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A General Model of Growth and Development on Kaldorian Lines Author(s): A. P. Thirlwall Source: Oxford Economic Papers, New Series, Vol. 38, No. 2 (Jul., 1986), pp. 199-219 Published by: Oxford University Press Stable URL: http://www.jstor.org/stable/2663141 . Accessed: 12/10/2011 05:51 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp 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 [email protected]. Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to Oxford Economic Papers. http://www.jstor.org
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Page 1: A General Model of Growth and Development on Kaldorian Lines (1986) OEP

A General Model of Growth and Development on Kaldorian LinesAuthor(s): A. P. ThirlwallSource: Oxford Economic Papers, New Series, Vol. 38, No. 2 (Jul., 1986), pp. 199-219Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2663141 .Accessed: 12/10/2011 05:51

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to OxfordEconomic Papers.

http://www.jstor.org

Page 2: A General Model of Growth and Development on Kaldorian Lines (1986) OEP

Oxford Economic Papers 38 (1986), 199-219

A GENERAL MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

By A. P. THIRLWALL*

I. Introduction

ARTHUR LEWIS says in his Presidential Address to the American Economic Association: "the economist's dream would be to have a single theory of growth that took an economy from the lowest level of say $100 per capita, past the dividing line of $2,000 up to the level of Western Europe and beyond. Or to have, since processes may differ at different stages, a set of theories growing out of each other longitudinally, and handing over to each other. Or putting aside what happens after $2,000 is passed, to have at least one good theory for the developing economy from $100 to the dividing line". (Lewis, 1984). Lewis's dream will probably remain as such, but I believe we know enough about the development process to provide the basis for his second best-namely a set of theories growing out of each other longitudinally and handing over to each other. Such a model would give pride of place to agriculture, and its complementarity with industry, in the early stages of development, with export growth taking over in the later stages. There can be little doubt from the empirical evidence (see Kaldor, 1966, 1967 and Sen, 1983) that the pace of long run growth and development is closely associated with the growth of industrial activities. The fundamental question is what determines the growth of industrial output? To anticipate the answer, in an individual country, which starts closed and then trades, agricultural growth is the driving force in the early stage of development and export growth in the later stages. These represent the two fundamental sources of autonomous demand for industrial output. Although the model that I shall develop below is abstract in places, and contains many simplifying assumptions, I believe that it contains a number of important insights, and appears to have the potential to explain a wide range of the phenomena we observe in the growth and development process. The complementary growth of agriculture and industry is well documented for individual developing countries, both historically and in the contemporary world economy (see later), and export-led growth receives

* The author is grateful to Professor Kaldor and Mr. David Vines for extensive discussions in the early stages of the preparation of the paper, and to Colin Clark, John Craven, Richard Disney, Charles Kennedy, Arthur Lewis and participants in Seminars at various Universities for helpful comments on preliminary drafts of the paper. The inspiration for the paper comes from a two sector (agriculture-industry) model that Kaldor lectured on in Cambridge for many years, hints of which can be found in his Harvard Lecture (1975b); his Presidential Address to the Royal Economic Society (Kaldor, 1976), and in his essay in honour of Tibor Scitovsky (Kaldor, 1979). Kaldor has always presented the model as representing the world economy, but I realized its potential as the basis of a general model of growth and development when listening to his lectures as a visitor in Cambridge in 1979. Two anonymous referees suggested useful amendments to the model and have helped to improve the clarity of expression.

(C Oxford University Press 1986

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200 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

strong empirical support in many developed and newly industrialising countries (see the work of Balassa, 1980, and some of my own work e.g. Thirlwall 1979, 1982).1

Before developing the 'longitudinal' model in the spirit outlined, I should like to mention briefly what I consider to be the major shortcomings of traditional development theories. In a fully neoclassical two sector develop- ment model (e.g. Jorgenson, 1969), the answer to the question of "what determines the rate of growth of industrial output" would lie in the allocation or supply of scarce factor endowments, technology and tastes, all exogenously determined. The first objection to this approach is that neither labour nor capital are scarce in the manner envisaged by the model. It is very doubtful, particularly when considered in a growth context, whether less labour on the land means less agricultural output. All the evidence suggests an enormous 'dynamic' surplus of labour, with increasing food production going hand in hand with a declining agricultural workforce. And capital is not "allocated", it is accumulated. There is no way of withdrawing capital from one sector for use in another. Rather the process of industrial production itself generates its own capital (A. Young, 1928; Kaldor, 1979). Secondly, there is no treatment of the complementarity between the output of one sector and the output of the other within the framework of reciprocal demand. There is no recognition that the level of output in agriculture may itself determine the demand for the output of the industrial sector and vice versa, and there is no explicit role for the terms of trade as the mechanism for achieving balance between the supply of and demand for output in both sectors, so that growth is neither supply or demand constrained below its potential.

