Law of the Accumulation and Breakdown, Henryk Grossmann 1929

2. The Law of Capitalist Breakdown

Is there a theory of breakdown in Marx?

Even if Marx did not actually leave us a concise description of the law of breakdown in any specific passage he did specify all the elements required for such a description. It is possible to develop the law as a natural consequence of the capitalist accumulation process on the basis of the law of value, so much so that its lucidity will dispose of the need for any further proofs.

Is it correct that the term ‘theory of breakdown’ stems from Bernstein, not Marx? Is it true that Marx nowhere ever spoke of a crisis that would sound the death knell of capitalism, that ‘Marx uttered not a single word that might be interpreted in this sense’, that this ‘stupid idea’ was smuggled into Marx by the revisionists? (Kautsky, 1908, p. 608) To be sure, Marx himself referred only to the breakdown and not to the theory of breakdown, just as he did not write about a theory of value or a theory of wages, but only developed the laws of value and of wages. So if we are entitled to speak of a Marxist theory of value or theory of wages, we have as much right to speak of Marx’s theory of breakdown.

In the section on the law of the tendency of the rate of profit to fall in the course of accumulation where Marx shows how the accumulation of capital proceeds not in relation to the level of the rate of profit, but in relation to its mass, he says, ‘This process would soon bring about the collapse of capitalist production if it were not for counteracting tendencies which have a continuous decentralising effect alongside the centripetal one’ (1959, p. 246). So Marx observes that the centripetal forces of accumulation would bring about the breakdown of capitalist production, were it not for the simultaneous operation of counteracting tendencies. However, the operation of these counteracting tendencies does not do away with the action of the original tendency towards breakdown: the latter does not cease to exist. So Marx’s statement is only intended to explain why this tendency towards breakdown does not enforce itself ‘soon’. To deny this is to distort the clear sense of Marx’s words.

However it is scarcely a matter of words which ‘might be interpreted in this sense’, and so on. Where the mere interpretation of words leads to is quite obvious from the directions in which Kautsky drags Marx’s theory. For us the question is: suppose initially we abstract from the counteracting tendencies that Marx speaks of, how and in what way can accumulation bring about the breakdown of capitalist production? This is the problem we have to solve.

Preliminary methodological remarks

We have to show how, as a result of causes which stem from the economic process itself, the capitalist process of reproduction necessarily takes the form of cyclical and therefore periodically recurring movements of expansion and decline and how finally it leads to the breakdown of the capitalist system. However if the investigation is to be fruitful and to lead to exact results, we shall have to choose a method that can ensure this exactness.

What should we regard as the characteristic, determining condition of the reproductive cycle? Lederer identifies this as the price movements in the course of the business cycle: in periods of expansion commodity prices, including the price of labour power, rise; in periods of crisis and depression they fall. Therefore his way of posing the question is the following: how is a general increase of prices possible in periods of expansion? Expansions in the volume of production such as characterise periods of boom are, according to Lederer, only possible due to price increases. Therefore price increases are what he has to explain first. Lederer sees the creation of additional credit as the sole impulse behind price increases. Consequently he attributes to this factor the major role in determining the shape of the business cycle.

Spiethoff’s explanation is quite different: ‘An increase in capital investments forms the true hallmark and causal factor of every boom’ (1925, p. 13). Here not one word is said about price increases and we could just as well choose a whole series of other forces as our basic indicators without moving one step further in explaining the problem. For the question is not one of which appearances are characteristic or typical of the business cycle, but which are necessary to it in the sense that they condition it. That price increases generally occur during an upswing does not mean that they are necessarily connected with it. If like Lederer, we were to assume that upswings presuppose rising prices we would be totally stumped by the American booms which were sometimes characterised by falling prices. That a wrong starting-point has been chosen is obvious. Both rising prices and expanded outlays on production are in themselves matters of indifference to the capitalist entrepreneur.

The capitalist process of production has a dual character. It is a labour process for the production of commodities, or products, and it is at the same time a valorisation process for obtaining surplus value or profits. Only the latter process forms the essential driving force of capitalist production, whereas the production of use values is for the entrepreneur only a means to an end, a necessary evil. The entrepreneur will only continue production and extend it further if it enables him to enlarge his profits. Expanded outlays on production, or accumulation, are only a function of valorisation, of the magnitude of profits. If profits are expanding production will be expanded, if valorisation fails production will be cut. Furthermore, both situations are compatible with constant, falling or rising prices.

