Dutt1992

A Kaldorian Model of Growth and Development Revisited: A Comment on ThirlwallAuthor(s): Amitava Krishna DuttSource: Oxford Economic Papers, New Series, Vol. 44, No. 1 (Jan., 1992), pp. 156-168Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2663430Accessed: 26/10/2010 16:48

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Oxford Economic Papers 44 (1992), 156-168

A KALDORIAN MODEL OF GROWTH AND DEVELOPMENT REVISITED: A COMMENT ON

THIRLWALL By AMITAVA KRISHNA DUTT*

1. Introduction

THIRLWALL (1986, 1987) has recently developed a formal presentation of Kaldor's (1975, 1979) model of the world economy examining the dynamic interaction between primary and secondary sectors, and thereby contributed to our understanding of Kaldorian growth and development economics. On the basis of his model, Thirlwall has claimed that the Kaldorian model captures the essence of the interaction of the agricultural and industrial sectors within dual, less developed economies, that is, the complementarity between outputs of the two sectors within the framework of reciprocal demand, and in particular, the role of the agricultural sector in providing a market for the industrial sector. By so doing, Thirlwall claims that the model is superior to earlier models of agriculture-industry interaction for less developed economies.

The purpose of this paper is to argue that there are problems with Thirlwall's specification of the structure of the Kaldorian model,' with its underlying dynamics, and with his claim that the model makes an advance over earlier dual economy models with regard to analysis of the contribution of agriculture to the market for industry. To do so, Section 2 develops the formal Kaldorian model,2 Section 3 analyzes its underlying dynamics, and Section 4 comments on the role of demand in the model.

2. A Kaldorian model

Consider a closed economy with two sectors, an agricultural and an industrial sector, each producing one good. The agricultural good is a pure consumption good, while the industrial good can be both consumed and invested. Both goods are sold in perfectly competitive goods markets.3

In the agricultural sector labour, land and capital are used for production. Labour is in unlimited supply and has zero marginal product so that its level

* I am grateful to two anonymous referees of this journal for their perceptive comments and useful suggestions. I would like to thank the participants of a workshop on Dynamic Models at Clare Hall, Cambridge, and Bill Gibson and Michael Landesmann, for their comments.

1 A similar Kaldorian model has also been developed by Targetti (1985), and many of our criticisms apply to that model as well.

2 We will develop a model which uses an internally-consistent set of assumptions which produces a model identical to the one developed by Kaldor, and use our version of the model for our critical analysis. This should not be taken to imply that it is not possible to develop models with alternative assumptions which also produce Kaldor's model, but our critical analysis remains valid unless this alternative analysis, which negates our critical discussion, is actually developed.

3This may appear to contradict Kaldor (1975, 1979). But see below.

\E! Oxford University Press 1992

A. K. DUTT 157

does not affect output. Land is given. Output may increase over time due to land-saving technical change, but this requires capital investment. Assuming strict complementarity between capital and this type of technical change, we have

Qa = aaKa (1) where Qj denotes output, a' the capital-output ratio, and Ki the capital stock, all in sector i, and where the subscript a refers to the agricultural sector. Note that the assumption of perfect competition ensures that production fully utilizes capacity. It is assumed that a fixed fraction Sa of total agricultural output is saved, and all agricultural saving is invested within the agricultural sector, so that

SaPaQa = Pn Ia (2) where Pi denotes (money) price, and Ii investment, in sector i, and the subscript n denotes the industrial sector. Dividing through by Ka, and denoting the rate of growth of capital in agriculture (which, in the absence of depreciation, is la/Ka) by ga, we get

ga = SaaalP (3)

where p = Pn/Pa, the industrial terms of trade. In the industrial sector output is produced with labour and capital using

fixed-coefficients technology. The labour-output ratio is bn and the output- capital ratio is as. Perfect competition ensures full capacity utilization, so that

Qnl = an Kn (4)

