Keynes and Sraffa: uncertainty versus determinism

Most, if not all, Keynesian fundamentalists and most neo-Ricardians would argue that it is impossible to close the gap between Keynes and Sraffa. This is one of the main conclusions of John King's excellent History of Post Keynesian Economics since 1936 (King Reference King2003). Broadly speaking, Keynes's General Theory is dominated by investors who act under uncertainty about the future and whose actions are coordinated by the functioning of the socio-economic system regarding employment determination through the principle of effective demand. This principle is embodied in the multiplier relation, which, given autonomous demand, governs output and employment in a monetary production economy. In sharp contrast, Sraffa's Production of Commodities pictures how value and distribution are governed, in principle, within the social process of production by technological and institutional structures. Here, determinism prevails. Given this sharp contrast between Keynes and Sraffa, Alessandro Roncaglia, for example, thinks that, at best, a loose bridge may be built ‘between Sraffa's analysis of prices and Keynes' analysis of production levels. [Sraffa] looks to conditions for reproduction of the economic system. . . . When the technology changes, the relative prices will [as a rule] also change’ (Roncaglia Reference Roncaglia2000, p. 64). These price changes cannot be known ex ante because ‘of that all-pervasive uncertainty constituting a key feature of Keynes' vision, leading him to grant expectations a central role in his theory. For this reason the two problems – Sraffa's and Keynes' – must be kept apart. Nevertheless, given Sraffa's approach to his problem – isolating it from the determination of quantities produced while avoiding any opening in the direction of “Say's law” – we may consider his analysis of the prices–distribution link conceptually compatible with Keynes' analysis of employment, once the latter has been cleared of marginalist encrustations’ (Roncaglia Reference Roncaglia2000, p. 65). Since the future course of prices and quantities is unknown, it is not possible to go beyond the short term. All that can be done is to replace the Marshallian marginalist price remnants in Keynes' General Theory, which vary with changes in output levels, with some kind of fixed prices based upon the mark-up principle. This would, incidentally, require that Sraffa's prices of production are no longer seen as conditions for reproduction (Roncaglia) but as a pure theory of prices of production, with applied prices of production being set on the basis of normal cost calculation. Sraffa must be anchored in the real world and should not stay at the level of (Kantian) ideas produced by the human mind. Conceiving of Sraffa prices only as conditions for reproduction leads, as far as we can see, inevitably to setting prices through some planning mechanism: these conditions would have to be imposed on the real world. Considering, however, the prices of production as picturing how the pricing process goes on in principle within the social process of production provides the possibility of linking distributional states – an institutionally determined rate of profits – not only to Sraffa prices but also to the determination of the level of employment through the propensity to consume. A rising profit share would reduce the propensity to consume and the level of employment, and vice versa. This way of looking at things can be elaborated; for example, the capacity effect of investment can be taken account of and combined with the income effect. This is, broadly speaking, the way taken by Kalecki in his theory of cyclical growth (Kalecki Reference Kalecki1971, pp. 165 ff.).

If post-Keynesian political economists want to erect a theoretical structure constituting an alternative to the neoclassical Walrasian–Marshallian system and its modern elaborations, then ‘broad consistency’ between Keynes and Sraffa, leading up to building loose bridges between the two theories, is clearly not sufficient. Even less satisfactory is to leave the gap as it is. Keynesian Fundamentalists and Kaleckians–Robinsonians would argue that Sraffa's theoretical system represents a long-period equilibrium model and that economies cannot get into long-period equilibria in a Keynesian world of uncertainty about the future, requiring a continuous revision of long-period expectations. The neo-Ricardians would reply that institutional–technological structures are the constant or slowly changing elements of the real world of the classical political economists which govern prices and quantities, and distributional outcomes, on a fundamental level. One cannot build economic theory upon psychological foundations, which echoes Sraffa's criticism of the General Theory.

The gap between Sraffa and Keynes is, probably, the fundamental reason why neoclassical economists do not take the post-Keynesian system of political economy seriously. Indeed, in an excellent textbook on old and new macroeconomics, it is argued that ‘post Keynesianism does not represent a coherent theory and can, therefore, not be dealt with in an introductory textbook’ (Felderer-Homburg Reference Felderer and Homburg2003, p. 101). The gap between Keynes and Sraffa is certainly the main reason why post-Keynesian textbooks, by Joan Robinson/John Eatwell and Francis Cripps/Wynne Godley, for example, were not successful. The descriptions of steady states and golden ages contained in both books were simply not taken seriously by the neoclassicals and most post-Keynesians, the most important – implicit – reason being the presence of time. It should be remembered that principles in general and pure theories in particular should be independent of space and time, hence of concrete institutional set-ups; principles, however, imply certain types of institutions.

The problem

In all likelihood, the only way to bridge the gap between Keynes and Sraffa is to set up a coherent set of principles bringing together the classical view of value and distribution, based upon the labour value principle and the surplus principle of distribution, respectively, and the Keynesian vision of employment and output determination through the principle of effective demand. Based upon Pasinetti (Reference Pasinetti, Baranzini and Scazzieri1986a), this has been attempted in Bortis (Reference Bortis, Rochon and Rossi2003a). This means reasoning, not literally but, in a broad-ranging way, in the spirit of Keynes and Sraffa. Based upon the set of classical–Keynesian principles, a broadly structured system of long-period, medium- and short-term theories along post-cum-classical–Keynesian lines may be erected (for a very sketchy outline see Bortis Reference Bortis1997). This would enable us to put the original works of Keynes and Sraffa – The General Theory of Employment, Interest and Money and Production of Commodities by Means of Commodities – in their respective places within a system of classical–Keynesian political economy, i.e. within a system of theories dealing with real-world phenomena.

The classical system, taken in a wider sense, embodies two aspects of the social process of production, i.e. the nature (inter-industry) approach and the (vertically integrated) labour approach, reflecting the famous Marxian statement that social production is an interaction between man (labour) and nature (land). The nature approach is pictured in François Quesnay's Tableau économique, the labour approach in Ricardo's Principles. Modern classical theory builds on these foundations: Leontief and Sraffa start from Quesnay's Tableau (Sraffa is explicit on this); Pasinetti, evidently, builds on Ricardo's Principles. As will be seen below, the Pasinetti transformation links the inter-industry and the labour approach such that the labour model embodies the inter-industry model at the basis of principles. The crucial point to be developed is that Luigi Pasinetti's labour model, set forth in five pages of his splendid article on the Theory of Value – a Source of Alternative Paradigms in Economic Analysis (Pasinetti Reference Pasinetti, Baranzini and Scazzieri1986a, pp. 421–427), provides the analytical vehicle for bringing together Keynes and Sraffa at the level of first principles (see on this Bortis Reference Bortis, Rochon and Rossi2003a). Based upon these principles it should be possible to erect a broadly coherent, and open, system of classical–Keynesian political economy which would appear as a synthesis, an elaboration and an extension of post-Keynesian political economy. Thus, at the level of theories, very little would be new. The great number of fine pieces of existing post-Keynesian theory would have to be adapted, elaborated, completed, synthesised and put at the right place.

At this stage it may be asked why the starting point to bring Sraffa and Keynes together should be Pasinetti's Theory of Value (Reference Pasinetti, Baranzini and Scazzieri1986a) and not Structural Change and Economic Growth (Pasinetti Reference Pasinetti1981), or ‘Sraffa's circular process and the concept of vertical integration’ (Pasinetti Reference Pasinetti1986b), which contains a final section entitled ‘Sraffa and Keynes – a meeting point’ (pp. 14–16).

In Pasinetti (Reference Pasinetti1981), the Leontief–inter-industry model is integrated into the labour model to study structural changes in a growing economy. In addition, we gain, in a classical environment, ‘profound insights into the nature of technical change (pp. 61 ff. and 206 ff.), the basic functions of the price system (pp. 133 ff.), the significance of the rate of interest (Ch. 8), the meaning and the implications of the choice of techniques (pp. 188 ff.), and one could go on’ (Bortis Reference Bortis, Rochon and Rossi2003a, pp. 428–429). The natural system set up by Pasinetti to deal with structural change and economic growth is a normative model which possesses highly desirable properties – for example, the full employment condition ought to be fulfilled. Moreover, ‘when there is both population growth and technical progress, there are as many natural rates of profit as there are rates of expansion of demand (and production) of the various consumption goods’ (Pasinetti Reference Pasinetti1981, p. 130). These are very specific requirements to ensure that structural change may go on smoothly. Deviations from the norm, brought about by structural unemployment, for example, can then be assessed and remedies proposed.

The aim pursued in Bortis (Reference Bortis1997, Reference Bortis, Rochon and Rossi2003a), however, is entirely different. Here, the problem is to distil invariable principles regulating value, distribution and employment out of a – humanist, social liberal – vision of man and of society. The questions are, for example: What is a price? How is distribution fundamentally regulated? Pasinetti (Reference Pasinetti, Baranzini and Scazzieri1986a) precisely deals with essentials or fundamentals regarding value. Moreover, contrary to Pasinetti (Reference Pasinetti1981), we need an explicit macroeconomic theory of the Keynesian type to be able to deal with the problem of determining the level, the scale, of employment and output as a whole. Employment determination through effective demand must be macroeconomic since monetary effective demand affects, in principle, all the sectors of an economy in the same way. However, a theory of employment is only implicit in Pasinetti (Reference Pasinetti1981) through the necessary condition for full employment, for example relation II.2.8, p. 32.

Pasinetti (Reference Pasinetti1986b) starts from Sraffa's (Reference Sraffa1960) model of circular and social production, on which basis the problems of value and distribution are dealt with in a classical vein. Pasinetti's aim is to overcome Sraffa's limitation of given quantities in order to render possible dynamic analysis. To do so ‘Keynesian analysis must be developed beyond its macro economic original conception [which has to be] broken down into as many vertically integrated sectors as there are final commodities. The analytical device of the sub-systems’ (pp. 15–16) ‘“shows at a glance” [Sraffa] the amount of labour which directly and indirectly goes into producing each commodity’ (pp. 7–8). This opens the way to dynamic analysis: changing structures are incorporated in sectorial output and employment levels which may change, grow or decline over the course of time. Pasinetti (Reference Pasinetti1986b) provides exciting perspectives for theoretical and empirical work regarding the interaction between structural changes-cum-technical progress, prices of production, distribution and output and employment levels. Once again the link between the classics and Keynes is established, but at the level of theories (structural change, value, distribution and growth), not of principles. For example, Pasinetti (Reference Pasinetti1986b) implies prices of production, a specific type of price. The question as to the nature of the price is not, and need not be, asked.

However, the question as to the nature of price is asked in Pasinetti (Reference Pasinetti, Baranzini and Scazzieri1986a). Indeed, the meaning of prices in a pure exchange or preference economy is compared with a pure labour model and the meaning of prices therein (pp. 416–424). In a few pages Luigi Pasinetti brings to the open ‘the fundamental differences between exchange-based neoclassical pure theory and production or labour-based classical theory [which are] set forth on the level of principles, illuminating thus the basic options in economic theory open at present’ (Bortis Reference Bortis, Rochon and Rossi2003a, p. 415). Now, the problem of value is, in a way, the key problem in economic theory. Starting from a subjective or preference, exchange-based theory of value or from an objective, production or labour-based theory of value leads on to entirely different theories of distribution, employment, money, international trade and so on. Neoclassical theory builds upon the subjective theory of value. Hence the starting point for an alternative to the neoclassical theoretical system must be the pure labour model (Pasinetti Reference Pasinetti, Baranzini and Scazzieri1986a, pp. 421–427), which contains the pure nature (inter-industry) model. Pasinetti's labour model may quite easily be elaborated to yield a complete classical model at the level of principles (Bortis Reference Bortis, Rochon and Rossi2003a, pp. 445–460).

Subsequently, bringing together Keynes and Sraffa boils down to linking classical and Keynesian political economy on the basis of the principles underlying these theories (Bortis Reference Bortis, Rochon and Rossi2003a). Upon the system of principles a system of classical–Keynesian theories can be set up. It is within this latter system that the original works of Keynes and Sraffa have to be put at the appropriate place. However, this is, of course, only part of the project. The classical–Keynesian system of theories must comprise all the post-Keynesian strands, the Keynesian Fundamentalists, the Robinsonian–Kaleckians and the neo-Ricardians. But even more, the classical–Keynesian system must be open to allow all types of heterodox economics and (humanist) Marxist political economy as well as large parts of neoclassical economics – dealing with the behaviour of individuals and collectives – to come into the picture. In this way most differing aspects of an evolving real world may be tackled. And, to avoid misunderstandings, it should be mentioned that Walras and Marshall will, for ever, remain monuments in the history of economic theory because without knowing about their theories, one cannot understand the meaning and the significance of the twin Keynes–Sraffa revolution. Hence the purpose of the classical–Keynesian synthesis is essentially positive and constructive, nobody is to be excluded; rather, the aim is to gather all the forces required to meet the formidable challenges facing us on a world scale: social problems (poverty and misery), economic issues (employment and distribution), environmental problems and the issue of sustainable development on a world level, and last, but not least, the rebuilding of states.