Lewis's classical model (Lewis, 1954) is an improvement on neo-classical models in that labour is plentiful and capital is accumulated but it is still basically a supply orientated model, with the demand for the output of the industrial sector side-stepped. Lewis's discussion of the relationship between the two sectors focusses only on checks to the expansion of the capitalist surplus, and particularly on how a deterioration in the industrial terms of trade chokes the rate of capital accumulation. There is no recognition of the fact that a worsening terms of trade for industry may be associated with faster industrial growth because of higher rural incomes which accompany a faster growth of agriculture. There is no analysis of trade between the sectors. Johnston and Mellor (1961) recognised this worrying feature of the Lewis model many years ago when they perceptively remarked: "one of the simplifying assumptions of the (Lewis) two sector model is that expansion of the capitalist sector is limited only by a shortage of capital. Given this assumption, an increase in rural net cash income is not a stimulus to industrialization but an obstacle to expansion of the capitalist sector".

'Irma Adelman (1984) has recently formulated the notion of agricultural-demand-led- industrialisation (ADLI) and finds support in simulation studies.

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A. P. THIRLWALL 201

Johnston and Mellor continue "there is clearly a conflict between emphasis on agriculture's essential contribution to the capital requirement for overall development and emphasis on increased farm purchasing power as a stimulus to industrialization. Nor is there any easy reconciliation of the conflict".

The challenge of reconciliation has never been taken up in a satisfactory way, not even by Lewis himself who recognised the limitations of his 1954 model in his 1972 essay in honour of Prebisch (Lewis, 1972), where he distinguishes three models: (i) his original classical model with no trade between sectors and no foreign trade; (ii) a second version with a closed economy, but the capitalist (industrial) sector depending on trade with the non-capitalist sector for food and raw materials, and (iii) a third version with an open economy whose industrial sector trades either with the non-capitalist sector or with the outside world. The latter two versions are not well developed and in a sense the model to be developed corresponds to them.2 There is a resolution of the conflict in Lewis, referred to by Johnston and Mellor, if the complementarity between industry and agriculture is recognised from the outset, and it is remembered that there must be an equilibrium terms of trade that balances the supply of and demand for output in both sectors.

It would be wrong of course to give the impression that economists have not appreciated the need for an integrated model of agriculture and industry with emphasis on the complementary linkages between industry and agriculture, although it would be equally true to say that the importance is still not widely appreciated. In the 25th anniversary issue of the Manchester School of Economic and Social Studies, September 1979, celebrating the publication in 1954 of Lewis's original article, none of the papers there come to grips with the fundamental deficiency of the classical and neo-classical approaches to development stressed here; that is, the neglect of complementary demand. Ragnor Nurkse (1962) fully recognised the importance of demand linkages between the agricultural and industrial sectors: "the relation between agriculture and manufacturing industry offers the clearest and simplest case of balance needed for economic growth. In a country where the peasantry is incapable of producing a surplus of food above its own subsistence needs there is little or no incentive for industry to establish itself: there is not a sufficient market for manufactured goods. Conversely, agricultural improvements may be inhibited by a lack of market for farm products if the non-farm sector of the economy is backward or underdeveloped. Each of the two sectors must try to move forward. If one remains passive the other is slowed down". Fei and Ranis (1964), though (neo?) classical in outlook, believe that balanced growth lies at the root of Japanese economic success in the late 19th and early 20th century. They

2The capitalist-non-capitalist distinction is not wholly synonomous with the division between industry and agriculture, but it is clearly the growth of industry that Lewis is concerned with.

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202 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

quote Lockwood's (1954) study of Japan: "The growth of primary produc- tion was interrelated with industrialization and urbanisation at every point.... As industry developed, it offered a widening market for the food and raw material surpluses of the countryside.... On the other hand, the increasing productivity of the primary industries created a growing home market for manufactures and services". The World Development Report 1982 shows the very close correspondence between agricultural develop- ment and industrial growth: "In the 1970s agricultural growth exceeded 3.5 percent a year in 18 of the 31 countries whose gross domestic product (GDP) growth was above 5 percent a year. During the same period in 15 of the 22 countries with GDP growth below 3 percent a year, agricultural growth was only 2 percent or less. Meanwhile agricultural and GDP growth differed by less than two percentage points in 15 of 20 countries experienc- ing moderate growth. There have been exceptions, of course, but they prove the rule: fast growth in GDP and sluggish agriculture were evident only in countries with oil or mineral-based economies, such as Algeria, Ecuador, Mexico, Morocco, and Nigeria". (Walters, 1982). The World Development Report 1979 had earlier remarked "a stagnant rural economy with low purchasing power holds back industrial growth in many developing countries".

II. The basic two sector model of agriculture and industry

The significant features of the basic model to be developed are firstly that it formally models the complementarity between industry and agriculture, and secondly it explicitly derives the equilibrium terms of trade, and the consequences of disequilibrium. The basic model to be developed and extended is presented informally in Kaldor (1975b and 1979) who discusses it in the context of the (closed) world economy divided between primary producing countries on the one hand and industrial countries on the other.3 But clearly the model is equally applicable to an individual dual economy closed to trade. Having presented the basic model, I shall then extend it in various directions by: (i) introducing technical progress in agriculture through a technical progress function; (ii) introducing the possibility of labour supply constraints in industry (in the sense of a higher real wage having to be paid for labour); and (iii) opening up the economy to trade. A number of interesting things can then be seen and done with the model. For example: (i) it can be subjected to autonomous shocks (such as harvest fluctuations), and the attempt by the industrial sector (capitalists) to force the pace of growth; (ii) it can be seen how industrial growth becomes supply or demand constrained if the terms of trade between the two sectors are not in equilibrium; (iii) Prebisch effects can be seen i.e. the institutional mechanisms which may generate a long run tendency for the agricultural terms of trade to deteriorate (Prebisch, 1950); (iv) it can be seen how

3See Vines (1984) for a formalisation of the model in a 'North-South' context.

