechanism. This equilibrium will determine a particular level
of output for the investment goods industries. These investment goods serve
as capital stock for the next period. Given a fixed stock of land and labour
the medium period equilibrium is the limit of the sequence of short period
equilibria with changing capital stocks. The effect of a changed labour
supply on the short and medium run equilibria is then considered; the long
period behaviour of the system will depend crucially on whether labour
supply increases lead to rising, or falling, real wages.
In the short period a higher supply of labour tends to depress real wages.
However, profits on capital tend to rise and the medium period equilibrium
will have a larger capital stock. With increasing returns in the capital goods
industries the price of capital will become lower (provided there is sufficient
competition) than before. The real wage may now be either higher or lower
than previously, depending on whether or not the lower cost of farm
equipment outweighs the effect of increased demand pressure on the price
of food. If increases in the labour supply tend to lower the real wage
(measured in corn) in the medium period the economy must, in the long
run, tend to a position of subsistence wages which constrain population
growth. On the other hand, if a higher labour supply tends to increase the
real (corn) wage in the medium period there is no barrier to population
growth. The condition separating these two cases will be shown to depend
on the returns to scale in the investment goods sector and the degree of
substitutability of the factors of production.
The model investigated here assumes market clearing. Keynesian prob-
lems of effective demand are ignored. Costabile and Rowthorn (1985)
discuss a Malthusian model in which unemployment is possible, even in the
Assumingincreasingreturnsin industrygives the model manyfeaturesof
a Kaldorianframework;in particular,outputgrowthin the industrialsector
generatesincreasesin productivity.The studyof increasingreturnsto scale
and imperfect competition is becoming common in internationaltrade
theory (see Venables (1985)). It seems clear that the applicationof these
techniquesto growththeorywill producesome insights.Whileit is unlikely
that Kaldor would accept the limitations imposed by a simple, static
economiesof scale, fullemployment,model, it mayprovidea usefulstarting
point for formalisinghis ideas.
The most strikingthing in practice about the early stages of economic
growthis the shift of resourcesfrom agricultureto the industrialsectors,
two featuresthe presentmodel hopes to incorporate.
2. The model
There are three classes in the economy. Workers own an amount of
labour L which they sell in a competitivelabour market. They spend all
their income on either agriculturalgoods (corn) or manufactures,attempt-
ing in doingso to maximisethe utilityfunction
U(CaCl) =(Ca-C),c', Ca
and O.e > O? <+ 1<
PaCa + Pm col 1
where Caand cmare consumptionof agriculturalgoods and manufactured
goods respectivelyand Pa and pm are their prices. We take the wage as
represents subsistence consumption of corn without which the worker
cannotsurvive.The demandfor cornper workeris
Workersbuy the subsistencelevel of food and then dividethe rest of their
income in fixed proportionsbetween food and manufactures.As workers'
incomes measured in corn rise they spend a lower proportion of their
Landlordsrent out their land (of total size F) each period, spendingall
theirrents on agriculturalgoods. This is a simplifyingassumption,but will
not help our case; in fact it will tend to emphasizethe problemof excessive
Capitalistssell all their capital at the beginningof the period using the
proceeds to buy investment goods at the end of the period. These
investmentgoods then serve as the capitalstock of the next period. Capital
is completely used up in the process of production. The capitalists merely
accumulate capital; they have no other aim.
Entrepreneurs buy the factors of production at the beginning of the
period in competitive factor markets. They then use these factors to
produce goods for one of the three product markets, agricultural goods,
manufactured goods or investment goods. The production functions for
each sector are given by
Qa= F'-fIL4K! 0< ctfcvt+ <1
Q"I= L6K-6 0< 6, y-6 <I7y
Qi = LJOKO-? Of 0, 0 <1S
where Qa, Qmand Qjare the total outputs of agricultural goods, manufac-
tured goods and investment goods respectively. Agricultural goods are
produced under constant returns to scale with three factors, land, labour
and capital. Manufactured goods and investment goods are produced under
increasing returns to scale at the plant level. However, there are diminishing
returns to each factor. The outputs of each plant are added together to get
the industry output.
