Structural economic dynamics: an alternative approach to North ...

Cambridge Journal of Economics 2004, 28, 705–717 doi:10.1093/cje/beh031

Structural economic dynamics: an alternative approach to North–South models Ricardo Azevedo Araujo and Joanı´lio Rodolpho Teixeira* This paper isolates the mechanisms responsible for the difficulties facing poor regions in growing faster than rich ones. The analysis of uneven development is carried out in a framework where changes in demand composition are consistent with Engel’s Law. The standpoint of the analysis is the interaction between technical progress—which produces responses in per capita income—and changes of per capita consumption. The paper focuses on one case in which preferences are homothetic and there is capital dependence, showing that the latter assumption is sufficient to explain the inequalities between poor and rich regions. When dealing with the case of non-homothetic tastes, adverse movements in the terms of trade and the international demonstration effect, which are both due to the inelastic demand for goods produced by poor regions, are the mechanisms responsible for uneven development. Key words: Uneven development, Capital dependence, Engel’s Law JEL classifications: O19, F12

1. Introduction The results obtained from the North–South models are basically concerned with the explanation of the ever-widening gap between developed and underdeveloped regions. In discussions of the secular downward trend in Southern terms of trade, one factor that has received repeated attention is the decline in the share of consumer expenditures on Southern goods. The usual explanation for this phenomenon is the difference in the income elasticity of demand for industrial and primary products: Engel’s Law. Prebisch (1950, 1959, 1963), for instance, argues that the South typically exports primary products and the North industrial products: Engel’s Law would imply a lower income elasticity of demand for primary products, which explains a secular deterioration in Manuscript received 18 September 2001; final version received 7 October 2002. Address for correspondence: J. Teixeira, Department of Economics, University of Brasilia. ICC Norte, 70910900. Brası´lia, Brazil; email: [email protected] or [email protected] *Catholic University of Brasilia, and University of Brasilia, respectively. The authors are indebted to Jorge Araujo, Joa˜o Faria and two anonymous referees for useful comments. The usual disclaimer applies. Financial support from CAPES and CNPq is acknowledged. Cambridge Journal of Economics, Vol. 28, No. 5, Ó Cambridge Political Economy Society 2004; all rights reserved

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Southern terms of trade and balance of payment desequilibria as constraints on development.1 Despite the fact that Engel’s Law constitutes the primary abiding causal mechanism blocking rapid growth for poor regions, Prebisch (1950, 1959, 1963) and Singer (1950) referred to two other mechanisms: different institutional factors affecting wages in poor and rich regions and the market power of transnational agribusiness. With regard to the first, the argument is that workers in poor regions do not obtain gains in real wages commensurate with growth in their productivity, while those in rich regions do. The productivity gains of workers in poor regions are thus passed on to consumers in rich regions via lower prices, while workers in rich regions capture productivity increases through growth in real wages, which means that productivity increases in rich regions are not passed on to poor regions in the form of lower prices for the products of the North. The argument regarding the market power of agribusiness is that merchanting houses that deal in the products produced by the South tend to be based in the North and possess enough market power relative to Southern producers that they can force lower than competitive prices on them.2 Defining uneven development to be a sustained increase in the ratio of capital stocks in the North compared with that in the South, Dutt (1990) examined the possible role of the Prebisch–Singer effect and international demonstration effects in causing uneven development. The standard way to study this phenomenon in a formal model is to have non-homothetic tastes. As pointed out by Dutt (1990): ‘Neo-classical models of the standard trade-theory literature use this assumption to find conditions for deterioration of the terms of trade. North–South models considering capital accumulation, however, have typically not incorporated this phenomenon . . . It would seem difficult to examine long-run properties of such models allowing for Engel’s Law (Dutt, 1990, p. 189) Here, following a Pasinettian approach and in contrast to models designed to study North–South interdependence, consumption behaviour is assumed to mimic Engel’s Law. The analysis of uneven development is then carried out in a framework where changes in demand composition are consistent with Engel’s Law. Our aim is accomplished with the support of an extended version of Feldman’s model of investment allocation (1928), in which demand requirements are considered. The standpoint of the analysis, as suggested by Pasinetti (1981, 1993), is the interaction between technical progress—which produces responses in per capita income—and changes in per capita consumption. Araujo and Teixeira (2002) have shown that Feldman’s model can be treated as a particular case of Pasinetti’s (1981) model of structural change. From this perspective, the limitations of Feldman’s model concerning the passive role of per capita consumption demand are diminished. Here, the composition of investment will reflect, on the input side, the same order of priorities in which production of consumption goods is organised according to consumers’ preferences. The effects of the evolving pattern of consumers’ preferences on 1 This is the essential feature of the Structuralist perspective in its analytical work. Some question the methodological and conceptual foundations of the empirical terms of trade analysis. Naturally, the importance of selecting the correct methodology is an important issue, although exactly how important is controversial. See Hunt (1989) for a summary of the historical background of the emergence of the Structuralist school of development economics in Latin America. For an interesting comparison between the import substitution paradigm and the export oriented approach see Bruton (1998). Ardeni and Wright’s (1992) reappraisal of the Prebisch–Singer hypothesis of the deterioration in the terms of trade sheds light on earlier discussion on this matter. 2 In this paper, we have had to omit these two lines of analysis, since they emphasise institutional issues rather than analytical ones. It has seemed to us that the Engel’s Law and capital dependence constitute the primary abiding causal mechanism for the problems faced by poor countries. The other two issues are less central and more difficult to deal with via a modelling approach.

