Marxian Reproduction Schema

Andrew Trigg

• Publisher: Routledge
• Year: 2006
• ISBN:
  9781134305650
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

In 1878 Karl Marx developed the reproduction schema: his model of how total capital is produced and reproduced. This is thought to be the first two-sector economic model ever constructed. Two key aspects of Marx's writings are widely agreed to be undeveloped: The role of aggregate demand and the role of money. This book synthesizes various strands of economic thought to enable the reader to understand and clarify the structure of the reproduction schema. This synthesis will challenge prevailing orthodoxies.

This book constructs a macro monetary model which draws on a wide range of economic theories, within both the Marxian economic tradition, and the tradition of Keynes, Kalecki, Domar, Sraffa and Leontief. Marxian economics has been dominated by supply-side thinking, including general equilibrium theory and pronouncements about the shortage of surplus value, whilst Post Keynesians have failed to take seriously the importance of reproduction and the multisectoral structure of capitalism. By locating aggregate demand and the circuit of money in the reproduction schema, this key book provides an analytical contribution to both Marxian and Post Keynesian economics.

1
Introduction

It may be hard to imagine that the origins of macroeconomics, as we know it today, came from a German revolutionary, exiled to England and ignored by the economic establishment. In 1878, working for the last time on his great writing project, Capital, Karl Marx developed the reproduction schema: his model of how total capital is produced and reproduced. This is thought to be the first two-sector economic model ever constructed, with two great departments producing means of production and means of consumption. Not only did this model capture the division between consumption and investment that later became the centrepiece of Keynes’s General Theory (1936), it went beyond the short-term focus of Keynes to explore the structure of economic growth. Marx has thus been described as the forerunner of macroeconomic growth theory.¹

As with all great works, a common complaint is that they are never properly read in the original. Marx’s Capital is no exception. After the publication of volume 1 in 1867—the only part which Marx was able to finish—his wife, Jenny, complained:

You can believe me that seldom has a book been written under more difficult circumstance, and I could write a secret history that would uncover an infinite amount of worry, trouble and anxiety. If the workers had an inkling of the sacrifice that was necessary to complete the work, written only for them and in their interest, they would perhaps show a bit more interest.

(McLellan 1973:353)

Of course, for those who manage to make it through the material, Capital is a work of art: a masterpiece exposing the vagaries of unbridled capitalism. But even leading figures in the labour movement have found this a struggle. On receiving the first volume, a trade union colleague of Marx ‘felt like a man who had been given an elephant and did not know what to do with it’ (ibid.: 353). Similarly, the British Labour Prime Minister, Harold Wilson, admitted that he had not got past the first page. The reason may have been as identified by Marx’s lifelong collaborator, Friedrich Engels, in his comment that Marx started the volume with the most difficult chapters, continually interrupted the flow with extensive examples and failed to summarize its purpose and direction.²

If the first volume of Capital is difficult to absorb, the reader of the second volume, where the reproduction schemes are located, faces an even greater challenge. Due to the unfinished form of the material, which Engels assembled from Marx’s notes, it is generally agreed that it lacks coherence. Engels viewed the part of the material on the reproduction schema as ‘excellent in content, but fearfully heavy in form, patched together from two treatments of the problems by two different models’ (quoted in Zarembka 2000:197).

Commenting on the unfinished state of the second (and third) volumes of Capital, Joan Robinson warned, ‘The waters are dark and it may be that whoever peers in them sees his own face’ (Robinson 1968:111). From these murky waters, a host of different models and perspectives have emerged. In the absence of any clear statement of the purpose of the reproduction tables, there is no agreement as to what they are for, how they relate to the rest of Capital, volume 2, and how they relate to Capital as a whole. For Tsuru (1994:191), ‘Participants in the discussion…concretized the original simple tableau of Marx in whatever way most suited for their respective conclusions.’