Of these three possible price situations the assumption of constant prices is the one most appropriate to theory, in the sense that it is the simplest case and a starting point from which the other two more complicated cases can be examined later. The assumption of constant prices thus forms a methodologically valid theoretical fiction with a purely provisional character; it is, so to speak, a coordinate system within economics, a stable reference point that makes possible exact measurement of quantitative variations in profitability in the course of production and accumulation.

The basic question we have to clarify is how are profits affected by the accumulation of capital and vice versa. Do profits remain constant in the course of accumulation, do they grow or do they decline? The problem boils down to an exact determination of variations in surplus value in the course of accumulation. In answering this question we also clarify the cyclical movements or conjunctural oscillations that define the process of accumulation.

These considerations underlie Marx’s analysis: ‘Since the production of exchange value — the increase of exchange value — is the immediate aim of capitalist production, it is important to know how to measure it’ (1972, p. 34). In order to establish whether an advanced capital value has grown during its circuit or by how much it has grown in the course of accumulation, we must compare the final magnitude with the initial magnitude. This comparison, which forms the basis of any rational capitalist calculation, is only possible because — in the form of costs of production and prices of the end product — value exists under capitalism as an objectively ascertainable independent magnitude. As something which is objectively ascertainable on the market, value constitutes both the basis of capitalist calculation and its form of appearance. Its explanation is thus the starting-point of any theoretical analysis.

From the very beginnings of free capitalism attempts were made to grasp the independent character of value — its aspect as an objective, external entity — in numerical terms. H Sieveking tells us that ‘the rational approach to economics was enormously speeded up by the introduction of book-keeping’ (1921, p. 96). The ability to calculate the yield on a sum of values originally invested is a vital condition for the existence of capital:

as value in motion, whether in the sphere of production or in either phase of the sphere of circulation capital exists ideally only in the form of money of account, primarily in the mind of the producer of commodities, the capitalist producer of commodities. This movement is fixed and controlled by book-keeping, which includes the determination of prices, or the calculation of the prices of commodities. The movement of production, especially of the production of surplus value ... is thus symbolically reflected in imagination. (Marx, 1956, p. 136)

Through prices the fluctuations of a given capital value in the course of its circuit become expressed in money, which serves as measure of value required for accounting. And with respect to this measure of value Marx proceeds from the assumption, which is purely fictitious and which forms the basis of his analysis, that the value of money is constant. At first sight this appears to be all the more surprising in the sense that, in his polemic with Ricardo’s ‘invariable measure of value’, Marx emphasised that gold can only serve as a measure of value because its own value is variable. In reality the values of all commodities, including gold, are variable. But science needs invariable measures: ‘the interest in comparing the value of commodities in different historical periods is, indeed, not an economic interest as such, but an academic interest’ (Marx, 1972, p. 133).

From historical surveys of the development of thermometry we know that a reliable measure of heat variations was established through the fundamental work of Amonton, with the discovery of two fundamental points (boiling-point and the absolute null point of water) for any liquid used as the measure of heat variations. This alone could establish the constant reference points with which it became possible to compare the variable states of heat (Mach, 1900, p. 8).

There are no such constant reference points for gold as the measure of value. So an exact measure of the value fluctuations of commodities would be impossible. On the one hand changes in the value of the money commodity may differ from the changes in the value of individual commodity types. In this case we have no exact measure to ascertain how far, say, the rising prices of a given commodity have been caused through changes in its own value and how far through changes in the value of the money commodity. In this case, suppose we were studying variations in the magnitude of surplus value; then, with a variable value of money, it would be difficult to tell whether a given increment in value (or price) was not something merely apparent and caused purely by changes in the value of money:

In all these examples there would, however, have been no actual change in the magnitude of capital value, and only in the money expression of the same value and the same surplus value ... there is, therefore, but the appearance of a change in the magnitude of the employed capital. (Marx, 1959, pp. 139-40)

Alternatively the value of money vanes in the same proportion as the values of other commodities, for instance due to general changes in productivity — a limiting case that is scarcely possible in reality. In that case there would have been enormous absolute changes in the real relations of production and wealth, but these actual changes would be invisible on the surface, because the relative proportions of individual commodity values would remain the same. The price index would not register the actual changes in productivity.