Structural economic dynamics

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the investment allocation between capital and consumption goods sectors are analysed in order to establish the rate of investment allocation. We intend to provide a comprehensive structural economic dynamics picture of North– South interdependence through the interaction between Feldman’s and Pasinetti’s models. One advantage of the approach adopted here is that it does not appeal to any specific trading mechanism nor does it assume any particular institutional set-up. This characteristic allows us to isolate, in each of the cases considered by Dutt, mechanisms responsible for the difficulties faced by poor regions attempting to grow faster than rich ones. Furthermore, any analysis of the North–South linkages from which reliable policy conclusions are to be drawn should take into account not only international trade but also international learning and technical progress. Pasinetti (1993, ch. 11) describes trade between developed and underdeveloped countries in terms of international learning, or developing countries’ constant efforts to learn developed countries’ technology. However, as pointed out by Singer (1950): ‘absorption of the fruits of technical progress in primary production is not enough; what is wanted is absorption for reinvestment’ (Singer, 1950, p. 485). This paper is structured as follows: in Section 2, we deal with one case in which preferences are homothetic and there is capital dependence, showing that the latter explains the inequalities between poor and rich regions. In Section 3, we consider nonhomothetic tastes, and we show that adverse movements in the terms of trade and the international demonstration effect, which are both due to the inelastic demand for goods produced by poor countries, are the effective mechanisms responsible for uneven development. Section 4 concludes.

2. Capital dependence and homothetic preferences As a first approach to the case in which North–South trade generates uneven development, Dutt (1990) considers that consumers’ preferences do not change over time. His model highlights mechanisms responsible for the poor South failing to grow constantly faster than the rich North, and may be described as follows: (i) there are two regions, a developed North and a poor South, each producing a particular good—the N good and S good— respectively; (ii) each good is produced with Leontief technology, using two factors of production, capital and labour; (iii) the S good is only a consumption good, but the N good is a consumption as well as an investment good (both in the North and South), and (iv) trade balances throughout. Some alternative closures, which assume specific structures and behaviours for capitalists and workers in each of the regions, are assumed. The South can obtain capital only through trade, exchanging primary products for manufactured investment goods from the North. The terms of trade exert a crucial influence on capital accumulation in the South, and hence on the Southern growth rate. In this section, we show that the effective mechanism responsible for the South failing to grow constantly faster than the North is its dependence on Northern capital goods. Thus, assumptions concerning the structure of the economy and the behaviour of agents are not necessary to prove the convergence of growth rates in the long run. A different approach to North–South trade is adopted here—a modified version of Feldman’s model1 of investment allocation, which considers the existence of three sectors: 1 It is worthwhile to recall that, like Feldman (1928) and Mahalanobis (1953), Lowe (1976) took as the starting point of his structural model of production, Marx’s well-known two departmental scheme of expanded reproduction. For an interesting reconsideration of some links between Lowe and FeldmanMahalanobis, see Hagemann (1994).