Before being able to deal in somewhat greater detail with the issue at stake, closing the gap between Keynes and Sraffa, two methodological issues have to be dealt with: first, as already alluded to, the difference between principles and theories, and second, the notion of equilibrium implied in the subsequent analysis.

Principles and theories

Principles and theories imply two entirely different methods to get hold, probably and sketchily, of aspects of socio-economic reality and are associated, broadly and tentatively, with two different but complementary concepts of social science.

In a way, theories are reflections of real-world phenomena; for example, the price of production is a theoretical concept which reflects essential elements of prices calculated within enterprises in the framework of normal cost calculation; as such, the price of production reflects technical conditions of production and the institutional determination of distributional variables such as money wage rates and target rates of profits. Principles, however, represent recreations or reconstitutions of essential elements of phenomena, for example prices, distributional outcomes and employment levels. The questions are: what, fundamentally, determines a price; is it labour or utility? Are the fundamental forces governing distribution social forces, associated with social power, or market forces, i.e. supply and demand? Is employment determined on the labour market or governed by effective demand? Alternatively, regarding value, the question is: what, fundamentally, is a price? What is its nature? And so for all other economic phenomena, distribution, employment and so on. Hence, ‘principles represent the essential elements underlying a certain phenomenon, or the constitutive elements of an object. [Distilling principles requires considering the whole of society and of man], and all information available must be examined, scientific and non-scientific, theoretical and empirical and historical, whereby the objectively given material is dealt with by reason based on a metaphysical vision that, in turn, is associated with intuition’ (Bortis Reference Bortis, Rochon and Rossi2003a, p. 412). In distilling principles, it is crucial to leave aside all accidental elements to put to the fore the constitutive, the essential or the fundamental. Since principles or sets of principles are reconstructions or recreations of essential elements of phenomena, these have not to be realistic in the scientific sense, ‘since they are not reflections or copies (Abbilder) of certain spheres of the real world that can eventually be associated with testable propositions. In their being reconstructions of essential aspects of real world phenomena, principles illuminate these phenomena from inside and initiate the formation of empirically testable theories. In this sense Walras's General Equilibrium Model contributes to understanding how Adam Smith's invisible hand might work in principle. With the Walrasian model in the background the neoclassical economists have built simplified textbook theories of value, distribution and employment upon the marginal principle which is behind all demand and supply curves; in many instances, the Cobb–Douglas production function or Samuelson's surrogate production function are used to elucidate the implications of the marginal principle – the Walrasian model is too complex for an easily understandable exposition of the neoclassical principles and their implications’ (Bortis Reference Bortis, Rochon and Rossi2003a, p. 413). Finally, in Pasinetti's Theory of Value (Pasinetti Reference Pasinetti, Baranzini and Scazzieri1986a), ‘the fundamental differences between exchange-based neoclassical pure theory and production or labour-based classical theory are set forth on the level of principles, illuminating thus the basic options in economic theory open at present. In the following it is suggested that the classical principles ought to be elaborated and to be brought together with Keynes's, adapted to the classical long-period method’ (Bortis Reference Bortis, Rochon and Rossi2003a, p. 415). This, as will be seen, implies bringing together Keynes and Sraffa at the level of principles.

The equilibrium notion

The clue for bringing together Keynes and Sraffa at the level of principles, in a way, to synthesise

Throughout his entire work, Luigi Pasinetti works with the classical method. Principles or fundamental pure theory (Pasinetti Reference Pasinetti1981) and pure theories (Pasinetti Reference Pasinetti1977) tell us how the relevant causal forces work in principle, independently of space and time, that is independent of specific institutions and of specific technological structures. However, principles and theories of the classical type imply a corresponding type of institutional set-up, the classical institutional and technological material basis and the institutional superstructure. To complete the picture we may add that neoclassical/Walrasian pure theory, fundamental and secondary, implies another type of the institutional set-up: the potentially self-regulating market stands in the centre, surrounded by a political, judicial, social and cultural framework.

Nature and man (land and labour), and the social process of production

The starting point is the social process of production, which, basically, may be seen as an interaction between man (labour) and nature (land) by means of real capital, i.e. tools and machines (Bortis Reference Bortis, Rochon and Rossi2003a, pp. 433–436). The nature or land aspect of social production is set out in Pasinetti (Reference Pasinetti1977). Here the (Leontief) inter-industry flows are pictured: primary goods taken from nature and intermediate goods are transformed into final products in a social and, in part, circular process involving production of commodities by means of commodities – and labour (Sraffa). The labour aspect of production is set forth in Pasinetti (Reference Pasinetti1981 and Reference Pasinetti, Baranzini and Scazzieri1986a): direct and indirect labour, in association with past labour embodied in fixed capital, produce the primary, intermediate and final products (Bortis Reference Bortis, Rochon and Rossi2003a, pp. 433–436).

Analytically, the land and labour aspects of the social process of production are linked by the Pasinetti transformation: the vector of direct labour is multiplied by the transposed Leontief-inverse to yield the total (direct and indirect) labour required to produce the various commodities (Bortis Reference Bortis, Rochon and Rossi2003a, p. 438).

Since the i-th row of the Leontief-inverse contains the quantities of each good required directly and indirectly to produce one unit of good i, the i-th element of the n-vector stands for all the labour used directly and indirectly in the whole production system to produce one unit of commodity i. Since production runs from primary through intermediate goods to final goods, there is, evidently, vertical integration, with the final goods summarising all the ‘lower-level’ efforts made to produce them.

Linking the classics with Keynes

The classical (Ricardian) labour model obtained by the Pasinetti transformation determines relative prices and quantities only (Pasinetti Reference Pasinetti1981, p. 23, note 30). To obtain absolute prices, the money wage rate (w) must be fixed; to determine absolute quantities requires fixing the level of employment (N) (Pasinetti Reference Pasinetti1981, pp. 32/33, Pasinetti Reference Pasinetti, Baranzini and Scazzieri1986a, pp. 422/423). Now, in Chapter 4 of the General Theory – ‘The choice of units’ – Keynes states: ‘In dealing with the theory of employment I propose . . . to make use of only two fundamental units of quantity, namely, quantities of money-value and quantities of employment. . . . We shall call the unit in which the quantity of employment is measured the labour-unit; and the money-wage of a labour-unit we shall call the wage-unit’ (Keynes Reference Keynes1973/1936, p. 41). Thus, the labour model emerging from the Pasinetti transformation links the whole body of classical theory to Keynes's employment theory and, as such, closes the gap between Keynes and Sraffa on the level of fundamental pure theory, i.e. on the level of principles. In doing so, Luigi Pasinetti has laid the long-period foundations for classical–Keynesian political economy, which may be considered a synthesis and an elaboration of the post-Keynesian strands of thought. To broadly sketch the classical–Keynesian system is the object of the next section. A central problem is to adapt Keynes's short-period theory of employment to the long run to make it compatible with the classical (Ricardian) theory of value and distribution which focuses on stable or slowly changing magnitudes (institutions and technology) and is, as such, of a long-period nature (Bortis Reference Bortis1997, pp. 142–204, and Bortis Reference Bortis, Rochon and Rossi2003a, pp. 415–423 and 460–467).

Some problems of method

The present remarks on method are linked up with the subsections on principles and theories and on the notion of equilibrium in section 2 above. These issues are now taken up in the context of the classical–Keynesian approach to economic problems.

The preceding remarks suggest that Keynes should not be associated with neoclassical economics (mainly Marshall) as Paul Samuelson has advocated. Indeed, his celebrated Neoclassical Synthesis is based upon Hicks's IS–LM diagram, which reduces Keynes to equilibrium economics. Following Luigi Pasinetti, we want to suggest that Keynes should be linked with classical political economy in a wider sense. Methodologically, this means setting up causal models and combining them subsequently. According to classical political economy, value and distribution are determined within the social and circular process of production. With values and prices of production fixed, Keynes's principle of effective demand would come in to determine quantities. It has been stated time and again that Keynes's theoretical model naturally implies a fix-price theory.

On a fundamental level the labour value principle plays an essential role. After all, in social production, conceived of as an interaction between man (labour) and land (nature), it is man (labour) who plays the crucial (active) role. The basic model must, therefore, be a vertically integrated (Ricardo–Pasinetti) labour model into which a simplified version of the horizontal (inter-industry) Leontief model may be integrated (Bortis Reference Bortis, Rochon and Rossi2003a, pp. 433–445). More sophisticated models picturing the Quesnay–Sraffa–Leontief nature aspect of production may then be grafted upon the basic labour model. Subsequently, classical models may conveniently be combined with Keynesian models. However, there is no need to construct a classical–Keynesian supermodel, since such a model would be completely unmanageable. An all-embracing model is required only at the level of principles, and it is this basic model we are mainly dealing with in the following.

In the spirit of classical political economy of the Ricardian type, we shall consider only the influence of permanent or slowly evolving factors – institutions and technology – upon economic phenomena, mainly prices, the distribution of incomes, employment and involuntary unemployment. Hence the long-period prices and quantities set forth below all depend upon technology and institutions and form, as such, a system equilibrium. Here, the entire socio-economic system enters the picture. This contrasts with the neoclassical market equilibrium, where the legal, social and political institutions are relegated to the framework surrounding the market.

The classical political economists have indeed conceived of society as a system of institutions. There is a material basis with the social process of production at the centre. The surplus emerging from this sector allows a society to build up and maintain an institutional superstructure, political, legal, social and cultural. Classical–Keynesian political economy is about the way in which the institutional and technological system governs the persistent economic phenomena: the fundamental prices rooted in production, the distribution of incomes and the level of employment, and, as a rule, persistent involuntary unemployment.

Now, institutions and technology are precisely facts of the existing situation on which we have little reason for expecting a change or on which the direction of change is broadly known, as is the case with technology where, moreover, changes occur, as a rule, at the margin. Regarding investment, the difference between the normal (satisfactory) rate of profits and the realised rate of profits precisely constitutes a given fact which is very important for investment decisions, and the importance of this fact increases if the difference is larger and more durable (Bortis Reference Bortis1997, pp. 207–214). In a way, then, Keynesian long-period analysis could be called Keynesian Institutionalism, which differs from the traditional system-based, institutionalism of the German Historical School, in the main, by its explicit theoretical foundations.

The output and employment trend may be conceived of as a – hidden – fully adjusted situation characterised by normal prices and quantities and normal degrees of capacity utilisation (Bortis Reference Bortis1997, pp. 75–89, 142–204). Normal or long-period prices and quantities, including investment volumes, depend upon the entire institutional system, i.e. on the material basis and upon the institutional superstructure. This is a crucial point. In the long run, the investment volume represents, like consumption, derived demand, depending upon the evolution of long-period output, with economic activity being set into motion by the autonomous demand components, exports and/or government expenditure.

Hence normal prices and quantities constitute a system equilibrium. Since normal output does not, as a rule, correspond to full employment output, permanent involuntary unemployment obtains. Normal prices are, in turn, governed by the conditions of production and distributional arrangements. The latter implies that normal prices are, in principle, associated with an equal (target) profit rate (r*) which entrepreneurs consider satisfactory and which, therefore, enters their (normal) price calculation.

In the following it is to be suggested how this determination goes on in principle. Dealing with principles means that a model need not reflect reality and, as such, need not lead to testable propositions. As suggested above, a model of principles represents a reconstruction or recreation of what is probably essential to specific real-world phenomena, leaving aside everything which is accidental (Bortis Reference Bortis, Rochon and Rossi2003a, pp. 411 ff.). Principles also contain a normative dimension that, again, points to the fact that models of principles are reconstructions of essential elements of specific real-world phenomena and not reflections. A striking historical example is Walras's General Equilibrium Model, which on the normative side is associated with a Pareto Optimum. This model was elaborated in time of economic crisis – the last quarter of the 19th century. Its purpose is to represent the ideal liberal economy and not the distorted capitalist reality.

In a wider view, the present set of principles is intended to constitute a theoretical alternative to Léon Walras's General Equilibrium Model, i.e. to the neoclassical principles, based upon an elaboration and extension of the (classical) labour model set forth in Pasinetti's (Reference Pasinetti, Baranzini and Scazzieri1986a) Theory of Value: A source of alternative paradigms in economic analysis. This choice has been justified above.

The social process of production as the starting point

The manner

Perhaps we may mention that Sraffa (Reference Sraffa1960) is treated here as a pure nature (inter-industry) model containing nature basics only, i.e. primary goods taken from nature, and as such has been included in the left top corner of our Leontief matrix. The two other types of basic goods, labour basics (necessary consumption goods) and land–labour basics (machine tools producing all capital goods), are included among the final goods. In fact, in Sraffa (Reference Sraffa1960), all three types of basic goods appear which, as will be suggested at the end of the next section, renders the treatment of value and distribution and the link with Keynesian employment models rather difficult.

Production, value and distribution

To deal with the principles (or fundamentals or essentials) of value and distribution within the immensely complex social and circular process of production sketched in the previous section, all accidental elements have to be left aside. In this vein, two simplifying assumptions are made, which, when given up, leave all the conclusions following from the principles qualitatively intact when the analysis moves to the level of theories reflecting aspects of the real world. First, a vertically integrated economy is considered, and second, the conditions of production are similar in all the sectors of production in the sense that the relationship between total labour – direct and indirect – contained in some capital good used to produce some commodity i and the total labour embodied in this commodity – n_iK/n_i – is the same in all the sectors of production (consumption goods, capital goods, intermediate and primary goods). The heterogeneity of the goods is ensured by two factors: in the first place, the absolute values of n_iK and n_i diverge between the various sectors; and second, the same quantity of abstract labour is contained in qualitatively very different goods.