Labour, as assumed above, is abundant, and this is formalized by assuming that it is available to the industrial sector at a constant wage in terms of the agricultural good,4 so that

Wn4/Pa = T (5)

where r is the fixed level, and Wn is the industrial (money) wage; firms hire all the workers they need at this wage. The workers consume all their income and capitalists, who earn the profits, save a fixed fraction sn of their income. All saving in the industrial sector is invested in that sector. Our assumptions imply, using equation (5), that

PnIr = sn[P -n (TbnPa)]Qn (6)

Dividing through by PnKn and using (4) gives the equation for the growth-rate of industrial capital,

gn = snI1 (Tbn/p)]an (7)

where industrial capital is assumed to be non-depreciating.

4 Kaldor (1979) took this to be fixed by custom. Following Lewis (1954), we could fix it in terms of average worker (or peasant) income in the agricultural sector, making appropriate assumptions regarding the institutional structure of agriculture.

158 A KALDORIAN MODEL REVISITED

Regarding consumption spending we assume, for simplicity, that a fixed fraction o of total consumption expenditure is spent on the industrial good, and the rest on the agricultural good.

To examine the determination of the equilibrium growth rate of capital and the terms of trade in the economy, we bring equations (3) and (7) together in the right-hand side of Fig. 1, which is Kaldor's diagram. Equation (3) yields the gq curve, and equation (7) yields the g, curve which has a p-intercept of zbn and a g-asymptote of s,,as. Defining equilibrium to be a state at which capital (and with fixed output-capital ratios, output) in the two sectors grows at the same rate, equilibrium is seen to be established at the intersection of the ga and gn curves and the equilibrium terms of trade and growth rates are, respectively,

P* =(saaa/sna,) + zb, (8) g = snansaaa/(saaa + zbsnan). (9)

Increases in the parameters Sa and aa shift the ga curve to the right and increase q* and p*, and increases in s,, and an and reductions in z and bn shift the gq curve to right and increase g* and reduce p*. Note that the pattern of consumption expenditure, given by or, has no effect at all on the equilibrium values of g and p.

So far the model appears to be the same as Thirlwall's, apart from some minor differences having to do with the fact that he assumes that all industrial saving is invested, and does not make specific assumptions about the agricultural savings rate.5 The significant difference between our model and Thirlwall's concerns the nature of industrial pricing. While he takes the agricultural market to be competitive, so that the price of the agricultural good varies to clear the market, Thirlwall assumes the industrial market to be non-competitive, and firms set the price as a markup on unit labour costs. Here he follows Kaldor (1975, 1979), who uses Kalecki's (1971) pricing formula,

PI, = (1 + z)Wnbn (10)

where z is the fixed markup rate, determined by the degree of monopoly in industry. Dividing by Pa this implies

p = (1 + z)ubn (11)

which is exactly Kaldor's equation in our notation. Instead of making this

5 For example, Thirlwall conducts the analysis in terms of a rate of agricultural surplus instead of a savings rate, and then assumes away the consumption of manufactured goods in the agricultural sector, suggesting that such consumption will shift the ga curve (our notation) downwards. This analysis is incomplete since it is not explained how this curve can be derived when manufactured goods are consumed in the agricultural sector. Moreover, this analysis conceals an interesting property of the model, that is, that the equilibrium rate of growth of the model depends on the saving rate in agriculture, and not on the marketed surplus rate which depends on both the saving rate and a.

A. K. DUTT 159

\ga /gn

0 k* k 0 g g

FIG. 1.

price-making assumption, we have assumed price-taking behaviour for both sectors.