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one of them is located in the South, and it produces consumption goods with the technology assumed by Dutt. The other two are located in the North, one producing capital goods and the other producing consumption goods. It is assumed that both consumption goods sectors require Northern capital goods. The usual assumptions of Feldman’s model are adopted, namely, capital goods are used by all sectors but, once installed, they cannot be transferred from one sector to the other (non-shiftability assumption). Also, in all sectors, technology is described by Leontief production functions, and the limiting factor of production in both countries is the stock of capital goods. For the sake of convenience only, it is assumed that there is no depreciation of capital goods. Using the following notation, we derive the growth rate in both regions: Yn is the production of Northern consumption goods; Yk is the production of Northern capital goods and Ys is the production of Southern consumption goods. In addition m, 1 $ m $ 0, is the allocation of the flow of investment goods between the Northern capital goods sector and both the Southern and the Northern consumption goods sectors. The total investment, I, is given by the following equation

I ¼ Yk ¼

Kk vk

ð1Þ

where Kk is the stock of capital in the capital goods sector, and vk is the capital–output ratio in this sector. Therefore, the change of total investment is given by

1 I_ ¼ K_ k vk

ð2Þ

The change in the capital stock in the sector of capital goods depends on the proportion of total production of this sector that is allocated to itself

K_ k ¼ mYk

ð3Þ

Y_ k m ¼ Yk vk

ð4Þ

By substituting (3) into (2) we obtain

One of the focuses of Feldman’s model is on the relationship between the growth rate of the economy, determined by the capital goods sector, and the rate of investment allocation, as given by equation (4). However, without a normative criterion, the rate of investment allocation cannot be determined. A reasonable criterion requires that investment grow at a rate compatible with demand requirements. Dealing with the case in which consumers’ preferences do not change over time, the growth rate of the investment sector has to be equal to the constant growth rate of population, n. From equation (4), the value of m is determined as: m ¼ nvk. Despite the fact that the value of m is endogenously determined, this has no implications for the proof of convergence (see Appendix 1), since this value is constant over time.1 It is also possible to establish the growth rate of the production of 1 Despite the fact that the rates of investment allocations are endogenously determined, they are constant over time. Pasinetti (1981) states that: ‘in the present (dynamic) analysis, variability or constancy refer to variability or constancy of long-run trends in time, quite irrespective of whether the magnitudes concerned represent unknowns (i.e., they have to be explained) or whether they represent data (i.e., they have to be accepted as given)’ (Pasinetti, 1981, p. 79). This is the point at stake here.


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consumption goods in both regions. The produced quantity of consumption goods in the South is given by

Ys ¼

Ks vs

ð5Þ

where Ks is the stock of capital in the Southern consumption goods sector, and vs is the capital–output ratio in this sector. The rate of change of the Southern production is

1 Y_ s ¼ K_ s vs

ð6Þ

It is assumed that (1 m) of total investment is allocated to consumption goods sectors. As we have two consumer sectors, one in each country, it is necessary to introduce another rate, denoted by u, 1 $ u $ 0, which represents the fraction of investment in the consumer sector, (1 m)I, that is allocated to the Northern consumption goods sector. Therefore, the change of capital stock in the South may be written as follows

K_ s ¼ ð1 uÞð1 mÞYk

ð7Þ

Substituting (7) into (6), we have

ð1 uÞð1 mÞ Yk Y_ s ¼ vs

ð8Þ

Dividing this expression by Ys we conclude that

Y_ s ð1 uÞð1 mÞ Yk ¼ vs Ys Ys

ð9Þ

By adopting the same procedure for the Northern consumption goods sector, we obtain the following growth rate for this sector

Y_ n uð1 mÞ Yk ¼ vn Yn Yn

ð10Þ

Comparing the growth rate of the Northern and the Southern consumption goods sectors, we conclude that in the short-run the latter will be larger than the former if and only if the following inequality holds

1 u Ks ð0Þ > u Kn ð0Þ

ð11Þ

This inequality shows that Southern consumption goods can grow faster than Northern ones if and only if the ratio between the fraction of investment allocated between the consumer sectors is larger than the ratio between the initial capital stocks of both sectors. The value of m does not matter for the comparison of the rates in the short run. This means, depending on the value taken by u, that capital accumulation in the South may be slower, equal to or faster than capital accumulation in the North in the short run. Despite this result, however, in the long run, the growth rate of both economies will converge to the growth rate of the Northern capital goods sector (see Appendix 1), that is