The following assumption is also made
/(a + f) = 61y = q/u
This implies that the optimal capital/labour ratio will be the same in each
sector. Factor prices therefore depend on the relative scarcity of each factor
and not on the pattern of output. The great advantage of this assumption is
that we can now discuss equilibrium at the level of the industry with
independent demand and supply schedules. Without this assumption any
variation in the output of one industry will change relative factor prices, the
incomes of the different classes in society, and the demand schedule for that
3. Shortperiod equilibrium
The short period is defined by the period in which all three factors of
production are fixed in size. Physical capital is assumed to be used up within
the period (100% depreciation) while the output of the capital goods
industries is not available for use until the following period. It is assumed
that there is free entry for entrepreneurs in all sectors; this keeps their
profits at zero. Capitalists merely sell their capital stock to entrepreneurs in
a competitive capital market; any short period divergence between the
demand price and the long period, or normal, supply price accrues to the
capitalists (or landlords) as entrepreneurs bid up the price of capital
equipment (or land).
It is assumed that all transactions in the short period take place
simultaneously. We can think of the factors of production being sold at the
beginning of the period in exchange for future contracts in terms of the
output of the productive sectors. This avoids the problem of constructing a
wage fund to bridge the gap between hiring factors and the sale of output.
In equilibrium we need to determine the output of each of the three
sectors, the price of each output and the three factor prices. Taking the
wage as numeraire this leaves eight unknowns to be determined.
(i) Agricultural goods. The demand for agricultural goods come from two
sources, workers and landlords. Adding these two demands gives:
Qa =caL + (r/pa)F
where r is the rent per unit of land. Given workers demand and our
production function this simplifies to
Qa a+ ,C 3+ 6
(P L) 1
since landlords consume a fixed fraction of agricultural output.
We now turn to the supply schedule. Given the price of the inputs (1 for
labour, r for land and Pk for capital) we can calulate the supply price of
Pa = (r/(1 - C- (2)
This is the cost of production of agricultural goods, assuming farmers use
the cost minimising factor proportions. The level of output does not affect
the agricultural supply price directly, it does so only through its effect on
(ii) Investment goods. We again start by considering the demand schedule.
Expenditure on investment goods is given by
QiPi = KPk (3)
where K is the initial, fixed, stock of capital. Capitalists sell their initial
capital, K, in the factor markets and spend the entire proceeds on
investment goods. A point to note is that Pk, the price of capital at the
beginning of the period, is independent of the level of output, Qi, of the
investment goods industry, because of our assumption of equal capital
intensities in all sectors. It follows that the price elasticity with respect to the
industry's output is -1, that is, demand for investment goods is fixed in
nominal terms. Equation 3 can be thought of as determining the demand
price of investment goods, pi. That is, it determines the price, pi, which can
be charged for any given level of output Qi.
Consider the supply schedule for investment goods. With increasing
returns to scale at the plant level the most efficient form of production in
the investment goods sector would be a single plant. However this would
lead to monopoly pricing and high profits in this sector. Allowing free entry
means that prices and profits will be driven down by competition between a
number of firms.
We begin by considering the number of firms in the industry to be fixed at
N. Each firm decides on a level of output qj. Given the aggregate output of
the industry the price pi of investment goods then clears the market. The
industry is assumed to be monopolistically competitive and we take the
symmetric Cournot equilibrium as our solution concept. Taking the
production of the N-1 other firms in the industry as given, each firm can
construct a demand curve for its own output. Given this, firm j attempts to
maximise its profits
J = Piqj- L- KPk
taking into account the fact that changes in its output qj will change the
industry price pi.
In general, with a finite number of firms, N, of significant size in the
industry, each firm will realise that changing its level of output will increase
its demand for the factors of production. This will, in general, change the
factor prices it pays (in addition changes in factor prices change the
distribution of income and the industry's demand curve). We can either
assume firms ignore these effects (that is, they think of themselves as 'small'
in the factor markets) or, as in this model, make factor prices independent
of the pattern of output.
Putting marginal revenue equal to marginal costs (where the marginal
cost of output is calculated on the basis of the use of the cost minimising
relative factor proportions derived from the production function) for profit
maximisation, we have
dp + 1 (KjPk + Li)
Note that for a > 1 marginal cost, the right hand side of the equation, is less
than average cost, AC, given by total costs divided by total output,
(Kjpk + Lj)lqj. Firms will expand output as long as marginal revenue
exceeds marginal cost. For equilibrium to emerge marginal revenue must
eventually fall fast enough, due to the lower price associated with higher
output, to outweigh the declining marginal cost (due to increasing returns)
as output rises.