We part company with Kaldor and Thirlwall because the markup-pricing assumption is inconsistent with the rest of the model.6 First, if z, z and b,, are exogenously fixed, as markup pricing and the rest of the assumptions imply, (11) fixes the terms of trade: thus they are not free to vary, and there is no reason for it to be consistent with the equilibrium level given by (8). Second, Kalecki's (1971) markup-pricing theory assumes that firms adjust quantities and not prices, and this requires that they operate with excess capacity (assuming fixed coefficients as is assumed in all our models).7 Yet, our model assumes full capacity utilization, which is implicitly assumed also by Thirlwall when he assumes a constant capital-output ratio in industry which is necessary for deriving equation (7) and drawing the gq, curve; it also seems to be implicit in Kaldor's own diagram.8

Thirlwall's error does not interfere with his formal model because the markup-pricing assumption plays no part in it. He does not use it in discussing the model, except for mentioning in an unnecessary footnote (p. 209) that quantities (and not prices) are assumed to adjust in the industrial sector. This does not mean, however, that the error is harmless: it will be argued later that

6 Our criticisms also apply to Targetti (1985) who also assumes markup pricing in industry. Markup-pricing and full-capacity utilization can be made consistent with each other, but only

if there is some other mechanism which clears the market. FitzGerald (1990), in his formalization of one of Kalecki's (1972) models, assumes that the government changes the tax rate to clear the industrial market.

8 Imperfect competition and a variable markup rate are not necessarily inconsistent. For example, the actual market rate can vary to clear the market and the degree of monopoly can set a lower bound to the markup. However, this makes the model formally equivalent to the perfectly competitive model as long as the markup is above the minimum set by monopoly power.

160 A KALDORIAN MODEL REVISITED

it is related to Thirlwall's incorrect emphasis on the role of agriculture in providing a market for the industrial sector.

3. Dynamics and stability in the Kaldorian model

While we have so far defined equilibrium in our Kaldorian model to refer to a state in which the growth-rates of the two sectors are equal, we now turn to a discussion of dynamics behind equilibrium and the question of stability.

This issue is briefly discussed by Thirlwall, who postulates an adjustment equation which makes the discrete-time change in the agricultural terms of trade, q( = l/p), depend linearly on the difference between the sectoral growth rates (g, - ga, in our notation), and shows that equilibrium will be stable unless the coefficient showing the speed of adjustment is 'too great'. Thirlwall appears to believe that 'quantities are assumed to adjust in the industrial sector and prices in the agricultural sector, in response to a disequilibrium between supply and demand' (p. 209n), but this analysis is not pursued correctly. He argues that for a disequilibrium terms of trade, g and gn are unequal, which implies a gap between the capacity of the industrial sector to grow and the growth warranted by the demand for its product from the agricultural sector, but he fails to point out why these magnitudes should be interpreted as demands and supplies, and why such a gap should lead to price adjustments except for a vague reference to the 'behaviour of food dealers and merchants' (p. 209). Given the competitive market assumption for the agricultural good, the adjustment equation is rather strange, for it implies that if the two sectors grow at the same rate, there will be no change in the terms of trade, even if there is an excess supply and demand in the agricultural market. The alternative Thirlwall suggests in a footnote, 'to consider adjustments of the terms of trade to differences in the levels of demand and supply', would seem to be clearly preferable.

To follow this route, however, we need an explicit statement of the characteristics of disequilibrium states, and of the dynamics when the economy is in disequilibrium. We consider two simple and plausible characterizations of such disequilibria and dynamics.

The first distinguishes between the short run in which sectoral levels of capital stock are given and the relative price varies to clear the goods markets, and the long run in which the stocks of capital grow due to investment. Market clearing in agriculture and industry, respectively, imply:

Qa = (1 - Y){[zb, + (1 - s,)(p - rbn)]Qn + (1 - Sa)Qa} (12)

pQI = o{[zbn + (1 - sn)(p - zbJ)]Qn + (1 - Sa)Qa} + P(In + Ia). (13)

Equations (2), (6) and (12) imply equation (13), which shows that the clearing of the agricultural market implies the clearing of the industrial one, so that we may confine attention to only the former. We assume that in the short run p responds positively to excess supply in the agricultural market (or excess