From these assumptions the labour principle of value emerges together with the surplus principle of distribution involving a uniform rate of profits. Both principles are put to practical use here in a broad humanist–ethical sense, not in the sense of class struggle (which, however, may arise if there is large-scale alienation, brought about by mass unemployment, for example).

In the sense of the classical political economists, but also of Aristotle and of Thomas Aquinas, the value of goods and services is, in principle, determined by the ‘quantity of direct and indirect labour’ contained in them. This quantity is, in turn, determined by three factors: first, by labour time; second, by the reduction coefficients, which reduce complex labour to simple labour – the reduction coefficients are expressed in the wages structure, the determination of which is a complex problem of social ethics and should be essentially based on an evaluation of work places; third, on the social appreciation of a product.

Distribution on the basis of the surplus principle is a complex social process. First, the great shares in income must be determined, i.e. the shares of (normal or ordinary) wages, made up of necessary and of surplus wages, and the surplus proper, made up of profits and rents. Profits are socially necessary to run the production system, i.e. the enterprises; they represent, very broadly speaking, an award for good management, investible funds, and render possible the setting up of sinking funds in view of an uncertain future (see Bortis Reference Bortis1997, pp. 158–175). Rents, in turn, are made up of land and labour rents. The latter are equivalent to surplus wages due to special abilities or privileges, e.g. of managers, engineers, surgeons, artisans, artists, sportsmen and so on. Second, the structure of necessary and surplus wages (normal or ordinary wages), surplus wages due to special abilities and privileges, and of profits and rents has to be broadly determined. Most important is the determination of the structure of ordinary and surplus wages, a task to be performed, possibly in an indicative way, through work evaluation inside the enterprises and through trade unions between industries and sectors. In a classical vein, the market would have to bring into line market wage and profit rates, and land rents into line with the socially determined magnitudes through changing output levels. All in all, distribution emerges thus as the core issue of social ethics.

The surplus produced in the ‘profit sector’ (the ‘productive’ sector of the classics) of an economy should be used to build up a socially appropriate, ‘non-profit’ sector (the ‘unproductive’ sector in classical terminology) in the widest sense of the word, comprising political, legal, social and cultural institutions. As such, the surplus is obviously socially necessary since it is required to build up an institutional superstructure upon the material basis. Hence, the surplus, if used in an appropriate way, leads to a good and proper functioning of society at large, including the material basis that produces the social surplus.

Inappropriate uses of the surplus lead to social and individual alienation: the distribution of incomes and wealth may become very unequal and involuntary (system-determined) mass unemployment may develop as a consequence; both lead, as a rule, to social exclusion, misery and an increasing number of crimes; terrorism, too, has deep roots in misery and despair. Hence, the production, extraction, distribution and use of the surplus is the most important problem of social and political ethics (Harcourt Reference Harcourt and Hamouda1986, p.5).

Value and distribution are regulated within or in direct association with the social process of production.

The price equations in a vertically integrated production system are as follows:

(1)

A is the broadly triangular Leontief–Sraffa matrix sketched above (see also Bortis Reference Bortis, Rochon and Rossi2003a, pp. 433–36). The coefficients of the matrix A

(2)

indicate the quantity of good i required to produce a unit of good j. p is the (row) vector of prices. At first, there are the prices of primary goods (land basics), subsequently the prices of intermediate goods and, finally, the prices of final goods.

Hence pA represents the monetary value of the basic and intermediate goods (the monetary value of inputs) utilised in the social process of production for each good (primary, intermediate and final). The expression

(3)

represents value added and its distribution between wages and profits (and rents). n_d is the (row) vector of direct labour per unit of each product (primary, intermediate and final goods). w_n (a scalar) represents the money wage rate per unit of simple, unqualified labour (with complex types of labour, qualified in most varying degrees, being multiples of simple labour). The scalar k is the ‘mark-up’ on average costs at normal capacity utilisation. In a microeconomic view, k governs gross profits such that invested fixed capital gets a normal rate of profits r* including the rate of depreciation. In a wider, macroeconomic, view, k may be reinterpreted to contain, in addition to gross profits, surplus wages, labour rents, due to specific abilities or privileges, for example, and land rents. Hence the microeconomic ‘mark-up’ is, on the macroeconomic level, transformed into the ‘surplus coefficient’, governing, in principle, the size of the social surplus over socially necessary wages.

Methodologically speaking, the present analysis is situated at the level of principles. Consequently, the relevant causal forces are presented in their pure form, independently of their historical realisations (Keynes' pure and applied theory). Moreover, we consider only what is essential to our analysis. In this sense, labour values constitute the essence of prices. This implies abstracting from specific conditions of production and from market conditions, and supposes a vertically integrated economy. Past labour is embodied in fixed capital.

The fundamental prices (Equations 4–7 below) emerge from the social process of production and represent, in principle, the social effort that has been made to produce the various goods; hence, in a classical–Keynesian view, prices of produced goods are not scarcity indicators. In fact, at the level of principles, direct and indirect labour is basic to the value of goods and services.

As has already been suggested, distribution is, essentially and ideally, a social process with trade unions, entrepreneurial associations and the state intervening to bring about as much distributional justice as is humanly possible (in present economic reality, however, the single worker or employee is frequently directly faced with the entrepreneur). The links existing between value and distribution at the level of principles emerge formally from isolating the price vector in Equation (1) on the left-hand side (see Bortis Reference Bortis, Rochon and Rossi2003a, pp. 436–445):

(4)

This operation, which links the nature (land or inter-industry) model to the vertically integrated labour model, might be called the Pasinetti transformation (Pasinetti Reference Pasinetti1981, pp. 109–112). Multiplying the (column) vector of direct labour, n_d, with the rows of the transposed Leontief inverse yields the vector of total – direct and indirect – labour (n) required to produce some good i:

(5)

Inserting relation (5) into Equation (4) and multiplying the capital good row for each good by a coefficient so as to make the ratio n_iK/n_i equal to unity for all goods (Bortis Reference Bortis, Rochon and Rossi2003a, p. 438) yields the classical – Ricardo–Pasinetti – price equations:

(6)

which can be interpreted sectorially (p and n as vectors) or macroeconomically (p and n as scalars).

Specifying the mark-up, k yields a simplified price equation for all goods:

(7)

The macroeconomic equivalent of these equations is the Kalecki–Weintraub price equation:

(8)

Since the mark-up k must equal the expression within square brackets in (7) for equal conditions of production in all sectors (n_iK/n_i is the same everywhere, to simplify equal to unity as is argued in Bortis Reference Bortis, Rochon and Rossi2003a, p. 443, rel. 19.16), we get – on the macroeconomic level – the following relations for the mark-up k and the wage share 1/k if the surplus consists of profit only:

(9)

and

(10)

Both relations imply that all economic values are created by the workers and employees in the profit sector (the classical productive sector).

From a distributional perspective, the social surplus may, as already suggested, be interpreted in a wider, macroeconomic sense, to include gross profits, surplus wages over socially necessary wages, labour rents as are due to exceptional abilities or privileges, land rents and profits. The use of the social surplus, ideally, provides the material basis for all the persons active in the non-profit sector in the widest sense, including the state, to create political, social, legal and cultural values through the actions of individuals and collectives within the institutions established in the institutional superstructure. These values cannot, in principle, be measured in money terms. Highly unequal distributions of the surplus and the ensuing inappropriate use of the social surplus are, as a rule, associated with alienated social states of affairs.

The Equations (6–8) capture the essentials of classical (Ricardian–Pasinettian) price theory: the prices of produced goods reflect the social effort undertaken to produce them in terms of direct and indirect labour; distribution, based upon the surplus principle, is a complex social process.

Proportions and scale: classical and Keynesian macroeconomics – monetary theory of production

In a classical–Keynesian view, the social process of production is at the centre of a monetary production economy. Distribution – the shares of wages, profits and rents in domestic income and the structure of wages, profits and rents – gives rise to specific proportions, that is part–whole relationships. Relative prices and quantities, and the distribution of labour between sectors and industries, are also proportions. These proportions and their explanation are at the heart of classical political economy, which deals also with the circulation of goods and money. The breadth of the circuit, or the scale of economic activity, is the object of Keynesian political economy. The next two sections deal with the proportions and the scale aspect respectively.

The synthesis of the proportions aspect and of the scale aspect yields a classical–Keynesian political economy, i.e. a monetary theory of production, where money is all-important to run the economy, since money always buys goods and never goods buy other goods, and where, as a consequence, the real and the financial sector are inextricably linked:

(11)

Entrepreneurs have money and finance (M) at their disposal to buy means of production (raw materials and intermediate goods, machinery) and to hire labour (C). Within the social process of production P, labour, using machines, transforms the primary and intermediate goods into final goods C′. These are sold on the final goods markets for money M′, which represents effective (monetary) demand for goods and services.

The proportions aspect of classical–Keynesian political economy

In this section, all equations are based upon Pasinetti's seminal Theory of Value (Reference Pasinetti, Baranzini and Scazzieri1986a) and slightly elaborated.

The price system (12) depicts monetary flows and has several aspects which are considered in turn: first, there is the formation of prices; second, the formation of incomes and their distribution is suggested; and third, there is the spending of income by private households, enterprises and the state:

(12)

In this equation system the c_i are fractions of real income – in terms of (full employment) labour embodied N_f – spent on good i (13), or demand coefficients per labour unit (13a):

(13)

(13a)

The formation of absolute prices within the social process of production can take place only once the distributional variables are determined, i.e. the money wage rate w_n of some labour unit, and the mark-up k, including the uniform target profit rate (r); as mentioned above, the labour unit could, for example, consist of simple, unqualified labour with qualified labour as multiples – reduction coefficients – of unqualified labour; obviously, the reduction coefficients have a wide normative dimension, associated with distributive justice. One must sharply distinguish between actually existing, normal, and natural, normative or socially desirable reduction coefficients. On the level of principles, the natural is, in fact, the normative form of the normal.

The (absolute) prices (Equation 14) represent the money value of the social effort to produce the individual goods within the social process of production. These prices result from multiplying the first m–1 rows in the above matrix with the price and income vector.

(14)

The A_i represents sectorial labour productivities.

The formation of absolute prices is intimately linked to the formation of incomes and its distribution. The price Equation (14), in fact, implies that the money value of sectoral outputs equals the sectoral incomes in money terms. However, this second aspect of the system (12) also implies, as will be seen below, that this system determines relative prices only. This means that distribution is a problem of proportions. In fact, proportions associated with the social effort to produce goods are intimately related to distributive justice, first, through the reduction coefficients governing the wages structure, as emerges most clearly through relative prices:

(15)

and second, through the distributional relationships governing the wages share and the ‘property share’, or, in a wider social view, the ‘surplus share’, which would also include surplus wages:

(16)

Third, the spending of incomes by households, enterprises, non-profit organisations and the state is pictured by the last equation in the equation system (12):

(17)

The economic meaning of this relation emerges more clearly if account is taken of the spending coefficients defined as demand per profit-sector labour unit (relation 13a above):

(18)

Taking account of the price Equation (14) in relation (18), we get the definitions

(19)

(19a)

From these relations immediately follows

(20)

To recall, N_i is total – direct and indirect – labour used to produce good i, N_f is the full employment labour force in the productive sector of an economy.

Definition (20) indicates the distribution of the profit-sector labour force within an economy, which represents a most important proportion in a monetary production economy. Indeed, the distribution of economically productive labour depends upon the way in which incomes are spent, if labour productivity is given; in fact, definition (20) has been derived from relation (17). In turn, the way of spending incomes depends heavily upon income distribution.

The quantity system

(21)

informs us, first, about the demand for and the circulation of goods (the first m lines of the matrix are multiplied by the quantity vector):

second, about the production and the supply of goods:

(22)

and third, about the ‘macroeconomic equilibrium of demand and supply’:

(23)

Relations (22) and (23) obtain from multiplying the last line in the above matrix by the quantity vector. In relation (23) supply is on the left-hand side; demand appears in the form of ‘real’ income (labour time) on the right-hand side of this equation.

Relation (22) implies that in a social production (or labour) economy, technical progress is always labour saving: less direct and indirect labour is required to produce a certain good. This renders possible an increase in money wages, with prices and mark-ups given, or enables the cheapening of production, given money wages and mark-ups, or the realisation of higher profit rates (an increase in the mark-up).

The determinant of the price system (12) and of quantity system (21) is given by the following expression (Pasinetti Reference Pasinetti, Baranzini and Scazzieri1986a, p. 422, relation 16):

(24)

Taking account of the definition of the demand coefficients c_i (relation 13a) and of the labour (production) coefficients n_i (relation 22) yields, again, an expression picturing the sectorial distribution of profit-sector labour:

(25)

These relations tell us that the distribution of direct and indirect labour among the various sectors of an economy, as indicated by definition (25), is governed by two elements (relation 24): first, the size of the demand for the different goods (c_i), and second, the quantity of labour required to produce a unit of some good (n_i). Both relations, (24) and (25), thus express fundamental proportions prevailing in any monetary production economy.