Y_ s Y_ n Y_ k m ¼ lim ¼ ¼ t/N Ys t/N Yn Yk vk lim

ð12Þ

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The long-run equilibrium in this framework is the state in which gn ¼ gs, where gn and gs stand for the growth rate of the North and South, respectively. This result shows that the dependence on capital goods is a sufficient condition in Dutt’s model for the South to fail to grow constantly faster than the North. Furthermore, the North controls the main decision variables of the model, namely, the rates of investment allocation. To highlight this point, let us assume that both regions intend to allocate investment in order to fulfil demand requirements. Under homothetic preferences, consumption goods sectors of the South and the North have to grow at a rate equal to n to meet the demand requirements in both regions, that is:1

Y_ s Y_ n ¼ ¼n Ys Yn

ð13Þ

But from the supply side, these growth rates are given respectively by equations (9) and (10). By equalising (9) and (10) to (13) and considering that m¼nvk, it is possible to determine the rate of investment allocation between the consumer sectors of the North and the South, u, that is compatible with demand requirements. For the South this rate is given by

us ¼ 1

nKs ð0Þ ð1 nvk ÞYk ð0Þ

ð14Þ

For the North, this rate is given by

un ¼

nKn ð0Þ ð1 nvk ÞYk ð0Þ

ð15Þ

These rates are equal, that is us ¼ un, if the following equality holds

nvk Kk ð0Þ ¼ 1 nvk Kc ð0Þ

ð16Þ

where Kc(0) ¼ Ks(0) þ Kn(0). Since the vector [Kc(0), Kc(0), Kn(0)] is given at time zero, there is no guarantee that this equality holds. Hence, the rate of investment allocation chosen by the South is in general different from the rate that is chosen by the North. Hence, there is little that the South can do to raise its growth rate2. These results confirm what was reported by Taylor (1983), namely: ‘There are not enough degrees of freedom in the international system to allow the South to choose its own growth rate or terms of trade . . . In steady state, the Southern growth rate remains determined by the Northern rate . . . ’ (Taylor, 1983, p. 178). In addition, despite the fact that balanced trade is assumed, circumstances do not seem favourable to developing countries, which must import advanced capital goods at any price, while they can export their products only if their prices are competitive. Short-term balance of payment adjustments may damage the long-term growth potential of the South.

1

It is important to note that is reasonable to assume that the rates of investment allocation are determined according to the demand requirements. In the South, however, the desired rate of investment is probably affected by the intention of policy-makers to increase the growth rate of this region. Of course, any policy in the South concerning investment allocation is subject to constraints such as balanced trade. 2 Some of these results are demonstrated by Domar (1957) and recalled by Jones (1975, ch. 5, Sections 6 and 7). For the proof of this result, see Appendix 1.


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3. Engel’s Law and uneven development In order to isolate the effective mechanism responsible for uneven development, it is important to study the case in which the South does not depend on Northern capital goods. In the previous section, it was shown that the dependence on capital goods is per se a reason for the South failing to grow faster than the North. Besides, empirical evidence shows that some poor countries and regions, such as India and Brazil, have to some extent escaped capital dependence and created their own capital goods-producing sectors, but have still not enjoyed persistently strong rates of growth. In this vein, we show here that, even when the capital dependence assumption is relaxed, poor regions still face difficulties owing to the operation of Engel’s Law. If a poor region does not have the internal means to develop a capital goods sector, it can in principle resort to international learning and also to international trade. By importing capital goods that it cannot produce, the underdeveloped regions may learn how to use them and how to produce them. There are spillover effects of exogenous shocks in the North. Knowledge of these spillover effects permits the gains from North–South interactions. On this basis, the South should establish a capital goods sector to enhance its efforts at international learning. Bruton (1998) considers that another possible way of developing a capital goods sector is through an overvalued exchange rate. He reported that The capital goods sector was small or non-existent in the newly independent countries, and most capital goods had to be imported. An obvious way to encourage investment was to maintain an exchange rate that kept capital’s domestic price low. This could be most easily done by maintaining an overvalued exchange rate (or, less frequently, multiple exchange rates). Overvalued exchange rates (relative to a free trade situation) appeared as a means to encourage investment . . . Where Mahalanobis’ view strongly prevailed—India, Brazil, and possibly other large countries—domestic production of capital goods was encouraged by keeping out imports and by direct subsidies. (Bruton, 1998, p. 908)