A. K. DUTT 161

demand for the industrial good), and formalize this with the equation

dp/dt = 0{L[a + sa(1 - a)]aak -(1 - o)[(1 - s)p + szb,]an} (14)

where 0 > 0 is an adjustment coefficient, k = Ka/Kn, and the terms within curly brackets is excess supply of agricultural goods divided by K,. In the short run, given k (with given Ka and K), p adjusts according to this equation. Since dp/dt is negatively related to p the adjustment process is stable, so that the economy converges to short-run equilibrium, when dp/dt = 0, where

p = {[( - /(l- )) + sa]aa/(1 - s)a,}k - -bs,,/(1 - sn). (15) This equation can be represented by the line in the left-hand side of Fig. 1. For any k, the short-run equilibrium value of p can be read off from this curve, and the short-run equilibrium values of ga and g, can be read off from the ga and g, curves.9 In the long run, k changes according to

dk/dt = k(ga - g) (16)

which implies, using (3) and (7),

dk/dt = k{(saaa/p) - s,[1 - (zb,/p)1a,} (17)

At long-run equilibrium, when dk/dt = 0, the expression within curly brackets must vanish, which implies that ga = g,. This long-run equilibrium is stable, since a rise (fall) in k implies a rise (fall) in p (from equation (15)) which in turn reduces (increases) dk/dt (by equation (17)). The convergence to long-run equilibrium can be shown using Fig. 1: starting from any k above (below) the long-run equilibrium one it can be seen that g, is greater (less) than ga, implying that k falls (rises) over time to take the economy to the equilibrium, as shown by the arrows.

The second characterization assumes that p is sticky, but that it adjusts over time.'0 Here p and k are given at a point in time and over time p adjusts according to (14) and k according to (17). The equilibrium for this characterization will be the same as that in the previous one, but the dynamics are different, as shown in Fig. 2. The pp line shows combinations of p and k at which dp/dt = 0 and is given by (16). Similarly, the kk line shows combinations of p and k at which dk/dt = 0, and is seen from (17) to be given by (8). As illustrated in the figure, the dynamics may be cyclical, but the equilibrium is

9 For meaningful short-run equilibrium with positive rates of accumulation in both sectors we require p > rbn (see equations (3) and (7)). From (15) this can be shown to imply

k > rbna,/[(c~/(1 - o)) + Sna a

If this condition is not satisfied, the relative size of the agricultural sector becomes too large to allow market clearing at a relative price sufficient to allow any industrial profits and hence industrial capital accumulation.

10 There are problems of reconciling fixed prices and excess supplies and demands which we do not go into here, following the fix-price disequilibrium models which assume perfect competition.

162 A KALDORIAN MODEL REVISITED

P

k \ k

Pa

0 k

FIG. 2.

necessarily stable, as can be seen by evaluating the Jacobian of the system around the equilibrium, given by

!( 1 -,:( - s,,)a,,0 [x + SaO 1 - X)]aaO]

L (Saaa + s jbjp )2 0

which has a negative trace and a positive determinant, which is sufficient for local stability.

Whichever characterization we adopt, for given p, equations (3) and (7) give us growth rates of Ka and K,, and these can be read off from the right-hand side of Fig. 1. For any given p we find the actual rates of growth of the two sectors, and these growth-rates move over time to take the economy to long-run equilibrium.

4. The role of demand

As mentioned above, Thirlwall emphasizes the role of agriculture in providing a market for the industrial good, and claims that the Kaldorian model is superior to Lewis's (1954, 1972) because the latter did not take demand factors into account. He stresses the importance of demand by labelling the Kaldor curves gd and g, (our ga and g, curves, respectively), stating that the agricultural growth rate curve represents 'the rate of growth of purchasing power, or demand, over industrial goods' (p. 204).

" If the market for the agricultural does not clear rapidly enough, in practice rationing and/or parallel markets will emerge. We have abstracted from such complications here.