The fact that the determinant of the coefficients matrix of the systems (12) and (21) is zero (relation 24) has important economic implications. This condition guarantees economically meaningful solutions for the equation systems (12) and (21), that is, positive prices and quantities. In fact, in both equation systems the last equation is not independent of the other equations. This implies that only relative prices and quantities, p_i/p_j and Q_if/Q_jf, are determined.

As has already been suggested, absolute prices are determined once distribution is regulated: the level of money wages w_n and the normal rate of profits implied in the mark-up k must be fixed in advance. This goes on through complex social processes. Hence, in principle, distribution ought to be determined before production can start. In a way, distribution is the primary and fundamental problem in political economy (Ricardo 1951, p. v).

Absolute quantities are determined once the level of employment (N) is given. Until now we have postulated the ideal case, i.e. full employment (N_f). In the next section, the determination of the long-period level of employment, governed by persistent factors, i.e. technology and institutions, will be considered. This amounts to looking for the factors governing the breadth of the economic circuit or the scale of economic activity in the long term.

The scale aspect of classical–Keynesian political economy

The scale of long-period economic activity is governed by long-period effective demand, which depends, in turn, upon the institutional and technological system, made up of the material basis and of the institutional superstructure, i.e. upon the socio-economic structure. Institutions partly determine behaviour through formal and material restrictions, as is the case with social institutions such as enterprises, associations, state administration, the legal system or ‘individualistic’ institutions, consumption habits, for example (on this see Bortis Reference Bortis1997, Chapters 2, 3 and 4). The long-period or trend level of domestic output may get established well below full employment, thus giving rise to permanent long-term involuntary unemployment. The existence of persistent involuntary unemployment is empirically well founded. For example, from the early 1980s onwards the trend unemployment rate was about 12 per cent in France and 10 per cent in Germany.

Formally, involuntary unemployment as determined by the socio-economic system is represented by the definitions (26–29) below – u is the rate of unemployment (26) and 1 – u is the rate of employment (27). Now, the quantity vector in system (21) must be multiplied by the coefficient 1 – u to obtain a new quantity vector (28) with the level of employment N lower than the full employment level N_f(29). Hence the coefficient 1 – u could be termed the employment scalar.

(26)

(27)

(28)

(29)

Definitions (28) and (29) imply that the structure of final output does not change as the level of employment varies. This, of course, is valid only as long as principles – independent of space and time – are considered. Considering principles enables us to separate the analysis of the pure (classical) proportions model (previous section) and the pure (Keynesian) scale model. In the real world (of phenomena) structures (proportions) will, of course, change as the level of employment or the scale of economic activity varies.

In definition (30) total supply equals total demand, whereby demand governs supply. Supply is given by the gross domestic product Q, which equals labour productivity A times employment in the profit sector N. The real wage rate is w = w_n/p, that is, the money wage rate w_n divided by the money price of a bundle of necessary consumption goods p. Normal wages wN are supposed to be entirely consumed. The surplus is made up of profits P and of land and labour rents R, with labour rents accruing on account of special abilities and dispositions; c_s is the fraction of the surplus (privately) consumed. I is gross investment, G state expenditures, π stands for the terms of trade [X/M = (ep_M)/p_X], p_X represents export prices in domestic currency, p_M import prices in foreign currency, e is the exchange rate, and X and M are export and import quantities respectively.

(30)

Imports M as a fraction b of GDP or domestic income Q = Y are of two kinds. Necessary imports M₁ = b₁Q (raw materials, necessary consumption goods, machines to produce necessaries) are related to production, while non-necessary imports M₂ = b₂Q are related to consumption out of the surplus.

(31)

In the price equation

(32)

the mark-up k governs the size of the surplus.

Distribution, i.e. the division of domestic income into ordinary or normal wages and the surplus (profits, land rents and labour (ability) rents) and the structure of normal wages, profits, land and labour rents, is a social ethical issue of immense complexity associated with the issue of distributive justice:

(33)

In the long run, the volume of gross investment I is governed by trend GDP (Q) and its evolution, with Q, in turn, being determined by the whole socio-economic-cum-technological structure. (The single investment project depends, however, on more or less certain expectations about the future.)

(34)

(v = K/Q is the capital coefficient.)

Hence the long-period volume of gross investment I represents derived or induced demand; only the capacity effect of investment is taken into account in a situation in which overall long-period effective demand equals long-term aggregate supply.

Net trend investment (gK) is governed by the long-period or trend growth rate g of the autonomous variables, G and X (see for some implications Bortis Reference Bortis1997, pp. 155–75, 204–220). ‘Replacement’ investment (dK) depends on the depreciation ratio d, that is, the fraction of the total capital stock to be replaced for physical, economic and technological reasons. The coefficient d indicates, therefore, the extent of the technical dynamism of the entrepreneurs in the sense of Schumpeter, i.e. regarding the introduction of new techniques of production and of new products.

Saving (private and state saving, t being the tax rate)

(35)

adjusts to investment through changes in output. This is particularly evident if we consider ratios:

(36)

Given an equilibrium of the balance on current account, a higher output can be achieved only if government expenditure increases, or, if private consumption increases, because of a decline in the saving/income ratio s or in the tax/income ratio t. Government expenditures (or exports) are of particular importance because they set economic activity into motion. The level of government expenditures G greatly contributes to determining the scale of economic activity. This is evident from our basic relation, the supermultiplier relation, which can be derived from Equations (30) to (34).

(37)

(38)

Relation (37), the supermultiplier relation, shows how output Q and employment N are governed in principle. Hence this relation represents the pure theory of output and employment in a monetary production economy.

Definition (38) represents the leakage coefficient z_s, which indicates the fraction of the surplus over ordinary wages that is not consumed, the fraction consumed being c_s. Consequently, the leakage coefficient is the sum of the fractions of the surplus paid for taxes (t_s) and saved (s_s). Since the long-period consumption coefficient c_s and the long-period tax coefficient t_s are both determined by institutions – consumption habits and tax laws – the long-period saving propensity s_s is a pure residual varying with the normal level of output and employment, given the rate of profits as is implied in the mark-up (Bortis Reference Bortis1997, pp. 166–168). This is perfectly analogous to Keynes's short-period theory of saving but different from the Pasinetti equation where, given the level of employment, the savings propensity of the capitalists and the rate of growth determine the rate of profits in a Keynesian Treatise on Money way (see again Bortis Reference Bortis1997, pp. 166–168).

Following Hicks, Equation (37) may conveniently be called a supermultiplier relation ‘which can be applied to any given level of [autonomous demand components] to discover the equilibrium level of output [Q] which corresponds to it’ (Hicks 1950, p. 62). Hence the autonomous demand components, G and X, set economic activity in motion, similarly to the expenditure of rents by the landlords in Quesnay's extended tableau économique (on this see Oncken Reference Oncken1902, p. 394).

Once output and employment are determined through the supermultiplier relation (37), the output and employment scalar 1−u (definition 27) is also fixed. In principle, the normal quantities corresponding to a specific output and employment level obtain if the full employment quantity vector in the quantity system (21) is multiplied by the employment scalar. The determination of normal output and employment is equivalent to fixing the output and employment trend around which cyclical fluctuations occur (Bortis Reference Bortis1997, pp. 149–151). It has already been suggested that the position of the output and employment trend is of considerable socio-economic and political importance because this determines the extent of long-period – system governed – permanent involuntary unemployment. The latter is, in turn, an important element governing the social and political climate in a country.

Methodologically speaking, the supermultiplier relation (37) represents, as suggested already, the pure long-period Keynesian employment theory, picturing how output and employment are determined in principle by the various demand variables and parameters on the right-hand side of this equation (Bortis Reference Bortis1997, pp. 142–204). In a way, this relation is a metatheory – a metaphysical theory – of employment to determine what is – probably – essential about employment determination in a monetary production economy (see on this the methodological introduction in Bortis Reference Bortis, Rochon and Rossi2003a, pp. 411–415). Determination in principle of some socio-economic phenomenon attempts to capture the essential features of the causal mechanism at work, which are timeless and invariable. Moreover, in a pure or ‘ideal-type’ model, the ceteris paribus clause is automatically implied, which is to say that the predetermined variables on the right-hand side of the supermultiplier relation (37) are considered independent of each other. This, as a rule, will not be the case if some real-world situation is considered.

In principle, normal output Q, and hence trend employment N, are positively linked to the autonomous variables G and X, and to the gross investment–output ratio I/Q = (g + d)v. This ratio depends on the rate of growth of the autonomous variables (G + X), g, which is also the rate of growth of long-period or normal output and employment, and upon the replacement coefficient d. In an open economy, the rate of growth of exports is crucial, as Nicholas Kaldor has always insisted upon (see on this Bortis Reference Bortis1997, pp. 155–156, 185–189, 190–198). The (Schumpeterian) d is an indicator of the technical dynamism of entrepreneurs. The effect of exports (X) on output and employment will be particularly strong if exports consist mainly of high-quality manufactured products with a large value added, i.e. a high content of direct and indirect labour (Kaldor Reference Kaldor1985, pp. 57–79). However, normal output will be lower if, given exports X, the technological and cultural dependence on the outside world is strong, as would be reflected in large import coefficients b₁ and b₂, and if the terms of trade (π) are unfavourable, which would show up in a high value of π. Very importantly, normal output (Q) is negatively linked with the property share in income, 1–(1/k), and with the leakage coefficient, z_s, associated with this share; as a rule, z_s will be larger if the distribution of property income is more unequal. Given government expenditures and gross investment, a higher leakage out of income (z_s[1–(1/k)]) reduces effective demand because consumption is diminished. Fundamentally, unemployment occurs because the saving–income ratio, s_s [1–(1/k)], exceeds the investment–output ratio, (g+d)v, at full employment. Full employment could be maintained only if private and/or public consumption were increased. A redistribution of incomes, i.e. raising the share of normal wages (1/k), would lead to higher private consumption through enhancing spending power. In principle, a higher level of public expenditures, G, would require a tax increase: the tax rate, t_s, would have to be raised to preserve budget equilibrium, which would reduce the saving coefficient s_s. If these measures are not undertaken, output, employment and tax receipts will decline and, given government expenditures, budget deficits will occur. These will reduce the saving ratio until it equals the investment ratio at some long-period equilibrium level of output and employment involving persistent involuntary unemployment. Hence the negative association between distribution and employment emerges, because the property share and the saving and the leakage ratio associated with it are too high; and s_s and thus z_s will be the higher the more unequally property income is distributed. Thus, the notion of unequal income distribution has a double dimension: the property share is high, and property income is itself unequally distributed. This leads to a high leakage out of income, given by z_s[1 – (1/k)] to which corresponds a reduced level of output and employment.

This crucial relationship between unequal distribution and involuntary unemployment represents, according to Schumpeter, the essence of the Keynesian Revolution: ‘[The Keynesian doctrine] can easily be made to say both that “who tries to save destroys real capital” and that, via saving, “the unequal distribution of income is the ultimate cause of unemployment.” This is what the Keynesian Revolution amounts to’ (Schumpeter 1946, p. 517). Indeed, Keynes held that the ‘outstanding faults of the economic society in which we live are its failure to provide for full employment and its arbitrary and inequitable distribution of wealth and incomes. [Up] to the point where full employment prevails, the growth of capital depends not at all on a low propensity to consume but is, on the contrary, held back by it [and] measures for the redistribution of incomes in a way likely to raise the propensity to consume may prove positively favourable to the growth of capital’ (Keynes 1936, pp. 372–373; on this see alsoGaregnani Reference Garegnani1978/79). The inverse long-period link between employment and distribution is the crucial feature of the supermultiplier relation. On the empirical level, Galbraith and Berner (Reference Galbraith and Berner2001) represents an important effort to deal comprehensively, in a Keynesian spirit, with inequality, unemployment and development on a global level.

Links with Keynesian and post-Keynesian political economy – the classical–Keynesian synthesis

The preceding sections deal with principles, that is, with the fundamental forces governing prices and quantities in a classical–Keynesian view. As such, these sections exhibit aspects of the pure long-period classical–Keynesian model of production, value, distribution and employment, and as such picture the functioning of the socio-economic system. The technical–institutional system partly determines the behaviour of individuals and collectives because the system imposes restrictions upon behaviour.

For example, through the supermultiplier relation the system sets a restriction to all workers and employees: no more than (1−u)100 per cent of the workforce can find a job (definition 27 and relation 37); however, who will be employed or unemployed depends on the behaviour of the various individuals. In the medium and the short run, behaviour of economic agents takes place within the – institutional – system, thus giving rise to specific behavioural outcomes that differ from the system outcomes (Bortis Reference Bortis1997, pp. 83–117). The issue of institutions and behaviour is, in fact, a central tenet in Bortis (Reference Bortis1997).