With only one firm in the industry, the monopoly case, the demand curve
faced by firms is given by total industry demand. The total revenue of the
monopolist, Qipi, is given by Kpk and is independent of the level of output.
To maximise profits the monopolist will take this fixed revenue with
minimum cost, that is with output as close as possible to zero, exploiting the
relatively inelastic demand schedule for investment goods.
With more than one firm each will still realise that the industry price is
sensitive to its output. However, as the number of firms, N, increases, each
individual firm's impact on industry price declines. In the general case, with
N firms, the symmetric equilibrium is characterised by the fact that
ej= (qj/pi) dpi/dpj, the elasticity of the industry price with respect to firmj's
output, is given by - 1/N. A one percent increase in total industry output
drives the industry price down one percent; a one percent increase in output
by a single firm represents a 1/N percent increase for industry output, if
there are N firms, and has a correspondingly small effect on the industry
price. Rewriting the profit maximising condition gives
(ej + l)p = AC/uo
where AC is average cost of production. In the case of N firms we have
ej= -1/N so
Pi 1 N
For N small price exceeds average cost and firms make positive profits.
Given that firms enter the industry as long as profits are positive N will
increase until profits fall to zero (ignoring the integer problem) and price
equals average cost. The number of firms increases to its equilibrium value
N= o/(o- 1).
The number of firms is smaller the greater the returns to scale. The profit
maximising equation only holds for N : 2, that is a s- 2. For a > 2 the
outcome is a monopoly with low output. Even if a is less than 2 but still
large, so there are very few firms, the problem of cartel behaviour, rather
than pure monopolistic competition, may appear. The equation only seems
appropriate for N large (arclose to 1). In any case, for a large the fact that
N may not be an integer becomes important. For example, if a is 1.6, N is
approximately 2.7, so an industry with 2 firms gives positive profits while
competition between 3 firms would give losses. Approximating N by an
integer is less important for small ar.In what follows I shall assume the aris
such that N = o/(o - 1) is an integer.
An important point is that N, the number of firms in the industry with
free entry, depends only on the returns to scale; it is independent of the
level of demand. Increases in demand lead existing firms to expand rather
than new firms to be created. It follows that the industry exhibits the same
degree of increasing returns to scale as the plant. With other production
functions this is not the case. In general expansion of an industry will
involve changes in the number of firms operating as well as the output level
of each firm, so that the industry's returns to scale will usually differ from
those at the plant level.
We can determine the average cost of production for any level of output
Qi, assuming this output is split between N firms who use cost minimising
factor proportions and pay market rates for inputs. This gives us a supply
price for each level of output, a price at which firms just cover costs,
pi= (or/(u-r ))(- (- P)f P N( l)/ pI (4)
The firsttwo termsare constants.The priceof investmentgoods (measured
in wage units)is increasingin the cost of capital,but fallingas a functionof
industryoutput due to increasingreturnsto scale. As N, the numberof
firms,rises the averagecost of productionrises, outputbeing splitbetween
more firms, losing scale economies. Putting N equal to the zero profit
equilibriumnumberof firms,equation4 gives the industrysupplyprice for
each level of output.
Puttingdemandpriceequalto supplypricewe candeterminethe industry
equilibrium.The reasonfor usingMarshallian"demandprice"and "supply
price"concepts, determineprice as a functionof demandon the one hand
andsupplyon the other, is, of course,the factthatgivenincreasingreturns,
and decliningmarginalcost curvesfor firms,we cannotconstructa supply
curve in the usual way, findingthe level of output firmswish to produce
takingthe marketpriceas given.
(iii) Manufacturedgoods. Firmsin the manufacturedgoods marketact in
exactly the same way as for investment goods. The expenditure on
manufacturesis given by
Qmpm= L(1 -cpa)/(O + E) (5)
so workersspend a constantfractionof their surplusincome (the surplus
over agriculturalnecessities) on manufactures.Again the elasticityof the
industry'spricewith respectto its outputis -1. We have M = y/(y - 1) as
the numberof firmsin the industryand
Pm= (y/(,y - ))(/y - 6)) PMky l)Iyp7 -)IyQ -YY (6)
is the industrysupplyprice.