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A. P. THIRLWALL 203

through time, the importance of export growth will come to dominate the growth process, and (v) the model is also versatile enough to incorporate the Mydral/Hirschman notion of circular and cumulative causation. Finally, the model helps to explain why some countries have industrialized and developed sooner than others, and points to a number of ways in which the smooth functioning of individual countries (and the world economy) could be enhanced. One of the fundamental conclusions of the closed economy model is that in the long run the growth of industry is fundamentally determined by the growth of land savings innovations in agriculture as an offset to diminishing returns. This contrasts with the standard neoclassical result that the long run steady state growth of industry is determined by the exogenous rate of growth of labour supply in efficiency units, as in the model of Findlay (1980), for example.

Production and expenditure assumptions in agriculture and industry

First of all, let us assume a closed economy with two activities, agriculture and industry. Agriculture produces wage goods, food or 'corn', by means of inputs of labour time, land and capital goods (steel). Industry produces a composite good, say steel, by means of labour and capital goods, that can either be invested or consumed. Industry sells steel to agriculture in exchange for food.

Agriculture

There is a reservoir of surplus labour in agriculture. Disguised unemploy- ment exists, which takes the form of work sharing-a ubiquitous feature of the agricultural sector of most developing countries. The marginal product of labour time in such circumstances is not necessarily zero but the marginal product of labour itself may be considered zero if the total number of hours worked on the land remains the same when a unit of labour is absorbed into industry. Thus changes in agricultural output are assumed to be independ- ent of changes in the number of men. In this section the level of technology in agriculture is also held constant. The price of agricultural goods is assumed to be determined competitively in free markets.

Capital is obtained from the industrial sector in exchange for the agricultural surplus or saving. The lower the price of industrial output in terms of agricultural output, the faster will be both the rate of increase in agricultural output and agriculture's purchasing power over industrial goods. This can be shown formally as follows:

Let a proportion of agricultural output be consumed in agriculture itself and a constant proportion (Sa) saved to exchange for industrial goods.4

4 A constant savings ratio in agriculture implies that agricultural output and population grow at the same rate. This would be the case if population growth was endogenous in the tradition of Malthus, and is consistent with the observation that the vast mass of people in developing countries are on the edge of subsistence.

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204 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

Agricultural saving may be expressed as:

Sa = SaQa, (1)

where Qa is agricultural output and Sa represents the agricultural surplus.5 The agricultural surplus may be used either for the purchase of investment goods from industry (Ia) or consumption goods (Cia). If p is the price of steel in terms of corn (or the industrial terms of trade), then the total amount of industrial goods obtained by the agricultural sector in exchange for the agricultural surplus is:

(Ia + Cia) = Sa/p (2)

Equation (2) is a market clearing equation. Now the growth of agricultural output may be expressed as the product of

the investment ratio in agriculture and the productivity of investment in agriculture (a).6

A Qa _rIa (3

Qa Qa

Substituting (1) into (2), and obtaining an expression for Ia for substitution in (3), gives:

AQa ( Sa a__) (4)

Equation (4) not only gives the rate of growth of agricultural output but also the rate of growth of purchasing power, or demand, over industrial goods (gd). The equation traces out a hyperbola showing an inverse relation between the industrial terms of trade and the growth of agricultural demand for industrial goods. The more favourable the industrial terms of trade the lower the rate of growth of demand, and vice versa. The relation is shown in Fig. 1 with the terms of trade between industry and agriculture (p) measured on the vertical axis and growth (g) measured on the horizontal axis. A rise in agricultural productivity will shift the curve outwards, as will a rise in the agricultural savings ratio. Notice that the higher the amount of agricultural saving devoted to industrial consumption, the lower the agricultural growth rate for any given term of trade, and vice versa.

Industry

Industry produces steel by means of inputs of labour and capital, and fixed coefficients of production are assumed. The productivity of labour can

'The agricultural surplus represents the food left over after all consumption claims have been met by peasants, capitalists and the vast numbers of tertiary workers (including civil servants and the armed forces).

6Equation (3) is definitionally true, but does not imply that output depends only on capital. a is the gross productivity of capital, not the net productivity holding other factors constant.

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A. P. THIRLWALL 205

P

SQa

g

FIG. 1

be improved by technical progress, but for the moment the level of technology is held constant. Because of the existence of surplus labour in agriculture, the supply curve of labour to industry is infinitely elastic at some conventional real wage. The determinants of this real wage are considered later. All steel which is not sold to agriculture for food or consumed by industrial workers is invested. There are assumed to be profitable investment outlets for all saving.7 The price of industrial goods is assumed to be determined by a markup on unit labour costs.