A. K. DUTT 163

While it is true that in the Kaldorian model the agricultural sectors buys products from the industrial sector, and a higher rate of agricultural growth implies a higher rate of growth of the demand for the industrial good (both for investment and consumption purposes) and this is shown by the fact that in our model an upward shift in ga will imply a higher equilibrium rate of growth of the industrial sector-this is true for any model in which the two sectors trade with each other. In the Kaldorian model the industrial good is demanded also within that sector, and if it grows more rapidly due to internal reasons (say due an increase in sj,) it will create a market for its own increased output. This is because each sector always (identically) invests its entire saving within the sector, and there is therefore no demand problem in any sector: if they sell their product to the other sector they simply exchange it for an equal value of the product of that sector, the gain in market due to the purchase of its product by the other sector exactly compensating the loss in market due to its purchase of the product of the other sector. Agriculture does not serve as a solution to industry's market problem simply because there is no market problem for industry in this model.'2

Agriculture's contribution to industrialization in this model is from the supply side, through the provision of wage goods and labour to the industrial sector. The wage goods problem arises from the terms of trade: if the industrial terms of trade deteriorates, industry will have to pay a higher product wage, its profits will be squeezed, and accumulaion in industry will be reduced, as shown by equation (7). If the agricultural sector grows faster at a given p (say due to a higher Sa) this will make the industrial sector grow faster in equilibrium, but only because it relaxes the wage-goods constraint, turning the terms of trade towards industry. The labour supply problem arises if z increases which, as we have seen above, will push the g,, curve to the left and reduce the rate of growth.

This discussion makes it clear that the role of agriculture in this model is similar to its roles in the neoclassical and classical models criticized by Thirlwall. All three models neoclassical, classical and Kaldorian assume away demand problems. The neoclassical one (Jorgenson (1961) for example) is different from the others because it assumes that labour is fully employed,

12 The dynamic analysis of Section 3 casts further doubt on Thirlwall's interpretations. In our first characterization there is no sense in which positions out of long-run equilibrium can be called 'demand-constrained', pace Thirlwall: the markets clear at any short-run equilibrium. Along a dynamic path when k changes, and given the parameters of the model, if g, rises over time g9 must fall, which is contrary to what would happen if a higher agricultural growth increased the demand for industrial output and made it grow faster. It is true that a rightward shift in the ga curve (due to a parametric shift) which increases equilibrium ga would increase the equilibrium growth-rate of the industrial sector, but this must be true in any dynamic equilibrium for any model with a balanced growth equilibrium path (as was the case for the Lewis and Jorgenson models as well). While the last two comments apply for our rigid-price model as well, the first does not, since disequilibrium states with excess demand and supply are possible. But, as Fig. 2 makes it clear, there is no one-to-one relation between excess demand or supply for the industrial good, and whether we are above or below the equilibrium p; the direction of excess demand depends on k as well.

164 A KALDORIAN MODEL REVISITED

but Lewis's and Kaldor's are similar: they both assume that surplus labour exists (so that the wage in industry in terms of the agricultural good is fixed), and that all savings are automatically invested. The only real difference between the two is that the Kaldorian model assumes that there is no intersectoral capital mobility, all savings being invested within the sector of origin, while the Lewis (1954, 1972) model in which the two sectors of a closed economy trade with each other assumes that there is no investment in agriculture where output grows only due to technological change, and the agricultural surplus is invested in the industrial sector.13 We are thus entitled to call the Kaldorian model a classical one, similar in spirit to the Lewis model.'4

If demand issues are to be adequately introduced into the Kaldorian framework we need to modify the model of Section 2. In that model we resolved the contradiction between the markup-pricing equation (10) and wage equation (5) by jettisoning the former, but demand issues can be brought in by retaining the markup equation and forsaking (5) instead.'5 This alternative model appears to be closer in spirit to some of Kaldor's other work on the terms of trade and growth, where it is assumed that there is markup pricing in industry, while the agricultural terms of trade are flexible and demand-determined.16