The manufacturingsectorplaysno real role in the model. The reasonfor
separatingit from the investmentgoods sector is to isolate any increased
scaleefficiencieswhichcome froma shiftin consumptionpatternsfromfood
to manufactures.With increasing returns to scale the level of industry
disaggregationin the model is important.If we assumethat two separate
goodsaremanufacturedby one productionprocessanincreasein the output
of one of the goods will tend to reducethe supplypriceof the other. If the
industrialsector is treated as producinga single good, whichcan be either
consumedor invested, a shiftin consumptionto manufacturestendsto give
scale economies to the entire industrialsector which lowers the price of
investmentgoods andcomplicatesour results.
(iv) The factormarkets.Given constantreturnsin agriculture,landlords
Thisis not the case in otherindustries,where, due to increasingreturns,the
sumof the factors'marginalproductsexceedstotaloutput.The totalincome
of capitalistsis the sumof theirsales of capitalto the threeindustriesgiven
paK = PkKa + PkKi + PkKfl
= LaJIcv+ Li(u - P)/I + Ln1(Y-)/y
pkK = L3I cv (8)
since L = La + Li + Lm, and the capital/labour ratios are the same in each
industry. The relative price of capital and labour depends only on the
Equations(1)-(8) allow us to solve for the eight unknowns.It is easy to
checkthat the systemsatisfiesWalras'law, thatis
PaQa+PmQm +piQi = rF +PkK + L
so total expenditureequals total factor income. For our purposesit is not
necessaryto solve the entiresystemexplicitly.Solvingfor the outputof the
investment goods industrywe have Qi= K(pk/pi). The supply price of
investmentgoods, pi, dependson the outputof that industryand the price
Pk of capital as an input. Substitutingfor pi and using the capital/labour
ratioto substituteforPk we canfindQi, the outputof the investmentgoods
industryas a functionof the startof periodstocksof capitalandlabour:
whereH is a constantdependingon the parametersof the model.
4. Equilibriumin the mediumperiod
If thereis little capitalat the beginningof the periodits pricewillbe high,
higherthanthe cost of the outputof the capitalgoods industriesat the end
of the period, and the capitalstock will accumulate.Similarly,if capitalis
too plentifulits pricewillbe low andcapitalistswillfindreplacementcapital
more expensivethan the proceedsof their existingcapital, and the capital
Takingthe quantitiesof land and labouras fixed, considera sequenceof
short periods in which the capital stock in each is given by the level of
outputof the investmentgoods industriesin the previousperiod.Thatis
Kt+1= HL 4Kc 4'
Proposition1. For Ko> 0, Ktconvergesmonotonicallyto
K* = H11(+O-a)LO1(1+0-a)
Proof. K* is obviouslythe only equilibriumof the system.SupposeKt< K*
Kt+llKt = H L4K~t-' - (K*/Kt)l+c-Ir> 1
so K,+1> K&.Further
Kt+I/K* = =--t )
O) - -O < 1
so Kt<Kt+i< K*. Since Kt+i< K*, Kt+l<Kt+2<K* and so on. There-
fore, if Kois less than K*, Ktis an increasingsequence which is bounded
above andhence converges.Its limitmustbe an equilibriumof the system,
andso is K*.
If Kostartsabove K* we can show by a similarmethodthat Ktdecreases
K* is the mediumperiodequilibriumcapitalstock.
The essentialpoint in the argumentis a - 4)< 1. Thisis easy to see near
the equilibriumpoint. Linearisingthe system aroundthe equilibrium,and
letting xt be the deviation from equilibrium,we have the approximation,
xt+1= (a - 4q)xt,for xt small.
5. Changesin the labourforce
Considerthe long run effect of a once off increasein the laboursupply.
Will this tend to increase or reduce the price of food measuredin wage
units?If it tends to increasethe priceof food then an indefiniteincreasein
populationcannotbe sustained,the amountof food each workercan afford
eventuallyfallingbelow subsistence.However, if food pricestend to fall as
laboursupplyincreasesthere is no barrierfrom agricultureto an indefinite
Substitutingfor factor prices in the agriculturalprice equation (2), and
takingthe capitalstockto be at its mediumperiodequilbriumlevel, K*,
Lt-l+(+'(l++- = A[CPa + ((0/0 + c))(1 - CPa))I-v'6Pa'1
Differentiatingthroughwith respectto Pait is easy to showthat
dPa _ __
In the medium period an increase in population and labour supply will
depressfood pricesif the returnsto scalein the investmentgoods sectorare
largeenough. The criticalvalue a*, the necessaryreturnsto scale, falls as
A'+ /3 rises and land becomes less importantin the productionfunction.