Post-Keynesianism prominently deals with the behaviour of consumers and producers in the medium term, whereby behaviour is coordinated by the system, represented by effective demand. A significant example of this interaction is the double-sided relationship between profits and investment (Joan Robinson, Michal Kalecki): profits influence investment behaviour, and the level of investment governs profits. This gives rise to a theory of employment determination in the medium term, in fact, in the course of cyclical growth, with the income effect and the capacity effect of investment interacting (Bortis Reference Bortis1997, pp. 204–220). The cyclical variations of output and employment may go along with a specific ‘pricing in the business cycle’. The domain of Keynesians is the determination of economic activity in the short term, where productive capacities are given and only the income effect of investment is relevant. Here, each investment project is associated with uncertainty and expectations, which, as a consequence, govern the short-period volume of investment, in contrast to the long-period investment volume, which is determined by the evolution of trend output and hence by the entire technical and institutional system. Finally, money and finance can be brought into the picture without any difficulty, starting, for example, from the concepts of industrial circulation and financial circulation in Keynes's Treatise on Money (Volume I, Chapter 15) and the whole of the General Theory (for a broad sketch see Bortis Reference Bortis1997, pp. 220–235). Hence classical–Keynesian political economy appears as a synthesis, an elaboration and an extension of Keynesian and post-Keynesian political economy.

From the theory of wants to utility theory

Indifference curves and utility analysis rest on a very specific understanding of rationality and of consumer sovereignty. This is the source of many analytical problems, most fundamentally the relationship between observed variables, such as prices, income and demand, and unobserved variables, such as preferences. These analytical difficulties are only one aspect of the inadequacy of traditional consumer theory to guide the analysis of consumer behavior. As observed by Zamagni (Reference Zamagni1986), consumer theory has a specific analytical purpose that reflects the role of demand in the Neoclassical theory of value. Indeed, we are not dealing with an attempt to analyze the consumer and consumption patterns (Gualerzi, Reference Gualerzi and Bianchi1998) but rather with an analytical apparatus necessary to derive demand curves with the desired properties, so that they can concur with supply curves to determine equilibrium prices.

For the present purposes it is of great interest to note that, as pointed out by Lancaster (Reference Lancaster1966) and Ironmonger (Reference Ironmonger1972), the approach based on utility maximization is a shift away from the notion of wants one finds in early marginalism. In the transition from the original focus on wants to the concept of diminishing marginal utility in Marshall, the discontinuity in the satisfaction of needs was lost. Discontinuity is indispensable in considering an order in the satisfaction of needs, which is the characteristic of lexicographic models. The attempts by Lancaster and Ironmonger to improve consumer theory rest indeed on the discontinuity of wants.

Characteristics and the consumption technology

Responding to one of the most serious limits of the theory, Kevin Lancaster's characteristic model (Reference Lancaster1966, Reference Lancaster1971) addresses the question of product innovation and differentiation. New products redefine continuously the domain of consumers' choice. In the traditional approach, ‘any change in any property of any good implies that we have a new preference pattern for every individual’ (Reference Lancaster1971, p. 4). It follows that ‘we can do only two things: (i) ignore the changes, and proceed as if the new variant is the same good as before or (ii) regard the variant as an entirely new good, throwing out any information concerning demand behavior with respect to the original variant, and start from scratch’ (p. 8).

This is so because utility indexes are associated directly to goods rather than to the ‘characteristics’ that make these goods the object of ‘wants.’ This has an important consequence. In early marginalism, especially in Menger, one can find the basis of ‘the consumption technology approach’ and of ‘the diet problem’ (pp. 9, 146). Hicks, Lancaster notes, drew explicitly the analogy with the entrepreneur choosing means to satisfy objectives, but abandoned the approach because of its ‘technical difficulties.’

Characteristics are the objective properties, the common substance in otherwise different goods. It is what makes them valuable in their capacity to respond to wants. Therefore ‘the relationship between people and things’ is a ‘two-stage affair. It is composed of the relationship between things and their characteristics (objective and technical) and the relationship between characteristics and people (personal, involving individual preferences)’ (p. 7). Lancaster's objective is to put the ‘characteristics model’ at the core of demand theory, and show that ‘product variations and new goods fit easily and naturally’ (p. 10).

A linear consumption technology expresses the relationship between the characteristics vector and the goods vector and transforms the characteristics space into the goods space. Given prices, a good becomes part of the consumption basket if it lies on the efficiency frontier. Thus, traditional analysis appears as a special case of this more general approach, one in which ‘the number of goods and characteristics is equal and the efficiency surface consists of a single facet’ (p. 50). As in the case of goods, consumption of characteristics is proportional to income for all consumers with the same preference parameters. Given these parameters and income distribution, aggregate consumption will depend on the preference distribution.

‘Operational use of the model requires identification of the relevant characteristics and data of the consumption technology. Neither of these requirements is yet easily met, partly because of the conceptual problems in identifying relevant characteristics and partly because the appropriate data have not hitherto been available’ (p. 113). For one thing, characteristics should be less than products, in order to have an advantage for the analysis of product innovation and differentiation. A priori criteria and the effects of satiation and dominance, both implied by the notion of hierarchy of wants, are the foundation for such identification, which is ultimately corroborated by a ‘revealed relevance’ analysis based on empirical study of markets. An intermediate step is ‘group analysis,’ intended to define the boundaries within which substitution effects are likely to be strong. This is important because ‘our model of demand behavior is . . . a “fine structure” model, designed to explain market behavior with respect to goods defined in a very narrow sense . . . this means that we are concerned with the spectrum of varieties or models within a broadly defined market, not with such aggregates as “food” or “automobiles” . . . At the same time the consumer is facing a consumption technology in which any specific characteristic might be obtained from any good’ (pp. 115–116).²

The consumption technology approach is grounded on goods' characteristic. The latter is ‘an objective, universal property of the good (or activity)’ so that ‘personal reactions are reactions to the characteristic, not reactions about what the characteristic is’ (p. 114). The ‘objective’ link characteristic–things allows for the identification of the consumption technology data. Assuming that there is enough information to identify characteristics, using the criteria mentioned earlier, we can infer individual preferences, the things–people relationship, based on what can be called a ‘revealed relevance’ mechanism: the market response will establish whether ‘consumers appear to react to these characteristics or not’ (p. 157).

The result is reformulating consumer choice as a linear programming problem. This approach has two major advantages. The first is ‘being able to sail through the otherwise dangerous problems concerning new goods, model changes, and so on.’ But more importantly it can ‘take account of such things as negative effects and interactions,’ which have implications for the evaluation of cost and benefit.

New commodities

Ironmonger (Reference Ironmonger1972) also takes the question of new commodities and quality changes as a starting point for a re-examination of consumer theory.³ His approach is centered on a consumption technology intended to satisfy ‘various separate wants,’ leading to the choice of an ‘optimum budget . . . (which) is found to be a solution of a linear programming problem’ (p. 12). There are some distinguishing elements that make this contribution more interesting for a theory of the evolution of consumer demand and innovation, be it the recognition of satiation effects, but most important, elaborating an independent role of new products in determining consumer demand.

Ironmonger's analysis rests not on characteristics but rather on wants separability. Wants arise from physiological and psychological needs. They are the object of satisfaction, rather than ‘a single desire, happiness or utility’ on which traditional theory has focused. Marshall, acknowledging the work of Menger, Jevons, and others, introduced wants and desires into economic theory. He then developed the notion of diminishing marginal utility in relation to satiable wants. Ironmonger observes that ‘with the mathematical development of the theory of consumer behavior, stemming from the work of Pareto and Fisher in the 1890s, and in the 1930s associated with the work of Hicks and Allen and the rediscovery of the work of Slutsky, the distinction (with separable wants) was dropped completely and commodities were invariably regarded as satisfying a single want’ (p. 11), i.e. utility. This, as Richard Stone points out in the book's foreword, ‘leads him to emphasize discreteness and discontinuities, which can best be handled by programming methods.’ The existence of separate wants ‘is particularly relevant from the point of view of technical change in the commodities entering into the consumption process’ (p. 13).

The objective is not simply incorporating the characteristics of new commodities into rational choice but examining how they define this choice. ‘New commodities and quality changes in commodities can be brought out of the pond of consumer tastes so that tastes can provide a more constant frame of reference than before’ (p. 13). The static nature of consumer theory is contained in the assumption that tastes are constant. But even without changes in the factors customarily taken to determine taste, such as age, sex, occupation, marital status, the ‘number and nature of commodities are constantly changing’ (p. 12). Ironmonger concludes that it seems desirable to have a theory which distinguishes between these two aspects.

New commodities add a dimension, independent from taste, income and prices, to the determination of consumer choice, which is pursued with the analysis of diffusion processes. The study of diffusion paths leads to new possibilities of empirical testing. Analyzing group behavior, it is possible to formulate hypotheses about the form of the diffusion curve, providing a picture of the relationship between new commodities and market demand; in the same way aggregation is used to identify the patterns of change for income levels (satiation) and prices. Ironmonger's contribution then focuses on the empirical study of demand. The diffusion processes are used to distinguish the effects of new products from those of the variables customarily taken into account in demand analysis, income and prices. He notes that ‘there have been only a few explicit studies of the phenomenon of diffusion following introduction. In general, the main demand studies have steered away from these commodities’ (p. 130).

Still, the consumption technology, and the optimization procedure associated with it, do not take us beyond comparative statics results. Although opening the way to consider wants, new commodities and social acceptability of evolving forms of satisfaction, the approach must ultimately make reference to wants and preferences as something given to the analysis. This is the problem with exogenous preferences – they make it possible and plausible to analyze consumers' choice independently from the economic process.

Structural dynamics and capabilities

An interesting way to look at Pasinetti's search for a dynamic theory of consumption is to consider structural dynamics in light of the approach based on capabilities presented by Amartya Sen. Interestingly, also Sen's theory of human capabilities follows from a dynamic perspective, that of development.

Sen is another critic of traditional consumer theory, the theory of the ‘rational fools’ (Reference Sen and Sen1977). He has pointed out that continuity of preferences is indispensable for the principle of substitution. However, once we abandon the example of trading apples for oranges and instead consider life styles, alternative systems of preferences individuals evaluate and choose from, the plausibility of the continuity assumption becomes far less obvious. He has also observed (1985) that preferences refer not to needs but rather to goods in the market, which are defined in a market economy by other economic agents. Moreover, needs can be satisfied by different types of goods, in different consumption forms (individual, family, social). It follows that there is a discrepancy between preferences and needs.⁴

The notion of ‘subject capability’ refers to what can be accomplished with the goods available. Though goods' characteristics are distinct from capability, the latter accounts for the result obtained in terms of need satisfaction. In more general terms, rather than in the sense of axiomatic maximization, rationality can be redefined as systematic exploitation of information and reasoning.

The relationship between Pasinetti's structural dynamics and Sen's capabilities approach is discussed by Walsh within a larger account of the developments of classical theory (Reference Walsh2003). Walsh quotes Pasinetti to stress how the question of change is at the center of the approach.⁵ ‘In the sense in which there can be said to be “equilibrium-” in his model, it is a continually changing equilibrium . . . the assumption of balanced technical progress plus the uniform expansion of demand “are not only unlikely, they are impossible” (Pasinetti, Reference Pasinetti1981, p. 66)’ (p. 371). This is why, he concludes, Pasinetti (Reference Pasinetti1993, p. 107) has stressed the importance of a theory of consumers' choice in a dynamic context (p. 373).

With respect to the analysis of Sraffa, Walsh notices that Smith's notion of necessaries and conveniences, the consumption basics as he calls them (p. 374), can suffice to highlight that ‘structural economic dynamics gives us new goods that do not remain wildly expensive luxuries – they may become new basics. And if they were made by new manufacturing processes, there are of course new technical basics, too’ (ibid.).

‘What then of the relationship between the evolving basics of a structural dynamic model and capabilities?’ asks Walsh. ‘I wish to stress from the beginning that the relationship is not a tight mapping . . . but there is . . . a significant relationship nonetheless’ (p. 376). Leaving aside for the moment the problem of defining a list of capabilities,⁶ the point is that ‘a Pasinetti-type model presents a truly dynamic process (emphasis added) in which commodities arguably necessary to the realization of vital capabilities appear sequentially over time.’ Actually, there are ‘two sequential aspects’ in Pasinetti's model and they ‘arise for different reasons’ (ibid.). The first is from the recognition that ‘human needs form a hierarchy, which can (and should) be addressed sequentially.’ But there is also a ‘technically sequential property,’ which stresses the lack of any necessary correspondence between commodities created by ‘unbalanced growth’ and need structure: ‘Sometimes a technical discovery may occur just when the need it can fulfill is becoming dominant, but of course there can be no guarantee in the structure of the model that it will be so’ (p. 377).

Hierarchy of needs implies an ordering and the obvious one is that going bottom-up, from basic needs, such as those relating to survival, to ‘superior’ needs, leading to the realization of personality. Walsh quotes Bertram Schefold as saying ‘[t]here are certain hierarchies of needs, from basic need up to higher needs such as the need for self-fulfillment’ (Reference Schefold, Bharadwaj and Schefold1990, p. 376). He concludes that ‘Schefold (and Pasinetti) both assume that human nature reveals the presence of an extreme hierarchy of needs,’ (p. 376) way beyond those of survival. Let's suppose that this is indeed the case and consider ‘a strict hierarchy of human needs all the way from water and nutrients up to the creative needs of a great artist. Again, there is no reason to suppose that the sequential development of the material basis for needs fulfillment (emphasis added) laid out in the path of a Pasinetti model of structural dynamics would map closely onto this structure of need. Conveniences that could make life better would indeed be arriving on the scene, and a genuine enrichment of classical kind taking place, but not necessarily for every important aspect of life at once, nor for one after another in a special order of need’ (p. 377). Nor is there any guarantee ‘that a particular amount of a particular commodity will be necessary (or sufficient) to allow the fulfillment of a particular capability,’ a point stressed by Sen. ‘Sometimes it will happen’ (ibid.).