One of the greatest schisms in political economy, since the early part of the twentieth century, is over the role played by aggregate demand in the reproduction schema. Where, argued the fiery Rosa Luxemburg, does the demand come from for every growing capacity generated by expanded reproduction? ‘In Marx’s diagram,’ she scathingly points out, ‘accumulation, production, realisation and exchange run smoothly with clockwork precision, and no doubt this kind of “accumulation” can continue ad infinitum, just as long, that is to say, as ink and paper do not run out’ (Luxemburg 1951).

The first main purpose of this book is to formalize the role of aggregate demand as a constraint on expanded reproduction. I will develop an analytical model which explores the conditions under which profits can be realized in the reproduction schema. This approach is in keeping with the spirit of Dillard’s (1984:425) statement that ‘Marx’s economics would be strengthened by a more formal treatment of the theory of effective demand.’

For daring to criticize Marx, Luxemburg was labelled a heretic, failing to properly understand the role of the reproduction schema in Marx’s system. In the wake of Stalin’s purges, the importance of demand was overtaken by Marx’s falling rate of profit, which he presented in Capital, volume 3. It was argued by Henryk Grossmann that capitalism is vulnerable to breakdown because of the falling rate of profit tendency. This theory of crisis has become the standard canon of the far left; for supply-side Marxists it provides a bulwark against the (reformist) Keynesian aggregate demand approach. Marx’s reproduction tables, though used to illustrate the Grossmann breakdown scenario, have been downplayed as a mere interlinking device between first and third volumes of Capital.

In the universities, a mathematical strand of supply-side Marxism has evolved that is closer to mainstream general equilibrium theory. Notably, for Morishima (1973:105), ‘Marx’s models are very similar to Walras’ in many aspects: Marx’s scheme of simple reproduction, or reproduction on the same scale, corresponds to Walras’ static general equilibrium system of production…’ Aggregate demand has hardly any role to play in this microeconomic approach.

Furthermore, a major shortcoming of the supply-side Marxists is their failure to consider the importance of money. In Brody (1974:9), for example: ‘Theories of money…are not discussed, although a parallel mathematical approach to them is much needed and indeed within reach’ (see also Roemer 1978). The problem is that money is essentially neutral in general equilibrium models, a characteristic more appropriate to a barter economy than to capitalism. And in the Grossmann falling rate of profit thesis, money is stripped from the reproduction schema despite its central importance to Capital, volume 2.

The second main purpose of this book is to develop an alternative interpretation of the reproduction schema in which money plays a key role. Some degree of formalization is required here with respect to circulation of money, which takes on various often contradictory guises in Marx’s work. As Foley (1973:viii) commented, ‘Marx’s writings on money remain in a “pre-model” stage.’ My objective is to develop a coherent model of how the circulation of money intertwines with the reproduction of commodities.

At the heart of this contribution to Marxian economics is an analytical framework for modelling aggregate demand in which a Keynesian multiplier is nested in the schema. Every economics student is taught that each pound of investment has a multiplied effect on total income. Lianos (1979) has shown how the multiplier relationship between income and investment can be modelled in one of Marx’s departments of production. My specific analytical contribution is to generalize this insight to the full multisectoral structure of Marx’s tables, without losing the simplicity of the scalar Keynesian multiplier.

The key role of money in the reproduction process is addressed by using some of the insights provided by Michal Kalecki. He was schooled in the rich vein of Polish Marxism at the start of the twentieth century—both Luxemburg and Grossmann were Polish—but became famous as the economist who discovered the rudiments of the General Theory before Keynes (or so it is claimed). Like Keynes, Kalecki emphasized the importance of aggregate demand for investment as the driving force of a capitalist economy. In a rudimentary model of the circuit of money, capitalists cast money into circulation as aggregate investment, and this returns back to them as profits. This is the Kalecki principle: that capitalists earn what they spend. A key starting point for considering the relationship between the Marxian and Keynesian traditions is Kalecki’s demonstration of how this macroeconomic principle works in the context of Marx’s reproduction schema.