The consumption of workers in the industrial sector depends on the real wage and the level of output. It is assumed that all wages are consumed either on the consumption of food from agriculture or on industrial goods. Therefore:

C = pQ + Caj = kQi (5)

where Ci is total consumption in industry; C11 is the consumption of industrial goods in industry and Cai is the consumption of food in industry; Qj is industrial output and k = wi is the wage bill per unit of steel output. w is the real wage measured in terms of food and 1 is labour input per unit of steel output (the reciprocal of labour productivity). For a given 1, k is determined by the real wage, which for the present is exogenous.

The growth of industrial output can be expressed as the product of the investment ratio in industry and the productivity of investment:

AQj QcIj (6)8

where Ai is the productivity of investment. Now Ii is equal to the total output

7 In other words, the natural growth rate is assumed to exceed the warranted rate, typical in developing countries. There is no independent investment function of the Keynesian type, but there is a discussion later of what is likely to happen in the model if the industrial sector attempts to 'force' the pace of industrial growth.

8Like equation (3), this equation is definitionally true and does not imply that industrial output depends solely on capital accumulation.

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206 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

of steel less the steel sold to agriculture and industrial workers:

Ii Qia CI a - Cii (7)

and from (2)

(Ia + Cia) = SaIP

Since the agricultural surplus is sold to industry for workers' consumption, Sa = Cai = avkQi, where ai is the proportion of the wage bill spent on food (CailkQi). Therefore Ia= ckQilp - Cia. Substituting for Ia in equation (7) and the result into (6) gives:

AQ, Qi (Q k C) =(lC- i k (8) Qi Q 1\p/\Q i P

Since it is assumed that all industrial wages are consumed, it follows from equation (5) that ca = 1 - pCj1/kQj, so that equation (8) may also be written as:

-Q - -k (8a) Qi P

In other words, the fact that workers consume only a portion of their wages on food, and the rest on industrial goods, makes no difference to the industrial growth rate. The surplus for reinvestment is the same however wages are disposed of. From (8a) the positive non-linear relation between the industrial terms of trade and the growth of industrial output (ge) is shown in Fig. 2. The curve has an asymptote, ,u, and cuts the vertical axis at k, which gives the minumum price of steel (in terms of food) at which no steel is reinvested in industry itself.

JO, P gs

k

it g

FIG. 2

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A. P. THIRLWALL 207

A rise in the productivity of investment in industry will shift the asymptote, A, outwards, and an improvement in labour productivity in industry, unmatched by an increase in the real wage, will shift the intercept (k) downwards. In discussing the equilibrium and stability of the model, and in extending it in various directions, it will now be assumed for simplicity that all industrial goods are used for investment. This will simplify the algebra without affecting the insights of the model. It has been shown that the consumption of industrial goods merely serves to lower the agricultural growth curve.

Equilibrium

The stationary equilibrium growth rate (g*), and the equilibrium terms of trade (p *), are found where the two curves (from Figs. 1 and 2) cross in Fig. 3. Formally these equilibrium values are found by solving the pair of

p 4~~~~~~~~~~Q1

AQ, k gd=

Qa

o 9g

FIG. 3

equations (4)9 and (8a). This gives:

* k (9)

and

I (10) k /rsa +-

The equilibrium growth rate will be faster, the higher is the productivity of investment in industry and agriculture, M and a; the higher is the

9 Assuming Cia = 0. The more agriculture consumes from industry, and the less it invests, the further to the left the gd curve will lie and the lower the equilibrium terms of trade and growth rate.

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208 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

agricultural savings ratio, sal and the lower are industrial wage costs per unit of output, k. The terms of trade move in favour of industry and against agriculture, the higher are k, a and sa, and the lower is M.10

This equilibrium solution implies that steel output and food output should be in a particular relationship to each other. If food demanded in exchange for steel is kQi" and food offered (the agricultural surplus) is sa Qa, then in equilibrium the ratio of steel output to food output must be:

Qi _S. Qa k~~~~~~~~(1

or

Qi= (where Ia = SaQa/P) (12)

This is the Harrod trade multiplier result that at a given terms of trade (p = 1) at which trade is balanced, industrial output is a linear multiple (1/k) of the 'export' of industrial goods (to agriculture), where k is the propensity to import (agricultural goods ) (see also Thirlwall, 1982).