Additionallyreducing4qand a, makingboth the agriculturalsectorandthe
investment goods industry itself more capital, as opposed to labour
intensive, will tend to decrease the criticalvalue a*. The absence of any
demand side effects on the criticalvalue a* is the result of the special
assumptionthat the capital/labourratio is the same in each sector. If, for
example, the manufacturedgoods sector is more capital intensive than
agriculturea shift in demandfrom food to manufacturesas the economy
growswill increasethe demandfor capital,loweringits priceto agriculture,
and lowering a*.
If a > a* then in the medium period an increase in population will tend to
increase the wage measured in corn. However, there may be a take-off
problem. The increased labour supply will initially drive wages down. This
is the usual result of adding labour to a world with fixed stock of land and
capital. If the real wage falls below the subsistence level population growth
will be reversed, perhaps before capital accumulation can enable the
economy to provide a higher wage. Only when the profits of capitalists,
generated by the higher labour supply and lower real wage, have been
reinvested to produce a higher capital stock, exploiting greater scale
economies, can the benefical medium term effects of a larger labour force
be achieved. If the economy starts with a real wage near subsistence growth
may not be possible, population increases being reversed before longer run
scale economies occur. However, provided the take-off problem can be
overcome, the economy can grow, in terms of population size and real
incomes, without bound, despite the fixed supply of land.
If a < a* any increase in L depresses wages measured in corn. The short
run effect of falling real wages with an increased labour supply is mitigated
somewhat by scale economies in the medium run. However, these scale
economies are insufficient and real wages (measured in terms of corn) are
lower even after they have taken effect. Successive increases in the labour
supply will lead to ever lower real wages. Eventually population growth
must end, with wages at their subsistence level.
The pattern of employment changes during the process of economic
La aV C + 02
L =( +fi 'Pao+C + C
In a dynamic economy capable of long period growth an increase in
population will tend to depress agricultural prices and reduce the proportion
of the labour force employed in the agricultural sector. Given that the
capital/labour ratio is constant across sectors this implies a falling propor-
tion of total resources in agriculture. Growth will be associated with
industrialization, in the sense of an increase in the proportion of total
resources employed in the industrial sectors. If the returns to scale in
industry are large enough the absolute numbers in agriculture may fall.
Growth tends to increase real wages, but reduces the cost of capital, and all
sectors become more capital intensive in the long period, reversing the short
period effects of the labour supply increase. If land is of different qualities
the extensive margin of cultivation may even shift inwards as cultivation
becomes more capital intensive.
In a static economy, without sufficient returns to scale in the capital goods
industries, increases in population tend to increase the proportion of
workers employed in agriculture. The capital stock increases, but the cost of
capital does not fall sufficiently. The price of corn in wage units rises, the
increased demand resulting in higher production costs (mainly higher rents
as land is used more intensively), and its per capita consumption by workers
Only a one-off increase in the labour supply has been considered. To
complete the model we really require a growth equation for labour supply,
perhaps in terms of the real wage. This complicates the model because we
cannot then assume that labour supply remains fixed as the economy tends
to its medium run equilibrium. The results set out in this section show that,
without sufficient increasing returns in industry, growth in the model, in
terms of population, must eventually come to a halt due to lack of
agricultural output. In the case where the returns to scale are greater than
the critical value, but not so high as to rule out competition, unlimited
growth of population, and real incomes, is possible, but depends on the
exact specification of any population growth equation, and the initial
position of the system.
The possibility of a cycle emerges if capital accumulation is slow relative
to population growth. A Kaldorian alternative to a population growth
equation would be to fix the real wage (the utility level of workers) and
assume an unlimited availability of labour at this wage. In this case
employment is determined by the capital stock and (X*is the dividing line
between those economies which grow without bound (in terms of quantities
of capital and labour) and those which tend to a stable equilibrium.
In an economy with increasing returns in industry, particularly in the
capital goods sectors, long period growth can be sustained despite the
presence of a fixed factor, and no technical progress, in agricultural
production. Growth will be accompanied by a process of industrialization as
the proportion of workers in agriculture falls and the economy becomes
more capital intensive (in physical terms).