Armed with the multiplier and the Kalecki principle, a potential contribution can also be made to Post Keynesian economics, in which there has been a tendency to take money seriously, but not reproduction. Although Keynes himself developed a two-sector model, he had great problems dealing with user cost—defined as constant capital in Marxian categories.³ How all capital is reproduced under capitalism has become a side issue for Keynesians, often by resorting to a one-sector framework. Similarly, the Franco-Italian circuitist school has focused on the circuit of money without paying any attention to the reproduction of commodities. Flows of money between banks, firms and consumers are modelled without considering the relationship between sectors of production. The money circuit has been given prominence without due attention paid to the circuit of commodities.

In addition, the importance of money and aggregate demand can be carried through to the modelling of expanded reproduction over time. It is well known in economic growth theory that the Harrod-Domar model has a close affinity to Marx’s reproduction model. For Kuhn (1979:40), ‘the Marxian growth model, in the framework of an essentially unstable economy, has anticipated the important conclusions of the Harrod-Domar analysis.’ However, it is not so widely known that money has a key role to play. There is a paradox of borrowing, in which capitalists have to secure credit for expanded reproduction to take place. Coupled with the key role of aggregate demand in the drive for capital accumulation, the Marxian growth model provides a powerful tool for highlighting the stringent conditions required for expanded reproduction.

My analytical contribution is to show how the Harrod-Domar model—more specifically, its Domar variant—can be derived from the multisectoral reproduction schema, with the multiplier and the monetary circuit as the key building blocks. These building blocks are defined using Leontief’s input-output analysis, a model which has its origins in the Marxian economic tradition.

Finally, this analytical framework is used to cast light on the Marxian theory of crisis. Once money and demand are taken seriously, the reproduction schema provide the basis for Marx’s possibility theory of crisis; his demonstration of the likelihood of economic crises taking place. The analytical precision provided by the Domar interpretation provides a platform for interpreting some of the great controversies of twentieth-century Marxism—in particular between protagonists such as Hilferding, Bauer, Luxemburg and Grossmann.

The book is thus a series of steps, from the multiplier and its role in the reproduction schema in Chapter 2 to the Kalecki principle in Chapter 3 and a detailed consideration of the circuit of money in Chapter 4. Having built up a macro monetary model of the reproduction schema, in which both money and aggregate demand are featured, Chapter 5 derives the Domar growth model from these analytical foundations. The relevance of this growth model to Marxian theories of crisis is explored and further developed in Chapter 6.

A subtext of this analysis is an attempt to address some of the limitations of the reproduction schema. Two main limitations of the schema, as modelled in Chapters 2–6, are the absence of free competition, based on the mobility of capital, and the lack of any room for technical progress. Chapter 7 examines the Grossmann model of how technical progress drives the tendency of the falling rate of profit. And in Chapter 8, free competition is considered by turning to Marx’s famous transformation problem; a problem that has dominated discussions in Marxian economics.

This analysis draws on a wide range of economic theory, both within the Marxian economic tradition and further a field in the traditions of Keynes, Kalecki, Domar, Sraffa and Leontief. In the same way that Marx was open to the whole corpus of classical economics in the nineteenth century, this book has as its aim the incorporation of various strands of economic thought in an attempt to understand and clarify the structure of the reproduction schema.

2
The multiplier

When first embarking on his study of economics, in 1851, Marx wrote to Engels, ‘I am so far advanced that in five weeks I will be through with the whole economic shit’ (McLellan 1973:283). As it turned out, he was to spend the next twenty-five years in the British Museum Library, defining a whole school of thought: the school of classical economics.

At the end of this journey, the Marx who worked up the second volume of Capital, in the late 1870s, was not the young philosopher engaged in Hegelian metaphysics. Of course, Marx’s philosophical background to some extent explains how his critique of cla...