Reproduction schema

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). 

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... 

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. 

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. 

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. 

Now economists are very fond of diagrams, and one of the few diagrams Marx ever used was to summarize Quesnay s Tableau Economique (Marx 1969a). Quesnay was the doyen of the physiocrats, who thought that land was the source of all value hence the tableau shows the circulation of commodities between farmers and landlords. As shown by Pressman (1994), Marx shaped this model into his reproduction schema a model of how commodities circulate between capitalists and workers. For Marx (1969a 344), the tableau was an extremely brilliant conception, incontestably the most brilliant for which political economy had up to then been responsible . 

The most developed expanded reproduction schema is referred to by Marx as schema (B) of the First Example in section 3 of chapter 21, Capital, volume 2 (ibid. 586-9). This is shown in Table 2.2, the numbers representing a modification of the simple reproduction table. The same assumptions are maintained as under simple reproduction, apart from relaxation of the restriction that all surplus value be allocated to capitalist consumption. 

In the large body of work that has explored the relationship between the systems of Marx and Keynes,5 there is no established understanding of the role played by the multiplier. This can be illustrated by some of the more recent attempts to interpret the multiplier from a Marxian perspective. Two main topics of concern are (1) the role of the multiplier in the reproduction schema and (2) the way in which Marx s category of surplus value relates to the structure of the multiplier. The following brief consideration of this recent literature provides the backdrop to a full critique, in which some of its limitations will be addressed. 

Lianos (1979) provides an accessible insight into how the multiplier can be located in the reproduction schema. By focusing specifically upon Department 1 he states, it is convenient to assume a one sector economy (ibid. 407). Only information from Department 1 of the example used by Marx (Table 2.2) is included in the Lianos reproduction schema, as shown in Table 2.3. The key modification which enables a translation to Keynesian economic categories is to interpret all value added, variable capital plus surplus value, as net income (T,) for Department 1. Assuming away for the moment the problems associated with Adam Smith s dogma, this income is net of constant capital. The net income of the one-good economy is 2,000, consisting of 1,000 units of variable capital and 1,000 units of surplus value. 

An analytical leap can now be made that provides the cornerstone of the rest of this book. Located in this reproduction schema is a Keynesian multiplier that enables a relationship to be specified between net investment and net income. The intuition runs as follows. Capitalists anticipate that they will expand their constant capital by 500 in the next period of production. There is therefore a net investment demand for 500 emits of output to be produced in the current period.6 Workers are hired to produce this... 

Having nested the multiplier in the reproduction schema, some attention can be given to its structure. As a starting point, the Keynesian income multiplier takes the form... 

The main problem with this decomposition of the multiplier is that it is restricted to a one-good model. A contribution which relates the Keynesian multiplier to a two-good model, along the lines of Marx s reproduction schema, has been provided by Hartwig (2004). As a starting point, net income in the two departments is captured by the identities... 

Having set up the expanded reproduction schema in an input-output format, the path is now clear for it to be modelled as a multiplier framework. To achieve this aim, input coefficients ay = Xy/Xj specify the ratio between physical flows of means of production (Xy), from department i to department j, to (physical) gross output (Xy) of department j. In Marx s reproduction schema, these input coefficients are applied to Department 1, the only sector producing means of production. For Department 2, different notation is required for our multiplier framework. Ratios to gross output of the total number of labour units employed in each sector (Ly) are represented by labour coefficients ly = Lj/Xy, and consumption coefficients ht = BJL are... 

The role of Marx s category of surplus value can therefore be identified in a macro scalar multiplier without the restrictive assumption of a one-good model. This scalar multiplier captures the inter-departmental structure of the reproduction schema without constant capital being assumed away. A formal model of aggregate demand in the reproduction schema is developed, which retains the simplicity of the Keynesian multiplier together with Marx s value categories. 

Table 3.2 Ex ante three- sector reproduction schema ...

Whichever interpretation is correct, Kalecki s silence on the labour theory of value leaves open the theoretical possibility that its relevance can be fruitfully explored. To relate Kalecki s model of reproduction to Marx s theory, a reconfiguration is required of the definition of profits. The problem, as we have seen, is that Kalecki s model requires a gross definition of profits that is different from Marx s category of surplus value. The Kalecki principle has not been precisely demonstrated in the context of Marx s reproduction schema, in which surplus value is the key category of analysis. 

Although Sardoni (1989 211) mentions these different specifications of investment in his comparison of Marx and Kalecki, he does not highlight their importance. To demonstrate the importance of this difference, the Leontief input-output framework can again be used to model the final demand of each department of production such that investment demand cuts across departments. This Leontief interpretation of the reproduction schema allows Marx s categories to be retained alongside the Kalecki principle. 

It should also be emphasized that this adaptation of the Kalecki system represents an interpretation of the reproduction schema that is consistent with Marx s system. As Lee (1998) has argued, Kalecki has a restrictive production model in which each department is vertically integrated, producing its own raw materials. In contrast, Marx assumes that raw materials are a part of constant capital, produced in the first department and circulated to other departments. A failure to fully take into account connections between industries leaves the Kalecki system vulnerable to a SrafFian critique. Steedman (1992), for example, has lambasted the Kaleckian price system for the absence of multisectoral relationships. By establishing the Kalecki principle in an input-output context, an interpretation of the reproduction schema is possible in which linkages between industries are taken seriously. 

Marx s two great departments of production in the reproduction schema. For exchange between such use-values to take place, however, they must also have exchange-value. 

What sets this circuit approach apart is its institutionally relevant analysis of the relationship between banks, firms and workers. A model of the circuit of money is developed in which prime importance is placed upon the role of banks in financing industrial activities. Central to this approach is an application of the Kalecki principle, that capitalists earn what they spend the question being how an injection of money can circulate around the economy and return back to the capitalists. Moreover, how is this circuit of money intertwined with the activities of industrial sectors And how much money is required for the circuit to be complete Marx s reproduction schema provides a natural starting point for addressing these questions. 

Although it has been shown that Nell s (2004) model of the circulation of money bears some resemblance to Marx s system, two key issues remain to be resolved. First, in adopting the Kalecki schema of intersectoral flows (Table 4.1), Nell narrowly associates accumulation with the production of means of production (capital goods). There is no mention of the accumulation of consumption goods, which are placed at the centre of Marx s reproduction schema. Second, the role of Marx s category of surplus value is obscured in the Kalecki table. As demonstrated in Chapter 3, for the... 

Key to modelling the circulation of money in this Marxian reproduction schema is a consideration of how it intertwines with the circulation of commodities between sectors. A precondition for the circuit of money is the commodity circuit. To explore in more detail how commodities circulate in Marx s system, the role of inventories has to be considered. Taking his lead... 

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