So, despite the fact that the notion of need hierarchy reaches well beyond survival and that capabilities open the way to consider what can be accomplished by individuals through different forms of consumption, the stumbling block remains the relationship between goods and need. Nor is the reference to capabilities, although clarifying the relationship between subjectivity and goods, of much help in this respect. The point is that both, need hierarchy and capabilities, imply a close relationship with commodities, in the sense of being fulfilled and, at the same time, of being revealed and made actual by them. In the latter sense they appear to depend on commodities, though this aspect is not much investigated.

The mapping problem

Walsh concludes that structural dynamics, and the evolving basket of consumption it implies, does not indicate a tight mapping to the list of capabilities, ‘but surely a soil and a climate in which capabilities can flourish’ (p. 377). However, focusing on the mapping problem highlights a problem internal to structural dynamics, i.e. the relationship between goods, or as Walsh calls it, the material basis of need fulfillment, and the need structure. There is a problem of technical feasibility, i.e. consistency with technical progress, and one of consistency of the means to the satisfaction of needs and the ascending pattern dictated by the needs hierarchy.

Pasinetti takes as a reference point the idea of market saturation, with learning on the part of consumers as the force driving consumption into new territory. Basic needs will be saturated first and, while they can be satisfied by better quality goods, this will inevitably lead to higher-level needs, so that new commodities will be added to the consumption basket. More so if learning is pervasive, as it is to the entire analysis.

Thus, a ‘basic need’ approach is built into the hierarchical pattern of need satisfaction, although quite clearly that does not imply a limitation on the kind of needs considered. Needs that are basic today might not have been such in the past. Indeed, structural dynamics implies a basket of necessaries and conveniences of an improved and more cultivated life (Walsh, Reference Walsh2003, p. 375). But then the problem arises of the relationship between these new commodities entering the standard of living of consumers and the underlying structure of need. And that is conceivably having an impact also on the fulfillment and development of human capabilities.

In fact, the lack of tight mapping exposes a more fundamental problem: not only is there no necessary correspondence between need, capabilities and the actual evolution of the means of consumption, other than that imposed by market saturation, but this relationship depends, it appears, on the commodities that the economic progress creates. This is the truly dynamic problem for a theory of consumption and it has not been solved by taking into account new products in consumer choice. The two sides of the issue are, on the one hand, the ordering built into the need structure, and on the other hand, an evolving set of commodities intended to satisfy needs.

Walsh's argument suggests considering commodities development beyond the logic that governs the structural dynamics of demand in Pasinetti's model. While it is then quite appropriate to point out that transformational growth will give us an evolving material basis for the fulfillment of need, that very evolution calls for an explanation.⁷ The point is to dig into the process by which new commodities come into being and become means to need satisfaction.

It is now clear that need hierarchy, even if understood as a sequence starting from basic, survival needs up to the highest level of human self-realization, is not sufficient to explain consumption patterns’ evolution. The law of non-proportional expansion of consumption expenditure, no doubt, plays an important role in it, but cannot further explain demand evolution. And yet, the reference to an evolving material basis emerges quite clearly as the condition for the sequential satisfaction of needs. Only the analysis of commodities development can give determinacy to a dynamic theory of consumption. The point is, it could be argued, that this material basis is not investigated within the process that structures consumption patterns.

Capabilities and need development

Need hierarchy does serve to establish the fundamental law of motion of the consumption structure and the difference with traditional consumer theory. And yet, the notion of need and need structure is not adequately investigated with respect to the very dynamic process that shapes consumption patterns. The reference to capabilities makes that more evident. To go beyond the notion of need as a given, and of the need structure itself as a hierarchical arrangement fundamentally given, we need a theory of need development.

In a basic need approach, needs can be fulfilled, not developed. The hierarchical arrangement implies a certain pattern for the satisfaction of higher-level needs that become areas of expansion of consumption spending. In this sense we could say that income growth reveals the structure of needs. But within this broad regularity we should search for the reasons that determine the forms taken by the satisfaction of needs, their effects on the volume of spending and the evolving structure of demand. These depend very substantially on product innovation and, more precisely, on consumption innovation (Gualerzi, Reference Gualerzi and Bianchi1998, Reference Gualerzi2001). Furthermore, the volume of spending and the choice of products, particularly new products, reflect a differentiation of consumers, i.e. an economic and social segmentation of the market, and in particular the distinction between consumers more capable and motivated to try new products and those who are not.

Capabilities move us a step forward because through them we can take into account what individuals, but also groups and possibly social classes, can accomplish with goods. It is then possible to look at the capabilities approach from another angle. A really interesting aspect of capabilities is how they allow us to speak of need, and in particular how they permit us to go beyond a basic need approach. How so?

The capabilities approach suggests that commodities are conditions, but their outcome depends on what one can make with them. It is a drastically different approach than that embodied in the diet problem, in which combinations of characteristics satisfy a given need, in a given need structure. If we think of capabilities as a way of referring to the subjective element in the interaction with commodities and an aspect of personality development, then capabilities become part of need development. It could be said that individuals, according to social rules and practices, define the feasibility of a form of need satisfaction, driven by their search for self-realization.

Thus, if we agree that the Pasinetti model depends very much on the structural dynamics of demand, then neither the neoclassical concept of preferences nor a theory of ‘basic needs’ might be sufficient to study such a transformation. Sen's theory of human capabilities can make the difference. It might allow for taking into account need development as it actually occurs, that is, by means of innovation of commodities and consumption practices. This defines also the proper space of commodities development within consumption theory. It should be observed that all of this follows from focusing on need development.

Need development depends on the development of commodities, which, together with social practices and consumer learning, define the forms of consumption. Not that the need for food or shelter matter for a dynamic theory of consumption, but rather a socially accepted, although differentiated, and technically feasible form of satisfaction of the need for food and shelter. The reason why it has proven to be impervious to traditional theory is possibly that it calls into question the traditional view of the consumer and of consumer choice (Gualerzi, Reference Gualerzi and Bianchi1998). But with the criticism of traditional theory offered by Pasinetti we have moved a long stretch away from that. An analytical development of the insights of Walsh into the relationship between Pasinetti's structural dynamics and Sen's capabilities approach is, then, quite possible within the larger perspective of the consumption–growth relationship and the transformation of the consumption sphere (Gualerzi, Reference Gualerzi2001).

The consumption–growth relationship

Why should we focus on the consumption–growth relationship? Which problems can we address that other approaches can't or only partially can? The main point is that this relationship is structured around the two dynamic processes which have emerged from the analysis above: need development and the process of developing new products. This allows for an analysis of consumption centered on the process of change. In turn, that clarifies the relationship between consumption evolution and growth. The two problems so clearly raised by Pasinetti's model – changes in consumption patterns and new markets formation, can then be addressed in this framework.

The approach based on the consumption–growth relationship rests on the idea that the research on consumption patterns can bring forward new results if the traditional distinction between the analysis of consumption and that of growth is overcome and the focus shifts instead onto their mutually reinforcing effects. When the main aspects of this reciprocal determination are clarified, a more specific kind of investigation, and the search for empirical evidence, might become considerably easier. Furthermore, much of the knowledge on consumption that is developed in different fields of investigation can be given coherence and relevance within an economic scheme.⁸

Consumption expenditure cannot grow without change in the ‘forms’ of consumption, and change in a market economy depends on investment in developing commodities. In other words, we cannot speak of change of the forms of need satisfaction without new products and investment in these products; alternatively, we cannot have a theory of investment and output composition without a view of the growth of the market, which includes a view of its transformation, i.e. its structural development.

Indeed, new products do not fall from the sky. They are the object of planning and speculation on the part of firms, and developing commodities bear a close relationship to the effort to expand their market, which in turn is linked to the growth of the market as a whole. The development of new commodities requires investment that therefore shows a particular two-sided relationship with market growth: on the one hand, it contributes to effective demand as spending in R&D; on the other, it builds productive capacity to serve the market as it grows according to the path set by the product cycle. Through investment in what we can call market development, firms pursue their goal of self-expansion, at the same time contributing to the growth of the market as a whole.

Ultimately, change in consumption depends on a logic that goes beyond the consumption itself, to include several aspects of the growth process.

Socially determined needs and the consumption sphere

To approach growth in this perspective requires a particular notion of need and need development. That is why we speak of socially determined needs.

We are indeed referring not to any notion of need belonging primarily to the sphere of nature, nor to a general notion of human and social needs, but rather to a specific notion of ‘socially determined needs’ (Levine, Reference Levine1981, Reference Levine1998). Socially determined needs suggest that an essential aspect of need is the possibility of development. Second, they stress that in a market economy need can be understood only in relation to commodities. After all, that is implied in the idea that any need, irrespective of its position in the need hierarchy, can be satisfied by higher-quality commodities and by adding new commodities to the consumption basket.

As opposed to subsistence needs, ‘which are imposed on the individual’ (Levine, Reference Levine1981, Vol. II, p. 280), socially determined needs contribute to the individual's self-seeking and personal identity. It is precisely the freedom according to which needs are developed, which makes them impossible to determine a priori. This is in sharp contrast with the notion of needs ‘by which the species renews itself within a determinate system of natural relations’ (Levine, Reference Levine1981, Vol. I, p. 45). While on the one hand indeterminate, and for this reason subject to development, they are on the other hand specifically determined, not by nature, or individuals as such, but rather by the social process shaping individual identity. Need development is, then, a constant stimulus to change and the potential for the expansion of the market.

The dynamic force implicit in the structure of production and consumption is the development and the multiplication of needs implied by the constitution of the individual personality within a system of persons. The development of need, latent in the idea of its social determination upon the basis of individuality, is, then, the potential exploited by firms and the basis for new market formation. The consumption sphere is the sphere of economic life that ensures the realization and development of socially determined needs, it is the economic space that can be exploited for purposes of market expansion. In a market economy, needs are satisfied by means of commodities, more specifically by a combination of commodities and consumption practices. This combination determines the forms of needs satisfaction. The transformation of the consumption sphere is therefore the result of the interplay of the processes of change originating both within the domain of personal identity and within industrial production. Its transformation follows from firms' logic of expansion and individuals' effort towards self-realization.

Consumption patterns and new markets formation

To clarify the process of determination that accounts for a) the evolution of consumption patterns and b) new markets formation, we have to consider the interdependence between the construction of socially determined individual identity through consumption and the drive to self-expansion of firms, based on their strategies of investment.

Change in the forms of needs satisfaction is the result of innovation in consumption; more specifically, individuals validate and establish new products as part of a form of need satisfaction devising the appropriate consumption practices, that is, ‘discovering’ the usefulness of products. In turn, new products are the most relevant aspect of firms' market development strategies, through which they pursue the goal of expanding their market. At the macro level these two processes determine the volume and direction of investment and the level and composition of consumption spending, therefore the structure and the rate of expansion of the market. In particular, autonomous investment determines not only the level of effective demand but also its composition. As a result, the system of socially determined needs is translated into a specific structure of consumption and a determinate stage of development of the consumption sphere. During this transformation new markets are created, because both new income is created and the structure of needs evolves. The development of needs acts as a force that, through change, can expand the market. In other words, change translates into the creation of markets through the development of the need structure.

This self-sustaining process of determination spells out the internal mechanism of endogenous growth; the expansion of aggregate circulation – the rate of growth of the system as a whole – depends on the intensity and success of the market development strategies.

The remarkable aspect of this mechanism is that the transformation of the consumption sphere may act again as a stimulus to change, since it recreates the conditions for more structural determination of the market and further expansion. When the structure of needs is manifested in a specific structure of consumption, the latter can act as the starting point for a new round of need development, mainly because of the potential implicit in the forms of satisfaction now established and the new interdependencies they reveal.

Transformation is indeed necessary for the growth process; it is driven by the social construction of need that shapes the consumption sphere. At the center of the process is the reciprocal determination of the structure of consumption and the structure of investment. Therefore, focusing on need development also permits clarification of the role of new products in the analysis of consumption, the issue discussed, although with partial results, by Lancaster (Reference Lancaster1966) and Ironmonger (Reference Ironmonger1972). The question remained confined to the problem of change of the items of choice, it was not related to the problem of the pattern of change. If we focus on that, it turns out that it cannot be analyzed independently from the growth process, and in particular from investment in new products.

The consumption–growth relationship and the principle of effective demand

It is possible, then, to draw a general conclusion. The ultimate reason for framing the question of a dynamic theory of consumption within the consumption–growth relationship is that of finding a solid ground for an endogenous dynamics of transformation, that is, internalize that question into the analysis of the growth process driven by investment. Ultimately, changes in consumption patterns are part of the theory of effective demand and of a particular understanding of the operation of the principle of effective demand in the long run (Gualerzi, Reference Gualerzi2001, 2005).

