Increasing Returns in Industry and the Role of Agriculture in Growth
Author(s): David Canning
Source: Oxford Economic Pape...
Oxford Economic Papers 40 (1988), 463-476
INCREASING RETURNS IN INDUSTRY AND
THE ROLE OF AGRICULTURE IN GROWTH
By DAVID CA...
importantly, given each sector uses different factor proportions, growth will
change the relative rewards of the different...
Assumingincreasingreturnsin industrygives the model manyfeaturesof
a Kaldorianframework;in particular,outputgrowthin the i...
is completely used up in the process of production. The capitalists merely
accumulate capital; they have no other aim.
Ent...
It is assumed that all transactions in the short period take place
simultaneously. We can think of the factors of producti...
lead to monopoly pricing and high profits in this sector. Allowing free entry
means that prices and profits will be driven...
individual firm's impact on industry price declines. In the general case, with
N firms, the symmetric equilibrium is chara...
The firsttwo termsare constants.The priceof investmentgoods (measured
in wage units)is increasingin the cost of capital,bu...
by
paK = PkKa + PkKi + PkKfl
= LaJIcv+ Li(u - P)/I + Ln1(Y-)/y
pkK = L3I cv (8)
since L = La + Li + Lm, and the capital/la...
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 K...
If a > a* then in the medium period an increase in population will tend to
increase the wage measured in corn. However, th...
as land is used more intensively), and its per capita consumption by workers
falls.
Only a one-off increase in the labour ...
deals to some extent with exhaustibleresourcesas well as agriculture,and
worksin an internationalcontext, the above analys...
productivity in agriculture and productivity in capital production as a
source of growth, if capital is measured in value ...
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Canning1988

  1. 1. 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 Accessed: 26/10/2010 14:32 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. Oxford Economic Papers 40 (1988), 463-476 INCREASING RETURNS IN INDUSTRY AND THE ROLE OF AGRICULTURE IN GROWTH By DAVID CANNING 1. Introduction 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 growth. 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 (COxfordUniversityPress1988
  3. 3. 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 long run.
  4. 4. 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, accompaniedbyanincreased(physical)capitalintensityinallsectors.Theseare 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 :,C, and O.e > O? <+ 1< subjectto PaCa + Pm col 1 where Caand cmare consumptionof agriculturalgoods and manufactured goods respectivelyand Pa and pm are their prices. We take the wage as numeraire(thisgivesmoresimpleequationsthanusinga cornnumeraire).c represents subsistence consumption of corn without which the worker cannotsurvive.The demandfor cornper workeris 0 /1 Ca=C+0 (--c 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 incomeon food. 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 demandfor agriculturalproduce. 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
  5. 5. 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 M Q"I= L6K-6 0< 6, y-6 <I7y j=1 N Qi = LJOKO-? Of 0, 0 <1S j=1 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 industry's output. 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).
  6. 6. 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 agricultural goods. 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 factor prices. (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
  7. 7. 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
  8. 8. 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 AC aoN-I 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)
  9. 9. 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 get theirmarginalproduct rF=paQa(l-oa-) (7) 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
  10. 10. by 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 capitallabourratio. 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: Qi =HLiPKa-iP 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 stockwill decline. 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* then Kt+llKt = H L4K~t-' - (K*/Kt)l+c-Ir> 1
  11. 11. 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 monotonicallyto K*. 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 growthof population. 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 _ __ = 1P) 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*.
  12. 12. 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 growth. 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
  13. 13. as land is used more intensively), and its per capita consumption by workers falls. 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. 6. Conclusion 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
  14. 14. 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 agricultural,region. 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, foreigncapitalistsexploitingtheirlow realwage. 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
  15. 15. 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 REFERENCES COSTABILE,L. and RoWTHORN,R. (1986) 'Malthus's Theory of Wages and Growth', Economic Journal, Vol. 95, pp 418-437. FINDLAY,R. (1980) 'The Terms of Trade and Equilibrium Growth in the World Economy', American Economic Review, vol. 70, pp 291-299. KALDOR,N. (1957) 'A Model of Economic Growth', Economic Journal, Vol. 68, pp 591-624. KALDOR,N. (1975) 'What is Wrong with Economic Theory', QuarterlyJournal of Economics, Vol 89, pp 347-357. KALDOR,N. (1976) 'Inflation and Recession in the World Economy', Economic Journal, Vol. 86, pp 703-714. KALDOR,N. (1979) 'Equilibrium Theory and Growth Theory', in Economic and Human Welfare: Essays in Honour of Tibor Scitovsky, M. Baskia editor, Academic Press. KALDOR,N. (1986) 'Limits on Growth', Oxford Economic Papers, Vol. 38, pp 187-198. MALTHUS,T. R. (1966) First Essay on Population. Reprinted by the Royal Economic Society. MEADE,J. (1961) A Neo-Classical Theory of Economic Growth. George Allen and Unwin Ltd. London. RICARDO, D. (1951) On the Principles of Political Economy and Taxation. vol. 1 of Works and Correspondence of David Ricardo., P. Sraffa editor, for the Royal Economic Society, Cambridge University Press. ROBINSON, J. (1952) 'Notes on the Economics of Technical Progress', in The Rate of Interest and Other Essays. Macmillan and Co., London. SOLOW,R. M. (1970) Growth Theory: An Exposition. Oxford University Press. London. THIRWALL,A. P. (1986) 'A General Model of Growth and Development on Kaldorian Lines', Oxford Economic Papers, Vol. 38, pp 199-219 VENABLES,A. J. (1985) 'International Trade, and Industrial Policy and Imperfect Competition: a Survey', Centrefor Economic Policy Research, London, Discussion Paper No. 74. VINES, D. (1984) 'A North-South Growth Model Along Kaldorian Lines.' Centrefor Economic Policy Research, London, Discussion Paper No. 26.

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