Dealing with the case of non-homothetic tastes, Dutt (1990) considers that changes in demand composition are due to the low income elasticity of Southern goods in the North and to the operation of the international demonstration effect. The South produces a comparatively simple kind of commodity, while the North produces a sophisticated one, which has a higher income elasticity of demand. In order to approach non-homothetic tastes, let us assume the existence of a capital goods sector in the South which provides the total supply of capital to this region. We then introduce a different notation: Ykn is the production of North’s capital good sector; Ycn is the production of Northern consumption good sector; Yks stands for the production of the Southern capital goods sector, and Ycs is the production of the Southern consumption goods sector. By adopting the procedure of the previous section, we obtain the following results with respect to the growth rate of each of the economies, gn and gs, in terms of the rates of investment allocation (see Appendix 2):1 n

g ¼

n n n m Y_ k Y_ c n ¼ lim n ¼ n t/N Y Yk vk c

ð17Þ

1 These results show that the growth rate of consumption goods converges to the growth rate of the capital goods in both countries. However, despite the fact that convergence is verified, the model is unstable, as shown in the Appendix 2.

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R. A. Araujo and J. R. Teixeira s

g ¼

Y_ ks Y_ cs ms ¼ lim s s ¼ s Yk t/N Yc vk

ð18Þ

where mn and ms are the rates of investment allocation in the North and South regions and vnk and vsk stand for the capital–output ratios in the capital goods sector in each region. In principle, with its own capital goods sector, the South would always be able to grow faster than the North provided that it had the right capital–output coefficient and the investment allocation ratio. In the previous section, this result was not possible since the long-run maximum growth rate of the South was given by the growth rate of the Northern capital goods sector. Note that the possibility of the South growing faster than the North disregards demand requirements, which are not contemplated in Feldman’s model. In order to mitigate the limitations of Feldman’s model in relation to the passive role of per capita consumption demand, Araujo and Teixeira (2002) have shown that it can be treated as a particular case of Pasinetti’s model of structural change (1983).1 This is accomplished using the device of vertical integration.2 This tool focuses on final commodities rather than on industries, allowing us to associate each commodity to its final inputs—a flow of working services and a stock of capital goods—thus eliminating all intermediate inputs. From this standpoint, it is possible to carry out the analysis of investment allocation in a framework where demand and productivity change at particular rates. Following these lines, a normative criterion for Feldman’s model can be derived, since the rate of investment allocation is determined subject to the evolving pattern of demand.3 As pointed out by Halevi (1996): ‘the theory of growth based on vertical integration revolutionises the very concept of choice of technique and, by focusing on the composition of per capita demand, it overcomes the limitations of Feldman’s strategy of growth’ (Halevi, 1996, p. 164). Let us consider that rn and rs represent the rates of change of demand of Northern and Southern consumption goods, respectively. In addition, we assume that the global growth rate of the population is equal to n. From Pasinetti’s model, it is possible to establish the growth rate of demand for the commodity of each region, which is equal to the growth rate of demand of the correspondent capital goods in every time period n n Y_ k Y_ c n n ¼ n ¼ nþr Yk Yc

ð19Þ

s s Y_ k Y_ c s s ¼ s ¼ nþr Yk Yc

ð20Þ

1 This is accomplished using the correspondence between the concepts of vertical integration, as used by Pasinetti (1981, 1990), and sub-systems, as defined by Sraffa (1960). The notion of a vertically integrated sector corresponds to what Sraffa called a ‘subsystem’, that is part of a self-replacing system of which the net product consists of a single commodity. Note that the economic system described by Feldman has the same characteristics of what Sraffa (1960, Appendix A) has called sub-systems, i.e., it is self-reproducible, it uses no intermediate goods to produce only one kind of final commodity. Therefore, it represents an economy in which sectors are vertically integrated. 2 In fact, the concept of vertical integration has been widely used in macroeconomics. As pointed out by Lavoie (1997): ‘the concept of vertical integration, although extensively but implicitly used in macroeconomic analysis, has always been difficult to seize intuitively’ Lavoie (1997, p. 453). What is behind this affirmation is that aggregated models with one or two sector, such as the case of Feldman, are based on the device of vertical integration. 3 Bose (1968) and Weitzman (1971) established an optimum rate of investment allocation in a context of dynamic optimisation of consumption.