Stability and the consequences of a disequilibrium terms of trade

Now suppose that equilibrium is disturbed. Is the model stable, and what are the consequences for growth of a disequilibrium terms of trade? Whether the model is stable or not depends on the nature of the adjustment process out of equilibrium. Since the model is set up in terms of growth rates let us relate adjustments of the terms of trade to differences in the growth rates of supply and demand.12 In this case, the stability of the model out of equilibrium depends on the slopes of the gd and gs curves and on the coefficient of adjustment of the terms of trade to divergences between gd

and gs. The last of these factors is crucial. The adjustment of the terms of

10 It would have been attractive to incorporate in the model an above-unitary income elasticity of demand for industrial goods; and likewise a below-unitary income elasticity of demand for agricultural goods. This has not been done for several reasons. First, it makes no difference to the structure, or basic insights, of the model. Secondly, it would be difficult to have income elasticities of demand different from unity with at the same time holding constant the ratio of food consumption to output in both sectors, as is assumed in the present analysis. Undoubtedly if the income elasticity of demand for industrial goods in the agricultural sector is greater than unity, the sector would partly meet this growing (proportionate) demand by consuming proportionately less food. Thirdly, in the two sector model the income elasticities of demand for industrial and agricultural goods would have to be the reciprocal of each other for there to be a constant terms of trade which balances the growth of demand and supply in the exchange of food for steel. This would be a restriction on the model which would be difficult to swallow empirically. By ignoring the different income elasticities of demand for agricultural and industrial goods, the equilibrium growth rates of the two sectors at the equilibrium terms of trade are constrained to equal each other.

1 Assuming Cii = 0. 12 The alternative would be to consider adjustments of the terms of trade to differences in the

levels of supply and demand.

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A. P. THIRLWALL 209

trade will depend on the behaviour of food dealers or merchants.13 Suppose that equilibrium at p * in Fig. 3 is disturbed by an autonomous shift in one of the curves giving a new equilibrium terms of trade. There will be stability if food dealers behave in such a way that the terms of trade moves smoothly from p * to its new equilibrium level. On the other hand, behaviour may be such that the terms of trade overshoot or become cyclical. The stability conditions can be modelled formally:

Let q = i/p be the price of food in terms of steel; and let El be the speed of response of prices to a divergence between the growth in demand for steel and the growth in supply of steel (El < 0). Such a divergence may come about either through a change in k or a change in Sa which causes a change

P

\ / O =~~~~~~~~~~~~gs

p1~ ~ ~ ~ ~ ~~~~~~~~~Q

P2

k

-gd

gx g ' gy growth

FIG. 4

in klsa (a constant klse implying gd = gs). The diagramatic representation of such shifts is shown in Fig. 4. We have:

gs = M[1 - qk] (13)

9d = osaq (14)

Aq =El(gd -gS) (15)

where Aq = qtl- q, This gives the first order difference equation:

qt+l = [1 + E1(usa + ik)]qt - l (16)

13 Because of differences in the nature of competition between sectors, quantities are assumed to adjust in the industrial sector and prices in the agricultural sector, in response to a disequilibrium between supply and demand.

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210 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

The behaviour of the model out of equilibrium depends on the value of [1 + El(USa + Mk)]. Since El <0, there will be convergence to equilibrium without cycles if 0 < IEl(asa + [k)I < 1.

If I Ei(asa + Mk)I > 1, the model will generate cycles which will be damped if 1 < IE1(asa + yk)I <2, but not otherwise. If t1 = 0, there would be no convergence to equilibrium; if E1 exactly equalled the reciprocal of asa + Mk, there would be immediate convergence to equilibrium, and if El was more than twice the reciprocal of (OSa + Mk) there would be explosive oscillations. Thus, for a given El, instability results if the responsiveness of supply and demand growth to changes in price is "too great"; or, for given values of this responsiveness, instability results if El is "too great".

The consequences of a disequilibrium terms of trade are illustrated in Fig. 4. At P1 the industrial terms of trade are "too high", and at P2 the industrial terms of trade are "too low".

Suppose there had been an autonomous increase in agricultural produc- tivity (a good harvest) which shifted the agricultural growth curve to AQa/Qa in Fig. 4, but the terms of trade overshoots to Pl. In this case, industry would.have the ability or capacity to grow at the rate gy, but because agricultural prices are "too low", agriculture's growth of demand for industrial goods is constrained to g,. In these circumstances, the system cannot grow at its equilibrium rate, g*, but is demand constrained to the lower rate, gX.

Conversely, suppose there is a bad harvest equivalent to an autonomous decrease in agricultural productivity and the terms of trade overshoots in the opposite direction, below its equilibrium level, to P2* In this case, the agricultural sector has the capacity to grow and buy industrial goods at the rate gy, but industry cannot invest enough to grow at that rate, and is constrained in its growth to the rate gx. As Kaldor (1976) writes "continued and stable economic progress requires the growth of output in these two sectors should be at the required relationship with each other-that is to say, the growth of the saleable output of agriculture and mining should be in line with the growth of demand, which in turn reflects the growth of the secondary (and tertiary) sectors. However, from a technical standpoint there can be no guarantee that the rate of growth of primary production, propelled by land saving innovations, proceeds at the precise rate warranted by growth of production and incomes in the secondary and tertiary sectors. To ensure that it does is the function of the price mechanism, more particularly of relative prices, or the "'terms of trade' between primary commodities and manufactured goods" (p. 704).