The conclusion to be drawn about the role of agriculture in industrial
development is almost the opposite of that found in Thirlwall (1986):
'we expect a healthyagriculturalsector to be the drivingforce behindindustrial
growthin the earlystages'
'The resultssuggestthat technicalprogressin agriculture(or the discoveryof
new land)will relaxthe ultimateconstraintson industrialgrowth,and only these
factorswill do so. Technicalprogressin industryaffectsthe terms of trade (by
changingk), but not the long runequilibriumgrowthrate.'
(k is the wage bill per unit output of industrial-including capital-goods).
The analysis presented here suggests that it is exactly by changing k, that is
to say by reducing the cost of capital to the agricultural sector, that industry
can, by itself, be the driving force behind a sustained process of economic
growth. Kaldor (1976) similarly fails to provide a role for cheap capital in
overcoming the problem of primary sector production, though since he
deals to some extent with exhaustibleresourcesas well as agriculture,and
worksin an internationalcontext, the above analysisdoes not necessarily
apply. Here a closed economy, with no exhaustibleresources, has been
assumed.In this case, providedthere are sufficientreturnsto scale in the
capital goods industries,the constrainton growth is not land but, as in
Kaldor(1986), the laboursupply.Increasesin the laboursupplyallow the
economyto exploitthe increasingreturnsto scale in industry.
Investigationsof North-South trade, assumingthatone regionspecializes
in primary,the other in industrial,production,have been undertakenin a
neoclassicalframeworkby Findlay(1980), andin a Kaldorianframeworkby
Vines (1984). Thirwall(1986)shouldbe consideredas a similarstudy,since
in his model the real wage, and rate of profit,may differbetween sectors.
Whilethe resultsfoundhere cannotbe applieddirectlyto suchmodels, the
realwage andrateof profitbeingequal acrosssectors,they do suggestthat
the long run growthrate may be determinedin the industrial,and not the
Putting the present frameworkin a North-South context by allowing
differentreal wages in differentsectorsgreatlycomplicatesthe model. The
crucialpoint in sucha model is the assumptionmade aboutthe mobilityof
capital.If physicalcapitalcan be tradedin the same way as other goods,
complete equalisationof factor prices between regions takes place very
quickly. Cheap capital is availableto the poorer region with the smaller
capitalgoods industry(in additionthere arescaleeconomiesfromrationali-
sation as the capital goods industrybecomes more concentratedwith one
world market). If capital is not physicallytraded but capitalistscan buy
capitaloverseas(therearecapitalflowsin the balanceof payments)thiswill
tend to aid poorer countries by speeding up their capital accumulation,
Withoutphysicalcapital flows the picture for less developed countries
maybe verybleak;they areforcedto concentratein agriculturebecausethe
developedcountrieshave a comparativeadvantagein producingmanufac-
tures with their cheap capital and scale economies. If the developed
countrieshave a home agriculturalsectorthis gets moreefficient,becoming
more mechanised to exploit the cheap capital which is available. The
developingcountries are then forced to compete with this efficient agri-
culturalsectorwithoutthe aid of cheap capital,whichgenerallyrequiresa
lowrealwage.Thisprocesscanbecomecumulativeif the developedcountry
continuesto grow and achieve furtherscale economies. This very bleak
picture depends on the developed countries being able to compete in
agriculture;it is less so if the underdevelopedcountriesare the only source
of food or rawmaterials.
It is worthnotingthat while the capitalstock in agriculturemay increase
as the economy convergesto its mediumperiod equilibrium,the value of
thiscapitalstock, andits sharein the nationalincome,willbe constant.This
maygive riseto an empiricalproblemin distinguishingbetweenincreasesin
productivity in agriculture and productivity in capital production as a
source of growth, if capital is measured in value rather than physical terms.
This will be true whatever production functions are assumed, since the
mechanism proposed is the falling price of capital goods as they become
more plentiful and are produced more efficiently.
While, in a formal sense, agriculture undergoes no technical progress in
the model, it does adopt different techniques. Growth in agricultural output
requires that farmers shift to more capital intensive methods of production.
As Robinson (1952) points out, there is little to distinguish between a
change in factor proportions along a production function and shift of the
function itself due to technical progress; both require new processes and
new techniques to be introduced, and a degree of learning by doing. While
this is indeed the case it still seems important, if we wish to trace the causes
of economic growth, to distinguish changes in agricultural output brought
about by spontaneous changes in farming techniques from those induced by
changes in factor prices which originate in the industrial sector.
Pembroke College, Cambridge
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