713

This is the growth rate that has to be observed in order to fulfil the demand requirements particular to each region in each point of time. But the feasible growth rates of production are given by equations (17) and (18). Hence, by equalising (17) to (19) and (18) to (20) we obtain the values of mn and ms that give the warranted growth rate of investment compatible with the growth path of demand n

n

n

ð21Þ

s

s

s

ð22Þ

m ¼ ðn þ r Þvk m ¼ ðn þ r Þvk

Such expressions introduce a normative criterion for Feldman’s model: capital goods have to be allocated according to (17) and (18) in each region in period t in order to allow the fulfilment of the corresponding capital accumulation condition in period t þ 1, given the hierarchical order in which the production of consumption goods should proceed. Since we are assuming that capital goods are non-shiftable, if the investment allocation condition does not hold in one period, it will not be possible to fulfil the capital accumulation condition from there on. The composition of demand of the underdeveloped region is different from that of the developed one. The relationship between regions at different stages of industrial development is conditioned by the disparities in the composition of per capita demand. If the consumption pattern of the Southern consumption good is already in the upper part of Engel’s curve, i.e., there is saturation of demand for this commodity, this implies a lower income elasticity of demand for the Southern good. Therefore rn > rs. By substituting (17) and (18) respectively into (13) and (14) and considering that rn > rs, we conclude that gn > gs, a situation of uneven development. Under the assumption that production has to proceed according to the dynamics of consumer demand, and given the Leontief technology, a higher rate of accumulation in the North than in the South seems to be expected. In fact, this is the central result of the North–South models with non-homothetic preferences. However, in these models there is some confusion of causal mechanisms holding for uneven development. Here by adopting the structural economic dynamics approach, we are able to sort these out and thereby isolate the key mechanism at work in North–South models—Engel’s Law and not capital dependence. The principal problem facing poor regions is the balance of payment constraint on growth that springs from Engel’s Law and its negative effect upon the terms of trade for primary products. The model makes preferences endogenous since the rs are endogenously determined in this framework. Through this rate, changes in consumption due to the expansion of income, described by Engel’s Law, are captured. This means that r depends not only on consumers preferences but also on their evolution through time, i.e., s s s s d s s r ðtÞ ¼ f lk ; lc ; ½lk ;lc ð23Þ dt n

r ðtÞ ¼ f

n

n n d n n lk ; lc ; ½lk ; lc dt

ð24Þ

where l sk and l sc stand for the labour–output ratios in the capital and consumption goods sectors of the South. Of course lkn and lcn have the same meaning in relation to the North. As pointed out by Pasinetti (1981, p. 82), functions f s and f n depend on consumers’

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preferences and on how they evolve through time. Equations (19) and (20) represent the link between technical progress and changes in demand. Increases in productivity, captured by the labour–output ratios and their variations through time, imply increases in per capita income. This increase does not expand proportionally for each commodity owing to Engel’s Law. In essence this shows that Feldman’s model is consistent with Pasinetti’s emphasis on the role of per capita consumption demand. This analysis is an alternative characterisation of the interdependence between the North and South.

4. Concluding remarks In this paper, the analysis of uneven development is carried out in a framework where changes in demand composition are consistent with Engel’s Law. From a Pasinettian approach, which considers technical change and the evolution of preferences, we developed an analysis which attempts to capture the main channels of the North–South interdependence. Following these lines, two of the mechanisms responsible for the underdeveloped regions failing to grow constantly faster than developed ones were isolated. Considering the case in which preferences are homothetic, the Southern dependence on Northern capital goods was shown to be the mechanism for the convergence between the growth rates of the South and North regions in the long run. No further specification of the economies is required to obtain this result. When non-homothetic tastes were considered, we verified that both the low income elasticity of the Southern commodity and the international demonstration effect are required to guarantee that the North will grow faster than the South. These mechanisms were isolated using Feldman’s model as a particular case of Pasinetti’s methodology. The insight to be gained from this approach is that it allows clarifications on the connections between the rate of investment allocation and the role played by evolving patterns of demand and increases in productivity. Thus, it was possible to consider the effects of Engel’s Law in a North–South framework, where uneven growth is expected to occur. It seems that this analysis complements and reinforces the Structuralist paradigm that the periphery must begin to control its growth dynamics by deliberately introducing measures to reduce dependence on foreign demand as the engine of development. However, such is not the only policy conclusion that can be drawn from our analysis. In fact, in the light of the experiences of countries that have tried to shut themselves off from world trade, this strategy does not appear to be the best advice for poor countries. An alternative conclusion is that poor regions need to induce structural changes in their economies which encourage the expansion of export-oriented manufacturing industries, producing commodities with higher elasticities of demand than those for primary products.1 Therefore, we acknowledge that more than one policy strategy follows from an understanding of the obstacles to growth posed by Engel’s Law.