The consequence of violent shifts in the terms of trade between industrial and agricultural goods, and of a disequilibrium terms of trade, points to the need for mechanisms and institutions that can contribute to equilibrium and stability both within individual countries (and in the world economy) if growth is to be maximised. Keynes saw the nature of the problem with great clarity in a world context as long ago as 1942, which led to his proposal for a

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A. P. THIRLWALL 211

Commodities Control Scheme (see Moggridge 1980, pp. 113-114): "Assur- edly nothing can be more inefficient than the present system under which the price [the terms of trade] is always too high or too low. . . .". Within individual countries, credit to finance merchant stocks, and the pricing policy of Marketing Boards, are of prime importance and must be examined closely. Low (relative) prices for agricultural commodities, which in a classical model are beneficial for industrial growth, may in practice constrain growth if the implied terms of trade mean that there is an excess supply of industrial goods because agriculture lacks the purchasing power to buy them.

III. Credit, forcing the pace of growth, and inflation

In the model so far, capitalists in the industrial sector play a passive role, simply investing the surplus of steel. There are no mechanisms by which manufacturers may invest in excess of this. In practice, finance and credit mechanisms exist which allow capitalists to force the pace of industrial growth if 'animal spirits' move them. Within the structure of the model we can see the processes by which the industrial growth rate may be raised, and the various constraints.

If credit is increased to finance extra capitalist investment, the markup will rise in line with the extra aggregate demand for industrial goods, and the money price of steel will thus be higher. What happens then depends on three major responses. First, is the agricultural sector willing to supply more food at the existing money price? If so, this amounts to 'forced saving' in agriculture to finance the investment; the gd curve shifts out to validate an upward move along the g, curve. But the agricultural sector may resist such forced saving by attempting to raise the money price of food. Secondly, are industrial workers content with the same money wage in the face of a rise in the price of food as the demand for food expands? If so, this reduces k and pushes out the g, curve along the gd curve. If, however, there is real wage resistance, workers will demand higher money wages restoring k and pushing the g, curve back to its original position. This is the idea of the inflation barrier familiar from neo-Keynesian growth theory (and struc- turalist theories of inflation, see Olivera, 1964). Thirdly, are some individual capitalists unable to increase their money expenditures fully in line with the rise in the price of steel? If so, this will dampen the initial increase in investment. Monetary restraint will work in this direction. If, however, all producers and industrial workers are able to defend themselves against rising prices, there is a real danger of explosive inflation (see Cardoso, 1981).

There remains the possibility that the government may 'force' savings to match the increased investment by taxing the workers (shifting out the g, curve) or the corn producers (shifting out the gd curve). Even here the tax may be resisted with similar inflationary consequences which dampen or abort the development effort.

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212 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

IV. Technical progress, growth, and the terms of trade

In this model, demand growth for industrial goods must grow in step with supply growth. A lower price of steel has a positive effect on demand growth for industrial goods and seems to be necessary in order that the rate of industrial growth be higher. This would seem to imply that higher rates of industrial growth must be associated with a worsening of the industrial terms of trade, and would appear to conflict with historical experience which suggests that economies grow faster when the terms of trade move in industry's favour.

The explanation of this apparent contradiction lies in the fact that technical progress in both sectors causes both curves to shift about, and more so in agriculture where productivity improvements are not so quickly or automatically matched by increases in agricultural consumption. In industry, where labour productivity improvements tend to be matched by increases in real wages (and often more than matched) the share of wages in industrial output remains fairly stable (or increases) and the gs curve is therefore relatively stable. Variations in the rate of land saving innovations, however, both embodied and disembodied, will shift the gd curve outwards by varying degrees, and the growth of industrial output can then increase without any deterioration in the industrial terms of trade. An outward movement of the gd curve due to an increasing rate of technical progress, and the relative stability (and perhaps leftward shift) of the gs curve for the reasons mentioned, would account for a secular tendency of the industrial terms of trade to improve relative to agriculture-the so-called Prebisch effect-despite the fact that industrial activities tend to be subject to increasing returns while agriculture is a diminishing returns activity, and despite the fact that technical progress tends to be faster in industry than in agriculture. Spraos (1980) has confirmed the Prebisch thesis for the period 1870 to 1940, and the downward trend (excluding minerals) has continued in the post-war period since 1954 (see Thirlwall and Bergevin, 1985).

Diminishing returns and productivity growth in agriculture: the ultimate long run constraints on growth

In the short run equilibrium of the model, the importance of technical progress in agriculture is clear. If there are diminishing returns to land as a fixed factor of production, successive applications of capital will lower the productivity of investment in agriculture, shifting inwards the gd curve and lowering the industrial growth rate. In the long run equilibrium of the model it can be shown formally how variations in the pace of industrial growth depend fundamentally on the rate of land saving innovations, and that technical progress in industry affects only the equilibrium terms of trade.