Because industry practices markup pricing, it may be assumed that firms adjust output according to demand, so that they have excess capacity; thus we dispense also with the full-capacity assumption given by (4). Maintaining the full-capacity and flex-price assumptions for the agricultural sector, the supply- demand balance equations for the two markets can be written as

- [a(l - sa) + sa]aak/p + (1 - c){[l + (1 - s)z]/(1 + z)}u = 0 (18)

a(l- s)ak/p - {1 - a[1 + (1- s,)z]/(1 + z)}u + gn + gak = 0 (19)

where u = QI/Kn, a measure of capacity utilization in the industrial sector. To complete the model we assume that industrial investment depends positively on the rate of capacity utilization in industry,'17 so that, in a simple linear form,

13 Lewis (1954) appears at times to assume away trade between two sectors, but our comments are relevant for his model in which the two sectors produce different products and trade with each other (see pp. 172-3). This corresponds to the second of the three models in Lewis (1972).

14 See Dutt (1989) for a formal comparison of the alternative models discussed here as well as others-in terms of a common general framework.

15 We could actually retain both, determining the terms of trade from (11). In the short run, for given k, we could then determine the level of capacity utilization from the market-clearing equation for the agricultural sector see equation (18) below. In the long run, with p determined, the sectoral growth rates are determined by (3) and the agricultural market-clearing equation solves for k.

16 See Kaldor's (1976) analysis of the interaction between the primary producing and industrial sectors of the world economy. It is also consistent with Kalecki's (1971) views of pricing. Other 'closures' are possible, which endogenize the markup in industry but introduce an independent investment function, or which introduce foreign trade. While traces of such alternative models can be found in Kaldor's other work, for the sake of brevity we concentrate on just one model.

17This follows Kaldor (1940). It is also customary (see Robinson (1962)) to make the rate of profit an argument of the desired accumulaton function in neo-Keynesian growth models. But since (10) implies tha the rate of profit is given by

r z = ZA(1 + z)]U, and since we are assuming z to be given in our analysis, this influence is also being captured by the capacity utilization argument.

A. K. DUTT 165

gn = af + bu (20) with positive parameters, and that agricultural investment depends inversely on the industrial terms of trade so that

ga = /P. (21) The structure of this model is similar to those of the 'structuralist' models of Taylor (1982, 1983), the only major differences having to do with the precise specification of the sectoral investment functions.18

In the short run, given the sectoral capital stocks and hence k, we assume that the agricultural and industrial goods markets clear, respectively, through variations in Pa and Q, which imply variations in p and u. Substituting (20) and (21) into (18) and (19) we solve for the short-run equilibrium values,

U = 65[c(1 - sa) + sa]aa/1 (22)

p = Qk/{T(l -cx)[1 + (1 -S)Z]/(1 + Z)} (23)

where

Q = [x(l - sa) + s0]aa{sn[z/(1 + z)] - 5}

+ {(1 - cx)(saaa - 8)[1 + (1 - sJ)z]/(1 + z)}

Short-run stability requires Q > 0, which we assume.19 Observing that the short-run equilibrium value of u is independent of k, and substituting this into (20), we can obtain the gn curve of Fig. 3.20 Equation (21) is represented by the g. curve, and equation (23) by line OA. In the short run, given any k, we can determine p, gn and g.. In the long run k moves over time to a balanced-growth path at k*.

If ? increases equation (22) shows that u will increase: a higher rate of agricultural investment increases the demand for industrial goods for investment purposes and raises industrial output in the short run. Since (20) shows that the gn curve is pushed up as well, the rate of industrial growth is also increased in the long run. In this model, clearly, faster agricultural growth

18 Taylor (1982) assumes that g, and g9 are functions of sectoral rates of profit. Taylor (1983) takes g9 to be institutionally fixed and g, to depend on the gap between industrial and agricultural profit rates. Since with a non-capitalist agriculture the agricultural rate of profit is difficult to define, we have assumed that agricultural investment depends on the terms of trade.