Bibliography Araujo, R. and Teixeira, J. 2002. Structural change and decisions on investment allocation, Structural Change and Economic Dynamics, vol. 13, 249–58 Ardeni, G. and Wright, B. 1992. The Prebisch–Singer hypothesis: a reappraisal independent of stationarity hypothesis, Economic Journal, July, 803–12 1 This is clearly the strategy followed by the successful, newly industrialising countries of Asia. China, for example, has enjoyed a growth rate of 6–10% per annum for two decades following this strategy, combined with selected trade restrictions on imports in the early phase.


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Bose, S. 1968. Optimal growth and investment allocation, Review of Economic Studies, vol. 35, 456–80 Bruton, H. 1998. A reconsideration of import substitution, Journal of Economic Literature, vol. XXXVI, 903–36 Domar, E. 1957. A soviet model of growth, Essays in the Theory of Economic Growth, New York, Oxford University Press Dutt, A. 1990. Growth, Distribution, and Uneven Development, Cambridge, Cambridge University Press Feldman, G. 1928. On the theory of growth rates of national income, Planovoc Khoziaistvo, n. 11,12 (1928), translated in Spulber, N. (ed.), Foundations of Soviet Strategy for Economic Growth, Bloomington, IN, 1964 Hagemann, H. 1994. The economy in traverse: growth, technology and structural change, Economie Applique´e, vol. XLVI, 37–56 Halevi, J. 1996. The significance of the theory of vertically integrated processes for the problem of economic development, Structural Change and Economic Dynamics, vol. 7, 163–71 Hunt, D. 1989. Economic Theories of Development: An Analysis of Competing Paradigms, London, Harvester Wheatsheaf Jones, H. 1975. An Introduction to Modern Theories of Economic Growth, London, Thomas Nelson Lavoie, M. 1997. Pasinetti’s vertically hyper-integrated sectors and natural prices. Cambridge Journal of Economics, vol. 21, 453–67 Lowe, A. 1976. The Path of Economic Growth, Cambridge, Cambridge University Press Mahalanobis, P. 1953. Some observations on the process of growth of national income, Sankhya, September, 307–12 Pasinetti, L. 1981. Structural Change and Economic Growth, Cambridge, Cambridge University Press Pasinetti, L. 1990. Sraffa’s circular process and the concept of vertical integration, in Bharadwaj, K. and Schefold, B. (eds), Essays on Pierro Sraffa, London, Unwin Hyman Pasinetti, L. 1993. Structural Economic Dynamics, Cambridge, Cambridge University Press Prebisch, R. 1950. The Economic Development of Latin America and its Principal Problems, New York, ECLA Prebisch, R. 1959. Commercial policy in underdeveloped countries, American Economic Review, Paper and Proceedings, vol. 49, no. 2, 251–73 Prebisch, R. 1963. Towards a Dynamic Development Policy for Latin American, New York, United Nations Singer, H. 1950. The distribution of gains between investing and borrowing countries, American Economic Review, vol. XL, no. 2, 473–85 Sraffa, P. 1960. Production of Commodities by Means of Commodities, Cambridge, Cambridge University Press Taylor, L. 1983. Structuralist Macroeconomics, New York, Basic Books Weitzman, M. 1971. Shiftable versus non-shiftable capital: a synthesis, Econometrica, vol. 39, 511–29

Appendix 1 Let us prove that, in the long run, the growth rates of consumption goods sectors converge to the growth rate of the Northern capital goods sectors. The growth rate of the Northern capital goods sector is written as follows m Y_ k ¼ Yk vk

ð4Þ

While the growth rate of the Southern consumption goods sector is given by ð1 uÞð1 mÞ Yk Y_ s ¼ Ys Ys vs

ð9Þ

We know that Ks¼vsYs. Since the rate of investment allocation m is constant over time, we conclude from (4) that Yk ðtÞ ¼ Yk ð0Þeðm=vk Þt . Substituting these expressions into (9), we obtain