To consider productivity growth in agriculture, assume that output growth in the agricultural sector is a function of the amount of capital accumulated,

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A. P. THIRLWALL 213

the quantity of land and the rate of land saving technical progress. Assume further that land saving technical progress is partly disembodied and partly a function of the rate of capital accumulation itself. Let the production function be: Qa = TAKcv'R &2 (17)

where K is capital employed in agriculture; R is the quantity of land; TA is an index of the level of technology in agriculture, a,, is the elasticity of output with respect to capital and (X2 is the elasticity of output with respect to land. Labour (measured in terms of men) is absent from the production function since it is assumed to be in surplus with zero marginal product. From equation (17)

AQa ATA AK AR (18) -+ CV1 ~~+ CV

Qa TA K R

Now assume a (linear) technical progress function:

AT= PO + P1AK (19) TA K

where Po is the rate of disembodied land saving inventions, and P31(AK/K) is the rate of technical progress induced by capital accumulation. Substitut- ing (19) into (18) gives:

AQap AR AK (0 = Po + a2 R + (TV1 + PO) (20)

Qa R K

The steady state growth rate of agricultural output at which the capital- output ratio is constant is:

AR

AQa R-all-j1 (21) Qa 1 0 i43i P

The implication of this analysis is that for given values of the production parameters, a,, and (X2; given values for the parameters of the technical progress function, Po and f,3, and given the rate of growth of land, the steady state rate of agricultural output growth is a constant independent of the terms of trade. In effect, the gd curve in Fig. 1 becomes a vertical line emanating from the horizontal axis.

The steady state terms of trade p * must be that which is necessary to make industry grow in step with agricultural output. From equations (8a) and (21) this is:

_ k_(22)

~~~~Po= |

CV+a2 R1

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214 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

The importance of the model for an understanding of the pace and rhythm of industrial growth in a closed economy can now be appreciated. The results suggest that technical progress in agriculture (or the discovery of new land) will relax the ultimate constraints on industrial growth, and only these factors will do so. Technical progress in industry affects the terms of trade (by changing k), but not the long run equilibrium growth rate.

The terms of trade in the long run

It has been shown that diminishing returns in agriculture cause the terms of trade to turn progressively against industry but that this tendency can be offset by the increased availability of land and land saving technical progress. And we know that a rising real wage (by raising k) turns the terms of trade in favour of industry, which may be offset by labour saving technical progress. Long term secular movements in the terms of trade are thus the outcome of the balance of these four forces; these are themselves the outcome of geographical discoveries, invention, and institutional press- ures. Clearly, there can be no "iron law" of the industrial terms of trade, either deteriorating (as in Ricardo) or improving (as in Prebisch). What happens depends on the balance of these economic and social forces.

V. Is labour supply a constraint on industrial growth?

It is possible that in certain countries, at certain times, the rate of growth of industry may be constrained by a shortage of labour. Only if labour supply is strictly exogenous and unresponsive to demand can labour supply growth be regarded as a constraint on industrial growth in a direct sense. But this is not the case in the real world (Kaldor 1968, 1975a). In the process of development-at least up until the stage of maturity where the marginal product of labour in different sectors of the economy is roughly equal-there is not likely to be a shortage of labour to the industrial sector, and given the demand it may even be forthcoming at a constant real wage. Employment is then endogenous in the industrial sector at an exogenous wage. In the world economy at large there are ample supplies of labour for use in industry. Even in highly industrialised countries, when they have required labour, they have obtained it-often from other countries with surplus labour. Many countries, such as Germany, Canada, the U.S.A., Australia and France, operated generous immigration policies in the 1950s and 1960s specifically for this purpose. There has also been a big increase in female participation in the labour force in recent years which has partly been a response to the pressure of demand. The informal service sector, too, provides a source of labour for the industrial sector not unlike that provided by agriculture. There are a variety of ways in which the stock of labour can adapt its services to the need for labour if the demand is there, including variations in the number of hours worked. With seventy percent of the labour force still on the land in the developing countries, and with the

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A. P. THIRLWALL 215

new electronic revolution in developed countries, a global shortage of labour to produce industrial output seems a remote possibility for many years to come.

To obtain more labour, however, a higher real wage may have to be paid. This means that k and the g, curve will be higher than otherwise would be the case, thus raising the industrial terms of trade and lowering the rate of growth of industrial output in the short-run equilibrium of the basic model.14 In this sense labour supply can exert a constraint on industrial growth.

VI. The open economy

Let us now move from the closed economy and think explicitly of the model applying to a particular country which may trade. The importance of trade in this model is not that it may affect growth favourably through raising the overall rate of capital accumulation or improving the productivity of investment, but that export demand becomes another source of auton- omous demand for industrial output which, in practice, will come to dominate the growth of demand from agriculture. Trade by itself will not affect the rate of capital accumulation unless a country is allowed to import more than it exports or both industry and agriculture are able to buy their inputs cheaper abroad than domestically. 15 If goods are homogenous, however, a more favourable international than domestic terms of trade for agriculture would mean a less favourable international than domestic terms of trade for industry. Only if goods are sufficiently heterogenous, and the mix of inputs into each sector could be altered without affecting produc- tivity, might both the agricultural and industrial sector of a country benefit simultaneously from being able to trade internationally as well as internally.

But, as mentioned above, the real significance of trade is that the rate of growth of export demand for industrial output (g') will, as development proceeds, become an important source of autonomous demand for in- dustrial goods in addition to the rate of growth of demand emanating from the agricultural sector (gd). In a steady state the rate of growth of demand for industrial output (gb) will be a weighted average of the two rates of growth, where the weights represent the proportion of autonomous demand accounted for by agriculture and exports respectively: i.e.

9d = 0(gd) + (1 - 0)d(23)

The growth of demand for a country's industrial exports is a function of the

14 However, it does not lower the long-run equilibrium rate of growth given in equation (21), since this is independent of k.

15 Trade may raise the productivity of investment in industry if the availability of foreign exchange allows a fuller or more efficient use of domestic resources. We are not concerned with this issue here.

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216 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

growth of world income and a country's relative competitiveness so that:

gd =(gw) + Vp1d (24)

where gw is the growth of 'world' income, Pd is the rate of change of relative prices measured in a common currency; E is the income elasticity of demand for exports (E >0) and ip is the price elasticity of demand for exports (4'<0).

It would be unrealistic, however, to assume a steady state, with the two sources of autonomous demand growing at the same rate through time. In every country's economic history there is a date when export demand for industrial goods grows more rapidly than agricultural demand, and so the ratio of export demand to agricultural demand inevitably grows. This results from a combination of a number of factors. First, the growth in agricultural income and purchasing power will come to lag behind the growth of world income owing to the lower income elasticity of demand for agricultural goods. Second, the income elasticity of demand for industrial goods in the agricultural sector is likely to become less than the income elasticity of demand for the country's goods in world markets as the country begins to acquire the technology to make goods for which the income elasticity of demand in world markets is high.

There is a third reason why export demand may come to dominate. If the income elasticity of demand for imports of the industrial sector is greater than unity then industrial imports will grow more rapidly than industrial output. The rate of growth of industrial exports must be faster than the rate of growth of industrial output as a whole if overall balance of payments equilibrium is a requirement and the deficit in industry cannot be matched by a payments surplus in agriculture. Now if the growth of industrial exports is limited by the growth of demand in world markets16 then this limit will impose an upper ceiling on the growth of the industrial sector consistent with balance of payments equilibrium. Growth becomes balance of pay- ments constrained, at a rate independent of the rate of growth of demand emanating from the agricultural sector. This is also a significant turning point in a country's economic history, which might occur before the point when the growth of agricultural demand falls below the growth of world demand for industrial exports.

If in the long run, gdw > gd, then 0 -> 0, and equilibrium industrial growth becomes determined by the growth of demand for exports. Export growth becomes the driving force in the system to which other components of demand adapt.17 If relative prices in international trade are sticky so that

16 Because V is low so that it is not possible to greatly increase industrial exports by continuously cheapening them, or because the price of industrial exports is sticky (ad 0 ?) due to oligopolistic market structures.

17 This is the idea of the Hicks supermultiplier which Kaldor (1970) had in mind in developing his export-led growth model in a regional context.

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A. P. THIRLWALL 217

Pd -> 0; then equilibrium industrial growth approximates to eg,, which is the dynamic Harrod trade multiplier result assuming balanced trade, a constant terms of trade, and an income elasticity of demand for imports equal to unity (see Thirlwall, 1979, 1982 and Kennedy and Thirlwall 1979).18

If industrial output growth and productivity growth are positively related (through Verdoorn's Law) a process of circular and cumulative causation may set in which benefits industry relative to agriculture, widening disparities in living standards and income per head. This is the essence of centre-periphery models of growth and development articulated by Prebisch (1950) and Seers (1962) in the international context,19 and Dixon and Thirlwall (1975) in a regional context (see Thirlwall 1983).

VII Conclusion

In this paper I have attempted to develop a general model of growth and development (on Kaldorian lines) which formally analyses the complemen- tarity between industry and agriculture, in contrast to other models of the development process which either ignore this complementarity or discuss it non-rigorously. The model can be applied to both developing and de- veloped countries, and to closed and open economies. For any individual country in the course of development we expect a healthy agricultural sector to be the driving force behind industrial growth in the early stages, superseded by export growth in the later stages. In this sense the model reinforces the belated recognition of agriculture's importance in the early stages of development, and lends support to export led growth theory in the later stages.

The extension of the basic model provides several interesting and important insights: (i) the joint determination of industry's growth rate and its terms of trade with agriculture, and the consequences of disequilibria in the terms of trade for the growth process in individual countries (and in the world economy); (ii) the conditions under which the pace of industrialisa- tion can be forced; (iii) a rationale for the "Prebisch effect", but a demonstration that there is no "iron law" of the terms of trade; (iv) the importance of land saving innovations in agriculture as an offset to diminishing returns; (v) the consequence of labour shortages and rising real wages for industrial growth, and (vi) the ultimate role of foreign trade and export demand as the fundamental source of autonomous demand for a country's industrial goods.

University of Kent, U.K.

18 If, empirically, the ratio of imports to output in the industrial sector was increasing, the income elasticity of demand for imports would exceed unity, and growth would approximate to

(E/7r)g,, where Xr is the income elasticity of demand for imports. 19 See also Vines (1980).

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218 MODEL OF GROWTH AND DEVELOPMENT ON KALDORIAN LINES

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