Investment, i.e. firms' strategies of market development, redetermines through structural transformation the level and composition of output. Stripped to the bone, the mechanism outlined above says that the successful insertion of a new product in the consumption basket validates the underlying strategy that developed that innovation, modifying as a result consumption patterns. We have seen, in particular, that need development and development of commodities proceed on the basis of the same process transforming the consumption sphere. The dynamic theory of consumption sketched above rests on this mechanism, but the latter also articulates the particular long-run view of the principle of effective demand contained in the consumption–growth relationship. To that extent, it relates to the deeper level of analysis that Pasinetti associates with the shift of paradigm centered on that principle, the core of the Keynesian Revolution (Pasinetti, Reference Pasinetti2007).

The focus on new products is just a first step. It is indispensable in driving attention to investment and its effects in the long run. This is the question posed by the Harrod–Domar model, except the latter focused only on the level of investment and not on its composition. This overlooks changes in this composition aimed at the development of new industries and new products. Focusing exclusively on investment as creation of productive capacity, it implicitly contains the idea that growth could be just expansion of output, precisely what Pasinetti would call ‘pseudo-dynamics.’ A better story can be told about the growth process, one which rests on the particular role played by investment.

It appears plausible to maintain that investment sustains growth in the aggregate through the development of new industries and new products, although a question remains as to the size of the stimulus. New products can displace old ones, leaving open, at least in principle, the possibility of a zero sum game. This is contradicted by the additional expenditure that is necessary to develop these new products. But most fundamentally, the point is that new products act on need development, and that contains the possibility of developing new markets, well beyond the displacement of old products.

Thus, there is an ordering in the development of the material basis for need fulfillment and indeed it relates to the saturation of the markets serving certain needs. That ‘ordering’ comes from what can broadly be defined as product innovation, an essential aspect of markets in advanced industrial economies.⁹ But product innovation must be seen in light of the process of need development. The latter is reflected in the transformation of the consumption sphere and follows from the firms' efforts to develop the market and the drive to self-realization of individuals. While consumption patterns’ evolution, i.e. the very object of the theory of consumption, proceeds from that, it is governed by the level and composition of investment, therefore by the principle of effective demand.

Empirical analysis: stylized facts and institutions

Empirical evidence and observed long-term trends have an important role in the approach outlined above, although that requires some methodological clarification. The fundamental idea is that the basic mechanism manifests itself in the specific forms taken by consumption transformation and the underlying strategies that sustain it. Thus, empirical evidence can be used to illustrate and discuss the mechanism and the specific aspects of a certain phase of structural transformation. Actual dynamics can then be approached by focusing on the stylized facts and the institutional setting of that particular phase or cycle of expansion. This can narrow down the investigation to more limited goals in a second stage.

This use of empirical evidence and the facts of history is itself quite uncommon for economic analysis, at least for the traditional view of theory specifying testable propositions that are then proven correct or not by empirical analysis. It has also an important methodological consequence. It suggests how to articulate what Pasinetti regards as a second level of the analysis, concerning institutional dynamics.

In this respect, it might be useful to indicate the most pressing institutional problems for advanced market economies emerging from structural dynamics. One is clearly that of what we can call the institutions for full employment, that is, those institutions responding to the necessity of pursuing full employment as an explicit goal of policy. A second concerns the institutions appropriate to what, although still vaguely understood, is often called the knowledge economy, in light of, for instance, the problems raised by intellectual property and externalities. A third one may be indeed that of the institutional arrangements relevant to the transformation of the consumption sphere.

We can approach this last question from the point of view of which institutions are better suited to guide and govern, at least to some extent, this transformation and therefore also have an impact on the growth process. This would probably imply discussion of how consumption can evolve along socially desirable lines and which institutional setting is more conducive to efficiency and innovation. This is clearly too large an issue and is left to another discussion of structural dynamics. However, given the relationship between theory and evidence delineated above, one suggestion is immediate.

Learning, inequality, and patterns of consumption

Empirically observed trends of transformation of consumption patterns highlight the pattern taken by need development in a certain stage of development or cycle of expansion of the economy. That suggests grounding abstract notions, such as learning and consumption innovation, in the stylized facts and the socio-economic dynamics of a certain period. A useful way to address this aspect is to consider an overall phenomenon, such as the diffusion and increased sophistication of information and communication technologies (ICT), and to focus on its implications for learning and consumption.

Petit and Soete (Setterfield, Reference Petit, Soete and Setterfield2002) have pointed out two major trends of transformation in the past two decades: the skill-biased nature of technological change, associated with the spread of new information and communication technologies, and the rise of income inequalities. On the one hand, the particular nature of technological change ‘suggests a new complementary relationship between capital and skills’ (p. 281); on the other, it implies a growing difference between workers who acquire these skills and those who do not. This is reflected in the structure of employment. Petit and Soete also indicate the link between learning at the level of production and learning on the part of consumers, suggesting that ‘the divisions occurring in society in terms of the desire and ability of individuals or families to use new technologies are closely related to what is happening within working organizations’ (p. 288).

The rise of new complementarities between the ever-increasing capabilities of information technologies and the learning process of users, and of consumers at large, suggests, then, that new problems may arise from an uneven process of skills acquisition. The dualism arising from the uneven process of acquisition of ICT-related skills, depending on age, education, occupation, besides individual inclinations, affects both the development of consumption patterns and the labor market, with the latter feeding back on the former.

This might be taken as an example of a more general problem. The boom and the bust of the 1990s' cycle of expansion in the US economy suggested that there are obstacles to the transformation of consumption driven by ICT, and by the Internet in particular. This technological frontier highlights opportunities and limitations for the development of needs and the creation of markets, but also less than desirable changes in consumption patterns. Empirical evidence on these aspects could help to better understand the obstacles standing in the way of the ‘knowledge economy’ often advocated by the European Community. In this respect there might be a problem of institutional development and/or a problem of appropriate social policies capable of addressing questions such as Internet addiction and the impact of virtual reality on personality structures and social behavior.

The quantity system and the sectoral productivity change

In this section, we will consider a production system with no surplus in order to define the sectoral and social productivity in physical terms. Pasinetti (Reference Pasinetti1981, Reference Pasinetti1993) constructed a structural dynamic model in continuous time. However, we will consider a discrete time period, Period 1 and Period 2, in order to make the problems transparent. The number of commodities is assumed to be n. It is assumed that there is no introduction of new commodities. The notations of given data of Period 1 and Period 2 are shown as follows.

Notations of given data

1. A¹, A²: the (transposed) Leontief input coefficient matrix of each period. The input coefficient matrixes are assumed to be a semi-positive and indecomposable matrix, A¹≥0, A²≥0, A¹ ≠ A².

2. : the actual total labour of each period, .

3. : the standard total labour or in short standard labour of each period, which is normalized by the actual total labour . They are calculated as . Then we have .

4. : the Leontief labour input coefficient vector corresponding to the actual total labour respectively, .

5. : the standard labour input coefficient vector corresponding to the standard total labour respectively, . The standard labour input coefficient vectors are calculated as .

6. : the actual output vector of each period, .

7. : the actual net product vector of each period, .

8. : the output vector of the standard system of each period, . The vectors are an eigenvector of the matrix respectively and they are assumed to satisfy . We assume (t: positive scalar).

9. s¹, s²: the standard net product vector of each period, . By assumption, (t: positive scalar)

The produced means of production can be reduced to the indirect labour inputs by calculating the vertically integrated labour coefficient vector. If we denote the vertically integrated labour coefficient vectors corresponding to the standard labour coefficient vectors by , then they can be represented as

(1)

(2)

From the above notations and the vertically integrated labour coefficient vectors of (1)(2), the standard total labour of each period is represented respectively as¹

(3)

(4)

From this, we can consider that the vertically integrated labour coefficient vectors can be regarded as the indicator of division of labour.

We will define the labour productivity by the vertically integrated labour coefficient. The inverse of , the jth component of v_S, represents the physical productivity of labour of commodity j, i.e. . Thus the sectoral productivity of labour of commodity j of each period can be represented as

(5)

(6)

In order to define the rate of sectoral productivity changes, we will take Period 2 as the base year. If we denote the rate of productivity change of commodity j (the sectoral productivity change rate of commodity j) by ρ^(j), then it can be defined by²

(7)

It should be noticed that the definition of the sectoral productivity change rate ρ^(j) itself is given by the given data or , irrespective of the composition of output.

Measurement of social productivity change

The next problem is to find out the weighted average of the rates of growth of labour productivity of the entire economy. Pasinetti (Reference Pasinetti1981, Reference Pasinetti1993) calls this the ‘standard’ rate of growth of productivity of the economic system. It may be a difficult task to find an appropriate indicator of the social productivity change rate, or the ‘standard rate’ of growth of productivity. In order to measure the social productivity change rate, we must get some appropriate index number, because we are considering a multisector model and the net product of the economy is composed of a heterogeneous commodity bundle. Hicks (Reference Hicks and Hicks1981) suggested two different productivity indexes: the real cost approach and the opportunity cost approach. He considered the labour coefficients as the price weights for his productivity index. In Hicks (Reference Hicks and Hicks1981), labour coefficients indicates a given technique of each period and the total labour of each period is given exogenously. The index number of the real cost approach is constructed by the actual bundles of commodities produced under given production conditions. The index number of the opportunity cost approach is constructed by the bundle of commodities which can be potentially producible by the given production condition and the actual total labour. The opportunity cost approach will enlarge the applicability of cost approach and enable us to construct more productivity indexes.

As for the price vectors to construct index numbers, we can make use of the vertically integrated labour coefficient vectors . As for the quantity vectors to construct index numbers, according to Hicks (Reference Hicks and Hicks1981), both the actual net product and the potentially producible net product can be eligible as the quantity weights. Therefore, not only the actual net product vectors y¹, y² but also the standard net product vectors s¹, s² are eligible as quantity weights. In order to calculate the standard net product vectors s¹, s², we need only the input coefficient matrixes, the labour coefficient vectors and the quantities of actual total labour, i.e. a set of data . By using the standard net product vectors s¹, s² for quantity weights, we can focus upon the difference in techniques of different periods. The standard net product vectors are preferable for the construction of a productivity index because the composition of the standard net product has a direct connection to the technique and has no influence from the differences in demand composition. In addition, the standard net product vectors s¹, s² have a preferable property as standard in the Sraffian price system when the rate of profit is positive (see Section 4 below).

We will use Fisher-type index numbers because in our model the Fisher-type indexes bring about the quite interesting result that the inverse of the Fisher-type price index becomes equal to the Fisher-type output index divided by the labour input index. Let us denote the price index of Fisher type by P_sv, the output index of Fisher type by Q_sv, the input cost index by C_sv. If a set of data is given, we can obtain the data set . Then the indexes will be represented as³

(8)

From (3)(4), we have

(9)

From (9), the indexes of (8) can be rewritten as

(10)

We will call P_sv the Standard price index and Q_sv the Standard output index. From the theory of index numbers, the relationship between C_sv, P_sv, Q_sv becomes

(11)

From (8)–(11), we can define the productivity index as

(12)

We will call Λ_sv the Standard productivity index, or more precisely the Standard physical productivity index. The Standard productivity index takes out the effect of social productivity changes resulting from the difference in the structures of division of labour from equations (3) and (4). It should be stressed that Λ_sv is defined both by 1/P_sv on the price side (or cost side) and by on the quantity side, and therefore Λ_sv is considered as a useful measure of the productivity change rate of the entire economy. The reason we use the Fisher-type index number is so that we can derive the double definitions of Λ_sv of (12) (see Yagi(Reference Yagi, Egawa, Tomono, Uemura and Yagi1998, Reference Yagi, Nishikawa, Yagi and Shimizu2007)).

If we take Period 2 as the base year, the rate of social productivity change will be represented as

(13)

If we take Period 1 as the base year, the rate of social productivity change will be represented as

(14)

In the following, we will use both definitions of productivity change rate, and .

Effective labour and standard income

From (12) we can represent the standard output index as follows:

(15)

The right member is the product of the Standard productivity index and the standard labour. This is the same as the definition of effective labour which is considered in the case of Harrod-neutral technical progress. It will be convenient to denote the effective labour by

(16)

In our model, the effective labour is determined by the Standard productivity index and the standard labour. From (15)(16), we have

(17)

The standard output index is equal to the effective labour.

Corresponding to the effective labour , the effective labour coefficient vector will be defined as

(18)

Then the effective labour is represented by

(19)

From (3)(4)(19), we obtain

(20)

This means that the effective labour of Period 2 can be compared with the standard labour of Period 1. Equation (20) is an important basis for our intertemporal comparisons.

The vertically integrated labour coefficient vector given by the effective labour coefficient vector can be defined as

(21)

The relation between and is represented by

(22)

From this we have

(23)

From (3) (20)(23), we have

(24)

This is quite an interesting result. Although the standard net products are composed of heterogeneous commodities and though the production technique changes from to , the standard net products can be compared with each other because the aggregated values of the standard net products are measured in terms of labour. The difference in the aggregated values of the standard net product comes from two factors: Λ_sv and L²_S.