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R. A. Araujo and J. R. Teixeira ð1 mÞð1 uÞYk ð0Þeðm=vk Þt Y_ s ¼ Ys Ks

ð21Þ

The stock of capital of the Southern consumption goods sector, Ks, may be written as Rt Ks ðtÞ ¼ Ks ð0Þ þ 0 ð1 mÞð1 uÞYk ðtÞdt. Substituting the dynamic path of Yk into this equation, we obtain Z t Ks ðtÞ ¼ Ks ð0Þ þ ð1 mÞð1 uÞ Yk ð0Þeðm=vk Þw dw ð22Þ 0

Solving this integral and substituting into (21), it yields Y_ s ð1 mÞð1 uÞYk ð0Þeðm=vk Þt h i ¼ Ys Ks ð0Þ þ ð1 mÞð1 uÞYk ð0Þ eðm=vk Þt 1 vmk

ð23Þ

Since both the numerator and the denominator become infinite as t approaches infinity, we shall apply L’Hoˆpital’s rule to evaluate this limit. Differentiating both members of the fraction with respect to t, we conclude that m Y_ s ¼ t/N Ys vk

ð24Þ

lim

which is equal to the growth rate of the Northern capital goods. A similar proof can be derived for the Northern consumption goods.

Appendix 2 Let us show that the growth rate of the Southern consumption goods sector converges to the growth rate of the Southern capital goods sector. A similar result can be proved for the North. In order to prove this result, it is important to focus on the determination of the growth rate of demand. According to equations (19) and (20), this growth rate varies through time owing to the technological progress that is transformed into higher levels of per capital income, which is spread unevenly among the commodities. However, as pointed out by Pasinetti (1981). An upper saturation level exists for all types of goods and services although at different levels of real income: it may be reached sharply—in the case of goods satisfying physiological needs—or only through a slow and long process as income increases—in the case of services yielding very sophisticated kinds of satisfaction—but its attainment is eventually inevitable. (Pasinetti, 1981, p. 77) This means that for both Southern and Northern commodities, there is a time when the growth rate of demand will remain constant, if not equal to zero. In order to prove convergence, let us admit for the case of the Southern consumption goods that the growth rate of demand will remain constant after time t¼t. The growth rate of the Southern capital good sector may be written as follows ms Y_ ks s ¼ Yk vsk

ð25Þ

While the growth rate of the Southern consumption goods sector is given by ð1 ms Þ Yks Y_ cs s ¼ Yc Ycs vsc

ð26Þ

The Southern capital goods production is given at time t > t by s

s

Yks ðtÞ ¼ Yks ðtÞeðm =vk ÞðttÞ

ð27Þ


717

The stock of capital of the Southern consumption goods sector, Ks, may be written as Z t ð1 ms ÞYks ðtÞdt Kcs ðtÞ ¼ Kcs ðtÞ þ

ð28Þ

t

Substituting the dynamic path of Yk in the above equation, we obtain that the growth rate of the Southern consumption goods sector is given by s

s

ð1 ms ÞYks ðtÞeðm =vk ÞðttÞ Y_ cs Rt s s s ¼ s Yc Kc ðtÞ þ t ð1 ms ÞYks ðtÞeðm =vk ÞðttÞ dt

ð29Þ

Since both the numerator and the denominator become infinite as t approaches infinity, we shall apply L’Hoˆpital’s rule to evaluate this limit. Differentiating both members of the fraction with respect to t, we conclude that ms Y_ cs s ¼ t/N Y vsk c

ð30Þ

lim

However, it is important to note that the steady-state equilibrium is unstable. In order to verify this, let us consider the system formed by equations (25) and (26) which can be written as ms Y_ ks ¼ s Yks vk

ð31Þ

ð1 ms Þ s Yk Y_ cs ¼ vsc

ð32Þ

After some algebraic manipulation equation (32) may be rewritten as ð1 mÞ Kk Yc Y_ c ¼ vk Kc Considering that the steady state is characterised by steady state yields

Kks Kcs

ð33Þ ¼

ð1ms Þ ms ,

equation (33) evaluated in

m Y_ cs ¼ Ycs vk The Jacobian matrix associated to this system of equations (31) and (33) is "m # 0 vk J ¼ 0 vmk

ð34Þ

ð35Þ

We conclude that det J > 0 and tr J > 0, which gives rise to an unstable system. A similar result holds for the North.