'9 This condition will be satisfied when snz/( 1 + z) > 6 and saaa > B. The first of these conditions is the familiar condition that the saving response (to variations in u) in the industrial sector exceeds investment response. The second condition implies that capital always flows out of agriculture; Saaa = E implies, from (21) that there are no intersectoral capital flows. Capital flows into agriculture are not necessarily destabilizing, since this is a sufficient, and not a necessary condition for stability.

20 If we substitute for Q from (24) into (23) we will get an inverse relation between p and u given k, and hence an inverse relation between p and gn from (21). However, since this curve would take k as given it could not be used to examine the dynamic path of the economy. What our horizontal gn line takes into account is the fact that changes in k and p are proportional and leave unaffected the levels of u and gn.

166 A KALDORIAN MODEL REVISITED

P P

/A

0 k* k 0 g *

FIG. 3.

increases industrial growth by providing a more rapidly-expanding market for its product.

A comparison of this amended Kaldorian model with the model of Section 2 shows why the latter (and Thirlwall's) does not allow the agricultural sector to play a role in providing a market for the industrial sector. This model differs from the previous ones in two crucial ways. First, it departs from the notion that all saving is identically invested; this is achieved by introducing the independent investment functions. The investment function for the industrial sector implies that the aggregate demand for the industrial good will not identically be equal to its aggregate supply, so that a demand problem for that sector can arise. Second, it allows for intersectoral capital mobility and thereby ensures that the agricultural sector can actually solve the demand problem for the industrial sector by buying from it a different amount than what it sells to it. If we assume away intersectoral capital mobility in the demand-constrained model just discussed and assume saaa = a, we find, using (18) and (19), that saving equals investment in the industrial sector, or that

1 = s,1z/(1 + z)]u. (24)

Equations (20) and (24) then solve for the equilibrium value of u (in both short and long runs), from which it follows that g,, depends only on z, s, and the investment parameters in the industrial sector. The industrial sector is demand- constrained in the sense that an increase in demand (for instance an increase in a) will increase the levels of capacity utilization and capital accumulation; but there is still no room for agriculture to solve the market problem for industry: if agricultural income rises (say due to a rise in aa) the terms of trade will turn against agriculture, but u and g,, will be unchanged. Agricultural

A. K. DUTT 167

expansion does expand industrial demand by raising agricultural income, but since trade is balanced it is exactly offset by a higher demand for agricultural goods by the industrial sector.

5. Conclusion

This paper has developed a consistent, formal Kaldorian model of growth and development, drawing on the work of Thirlwall (1986, 1987). It has also analyzed the disequilibrium dynamics behind the model and demonstrated its dynamic stability, something not adequately done before. This analysis has shown that Kaldorian model is not what Thirlwall and indeed Kaldor himself thought it to be, that is, a model of an economy with a fixprice industrial sector and a flexprice agricultural sector, and one which adequately captures the role of the agricultural sector in solving the problem of demand for the industrial sector. Instead, it has shown that the model is similar to that of Lewis which, according to previous interpretations, did not adequately focus on the demand issue.

Though the Kaldorian model does not live up to Thirlwall's expectations, however, we still believe that it is an useful contribution. First, although similar to the Lewis model, it departs from Lewis's static focus on disguised unemployment and develops a dynamic analysis of capital investment and technical change in agriculture which is more relevant for understanding the behaviour of dual economies using industrial capital in agriculture. Second, demand issues can be introduced easily by modifying the model to make it consistent with some of Kaldor's other work. Finally and this is a direction not pursued in this paper the model has laid the foundation on which the analysis of several important issues can be based: Canning (1988) demonstrates how the role of increasing returns to scale in dual economies can be analyzed using a Kaldorian model and Dutt (1990) uses the model to analyze the implications of intersectoral capital flows.

University of Notre Dame, Indiana

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