A simple price system

Let us consider the intertemporal comparisons of prices when the rate of profit is equal to zero. A set of given data is . Let us denote the price vector of Period 1 by , that of Period 2 by , the wage rate of Period 1 by , that of Period 2 by . Then we have the price systems of each period respectively as

(25)

(26)

These price vectors will be rewritten as

(27)

(28)

Each price system has n independent equations and (n + 1) variables.

Case 1: commodity h as numéraire

If we take commodity h as numéraire, the price of h will be set equal to unity as

(29)

Let us denote the price vectors and the wage rates expressed in terms of commodity h respectively by . Then they will be defined as

(30)

Then from (27)(28)(30) we have

(31)

(32)

Let us denote the rate of change of the price of commodity h by , the rate of change of the price of commodity i by , the rate of change of the wage by , the rate of change of productivity of commodity h by and the rate of change of productivity of commodity i by . Under the condition of of (29), we have

(33)

(34)

(35)

In this case, the general price level does not necessarily become constant.

Case 2: labour commanded

If the wage rates of both periods are equal to unity, then the rate of change of the wage will become equal to zero, i.e.

(36)

(37)

And if we denote the price vectors under the condition (36) by

(38)

(39)

These vectors are measured in terms of physical unit of labour. When the rate of profit is equal to zero, the price systems (27)(28) become

(40)

(41)

Since the vertically integrated labour coefficient vectors can be compared with each other, the price vector of Period 2 can be compared with that of Period 1. From (7), the rate of change of the price of commodity i will be represented by

(42)

The general price level becomes

(43)

If we denote the rate of change in the general price level by , then we have

(44)

Therefore, from (13)(44), we have

(45)

In the present case, the general price level will decrease at the rate of social productivity change.

Finally, the value of the standard net product of Period 2 becomes

(46)

Case 3: the effective wage

Let us define the effective wage by the product of the standard productivity index and the standard wage, i.e.

(47)

Let us denote the price vector of Period 2 by and define it by

(48)

The general price level corresponding to the price vector will become

(49)

In this case, the general price level is constant from Period 1 to Period 2.

This is the case where the wage grows at the standard rate of productivity change of the economy. Let us denote by the effective wage of Period 2 which grows at the rate of of (14). The condition will be given by

(50)

Under the condition of , the rate of change of the wage will be represented by

(51)

The rate of change of the price of commodity i will be represented by

(52)

Finally, the value of standard net product will become

(53)

Case 4: effective labour

If we use the effective labour coefficient vector, by multiplying (28) by , we have

(54)

In this equation, the wage rate means the wage which will be paid for one unit of effective labour . If we want to obtain the wage rate which will be paid for one unit of standard labour , we should rewrite the price system (54) as

(55)

The wage rate means the wage which will be paid for one unit of standard labour . In this case, the general price level will be represented by

(56)

The general price level is constant from Period 1 to Period 2. The value of standard net product will become

(57)

Sraffa's standard commodity and Pasinetti's dynamic standard commodity

From the above analysis, we can conclude that if the value of the standard net product is set equal to unity, then the general price level will decrease at the rate of the social productivity change given by the Standard productivity index. Also, if the value of the standard net product is set equal to the effective labour, then the general price level will become constant. These results bring us to the proposition that, in the system with no surplus, in order to keep the general price level constant, the value of the standard net product should be kept equal to the effective labour. From (53) or (57), we have

(58)

The left member of (58) is the value of standard labour embodied in the standard net product. It means the value of the standard net product produced by means of one unit of standard labour. It can be called the value productivity of the standard net product. In the system with no surplus, the condition to keep the general price level constant can be considered as the condition that the rate of change of the value productivity of the standard net product is set equal to the social productivity change rate .

Pasinetti (Reference Pasinetti1993) admits the difficulty of computing the dynamic standard commodity and states: ‘It is not easy to visualize such a composite commodity’ (p. 71). This difficulty may lie in a mixture between the difficulty in solving the index number problem and the difficulty in finding an invariable standard commodity. First, it may be difficult to calculate the social productivity change rate (the weighted average of the rates of productivity change of the entire economy), in order to keep the general price level constant. Second, it may be difficult to find the composition of the dynamic standard commodity at different times for the purpose of comparison. However, from the above discussions, to visualize the dynamic standard commodity in our model, we can define the dynamic standard commodity as follows:

(59)

In our present model, the dynamic standard commodity of Period 2 is defined as the standard net product of Sraffa (Reference Sraffa1960) divided by the standard labour and by the Standard productivity index . In Period 1, since both the standard labour and the Standard productivity index are set equal to unity, the standard net product is considered as the dynamic standard commodity of Period 1. In Period 2, the standard condition to keep the general price level constant can be represented as

(60)

The value of the dynamic standard commodity is constant from Period 1 to Period 2 even if the composition of the dynamic standard commodity varies from s¹ to and the price vector varies from to . Under the condition (60), the price vector becomes the vector of the real prices because the general price level is kept constant.

The Sraffa system

Now we proceed to consider the system with a surplus. Let us denote the rate of profits by r, which is assumed to be uniform all over the economic system. Moreover, let us denote the maximum rate of profit by R. Then the rate of profit will take real numbers ranging from 0 to R (0 ≤ r ≤ R). Similarly, a uniform rate of wage (post factum) is assumed to be prevailing in the economy. It is indicated by w_S. The Sraffian price system given by the standard labour coefficient vector can be represented as

(61)

From the equation system (61), we can derive the linear wage curve

(62)

This is the equation of the famous linear wage curve. Let us make clear the following two important properties. First, it is important that under condition (62), the difference between the actual income yp_S and the standard income sp_S corresponds to the profit which comes from the difference between the actual capital and the capital of the standard system (standard capital). From this the standard income sp_S can be considered as a useful proxy for the actual income yp_S and works as a helpful reference.

Let us explain this point. We can define the actual capital as m_y = xA and the standard capital as m_S = qA. Then, if we use the notations of the price vector measured in terms of the standard net product as p_sp = p_S/sp_S, and the notation of the wage measured in terms of the standard net product as w_sp = w_S/sp_S, from (61) and ql_S = xl_S (see Notations), we can derive the following equation⁴

(63)

This equation means that the difference between the actual income yp_sp and the standard income sp_sp is equal to the profit obtained by the capitalist from the difference of (). From this result, the linear wage curve (62) can be applied to the analysis of the actual economy if we neglect the profit which comes from the difference of ().

Second, we have an interest in the value of standard labour embodied in the standard net product (the value productivity of the standard net product) under the condition (62). From (61) we can derive the following equivalence⁵

(64)

In this case, the value of standard labour embodied in the standard net product becomes equal to unity. But now let us put it as

(65)

where v_L is the value of labour. Then we consider the enlarged price system (61) with (65). There are (n + 1) equations and (n + 3) unknowns (r, w_S, , ). And under the condition (62), from (64)(65), we can derive the following:

(66)

Therefore we can consider that, under the condition (62), the price vector is normalized by the condition v_L=1. The price vector will become

(67)

This price vector is measured in terms of unit of standard labour.

Evaluation system for two periods comparison

Let us proceed to consider the two periods case, and denote the rates of profit by r¹, r², the wage rates by and and the value of labour by and . When a set of data or is given, the model can be shown as follows:

In this system, if the rates of profit (r¹, r²) are given exogenously, there will be (2n + 2) independent equations and (2n + 4) unknowns (). If the condition of standard for each period is given, the above system will become determinate. Let us consider the case of R² ≤ R¹. In this system, the following proposition will hold.

Theorem In the above Evaluation System, the value of labour of Period 1 is equal to the value of labour of Period 2 if and only if

(68)

where 0 ≤ r¹ < R² and 0 ≤ r² < R² ≤ R¹.

Proof From price equations of the above Evaluation System, we have

(69)

(70)

Therefore, for all r¹ of 0 ≤ r¹ < R² and for all r² of 0 ≤ r² < R² ≤ R¹, we have

(71)

(72)

Then, for all r¹ of 0 ≤ r¹ < R² and for all r² of 0 ≤ r² < R² ≤ R¹, we have

(73)

From this, Theorem is verified.

Let us consider that the price system of Period 2 is given by the effective labour coefficient vector . By multiplying both members of the price system of Period 2 of the above Evaluation System by , we have

(74)

Under the condition (68), the prices and wages of both periods are measured in terms of unit of effective labour. The reduced forms of are represented as

(75)

(76)

The price vector of (76) is measured in terms of unit of effective labour and therefore can be compared with the price vector of (75).

Under the condition (68), for all r¹ of 0 ≤ r¹ < R² and for all r² of 0 ≤ r² < R² ≤ R¹, we have

(77)

(78)

Then, from (20)(77)(78), we have

(79)

This equation represents the physical output comparison when the rate of profit is positive. It should be noted that the value of is constant even if the rate of profit varies. It is given by the effective labour .

The effective wage curve

By multiplying both members of of (72) by Λ_sv, we have

(80)

By this condition, the value of standard income per standard labour is constant even if the rate of profit varies. This is the same condition as (58). Contrary to (58), in this case, the general price level will not be constant when the rate of profit varies (see p. 261). The condition (80) is the invariable standard condition for distribution. And therefore, this is the condition for the linear wage curve.⁶

In (74), the wage rate is represented by , which is the wage payable for one unit of effective labour. Let us change the wage variable from to . The effective wage rate is the wage which can be paid for one unit of the standard labour of Period 2. Because of , the price system (74) will be rewritten as

(81)

Corresponding to this price system, we can derive the following linear wage curve:

(82)

The condition of the effective wage curve of (82) will be given by (80). As for the effective total wage (), we have

(83)

Moreover, since the wage share is given by , we have

(84)

When we consider the effective wage curve of (83), the value of the standard net product (the standard income) is given by (78). These effective wage curves are shown in Figure 11.1.

Figure 11.1 Effective wage curve

Ricardo gave up measuring the absolute values; he was concerned only with the problem of the comparison of relative share of distribution. With our effective wage curves, we can do absolute comparisons of wages. The relationships between and can be represented as

(85)

Finally, corresponding to the effective wage curve, we can obtain the value of capital of the standard system. Since this becomes equal to 1/R, the value of capital of Period 2 will be represented as

(86)

It should be noted that, if we consider the effective wage curve, the value of capital is kept constant as the rate of profit varies.

Distribution effect to the general price level

Let us consider the case that the prices and wages of both periods are measured in terms of the unit of standard labour. Under the condition of (68), the reduction equations, or the reduced forms of , are represented as

(87)

(88)

These price vectors are measured in terms of the same unit of labour. The total labour of the economy can be represented by

(89)

(90)

By using the price vectors of (87)(88), let us consider the index numbers. The weight vectors for index numbers are given by [s¹, s², , ] and a set of the given data is . For the index numbers of this case, let us denote the price index of Fisher type by , the income index of Fisher type by and the input cost index by . Then they will be represented as

(91)

From (89)–(91), these indexes can be reduced to a simpler form as follows:

(92)

From the theory of index numbers, the relationship between becomes

(93)

In our model, however, from the above, we can obtain the following relationship:

(94)

In (94), the productivity change is calculated both from the cost side by and from the quantity side by . It should be stressed that is obtained by the given production techniques . In order to make a distinction between and , we will call this index the Standard value productivity index μ.⁷ It measures the social productivity changes in value terms. is independent of the composition of demand. From (12)(94), we have the price index

(95)

The term represents the effect of distribution to the general price level. Thus we denote the term by

(96)

In the case of , there is some effect of distribution to the general price level. It is quite interesting that the changes in the general price level between and are determined by the social productivity change measured by the standard productivity index and the distribution effect to the general price level defined by .

Real wage and real prices

Now let us consider the real values obtained by dividing by the Standard price index . If we denote the real wage by and the real price vector by , we can define them as follows:

(97)

(98)

These values mean the real values because they are denominated by the price index. From (47)(74) and (97)–(98), we have

(99)

(100)

Also we have

(101)

Corresponding to , let us define

(102)

Figure 11.2 Real wage curve

From this, we have

(103)

In (101), the labour which is equal to the value of the standard net product varies as the rate of profit changes. Dividing the price system of Period 2 by , we have

(104)

In this case, the general price level will be kept constant because the general price level corresponding to will become

(105)

Then let us consider the wage curve. If we rewrite the price vector (104) as

(106)

From this, we can derive the following wage curve:

(107)

We call this the real wage curve in order to avoid confusion with the effective wage curve.

Finally, the value of capital corresponding to this real wage curve will become

(108)

The ratio between and corresponds to the value of .

The general price level and the dynamic standard commodity

We have arrived at the important conclusion that there are two different invariable standard conditions over time: the invariable standard for the general price level and the invariable standard for distribution through time. As seen in (80), the condition can be considered as the invariable standard condition for distribution. In order to keep the general price constant, the condition of standard will become

(109)

The ratio between (80) and (109) will also correspond to .

From (109), we can define the dynamic standard commodity to keep the general price level constant as follows:

(110)

The condition can be rewritten as

(111)

Under the condition (111), the general price level becomes constant and the rate of inflation becomes equal to zero. But in this case, the wage curve does not become linear. Therefore the condition is not the invariable standard for distribution.