Thus it was entirely valid for Marx to substitute the ‘power of abstraction’ for the missing constant reference points, so falling into line with Galileo’s principle: ‘measure whatever is measurable, and make the non-measurable measurable’. For instance to ascertain the impact of changes in productivity on the formation of value and surplus value, Marx is forced to introduce the assumption that the value of money is constant. This assumption is therefore a methodological postulate that equips Marx with an exact measure for ascertaining variations in the value of industrial capital during its circuit. It is an assumption underlying all three volumes of Capital.

The variability of the measure of value, or of money, is only one of the causes of price changes. Such changes can just as well stem from causes that lie on the commodity side of the exchange relation. Here we should distinguish two cases. Either these variations of price are, from a social point of view, consequences of actual changes in value. (This is the case that preoccupies Marx initially, and it is these changes he wants to measure.) Or these variations of price represent deviations of prices from values, which do not in any case affect the total social mass of value because price increases in one sector of society correspond to price reductions in another.

The specific task that Marx set himself of measuring as exactly as possible increases in value over and above the initial magnitude of the advanced capital, forced him to exclude price changes of the latter sort. Price fluctuations that represent deviations from value are the result of changing configurations of supply and demand. Now if one proceeds from the assumption that supply and demand coincide then prices will coincide with values. Motivated by specific methodological considerations, Marx starts off his analysis with the assumption that supply and demand coincide. He assumes a state of equilibrium with respect to supply and demand, both on the commodity market and on the labour market, in order to be able to cover the more complicated cases later. Hence whenever production is expanded it is presupposed that this occurs proportionally in all the spheres so that the equilibrium is not destroyed. The reverse case, where production expands disproportionally, is taken up later.

Variations analysed at later stages are likewise exactly measurable only due to the simplifying assumptions that define this hypothesised state of equilibrium, which is not only directly reflected in the reproduction schemes but which forms the starting-point of the analysis as its coordinate system. Marx’s Capital has a mathematical-quantitative character. Only these methodological devices allow an exact analysis of the accumulation process.’[1]

Can accumulation proceed indefinitely without halts in the process of reproduction? To say ‘yes’ and to regard this as something self-evident without undertaking an actual analysis is to misunderstand the question completely. For instance professor Kroll argues that if commodities were exchanged at equilibrium prices, where supply equals demand, then there would be no conjunctural oscillations. He supposes that any decline in profitability is because wages are too high (Kroll, 1926, p. 214). But why were they not too high previously? What can ‘too high’ mean when we have no basis of comparison in the form of a ‘normal case’ such as represented by the reproduction scheme? If all the elements are variable, then the influence of any individual factor is impossible to assess. The causal relation that Kroll observes between the level of wages and falling profitability is not something we can presuppose; it has to be demonstrated. Therefore a scientific analysis is in principle bound to take as its starting point the case where wages are held constant in the course of accumulation, and it has to find out whether in such cases profits do not fall in the course of accumulation. If they do, then it would be a logically exact proof that falling profitability, or crises, bear no causal connection with the level of wages but are a function of the accumulation of capital. The assumption of equilibrium, or of constant prices, is nothing but the method of variation applied to the problem of the business cycle in a form that excludes from the analysis all oscillations produced by changes in the volume of credit, prices, etc; it studies only the impact of the accumulation of capital, on quantitative changes in surplus value.

This is the assumption behind Marx’s analysis of the crisis; ‘The general conditions of crises, in so far as they are independent of price fluctuations ... must be explicable from the general conditions of capitalist production’ (1969, p. 515). According to Marx crises can result from price fluctuations. But they were of no concern to him. Marx takes as the object of his analysis ‘capital in general’; he is concerned only with those crises that stem from the nature of capital as such, from the essence of capitalist production. However this essence is only penetrable when we abstract from competition and thus confine ourselves to ‘the examination of capital in general, in which prices of commodities are assumed to be identical with the values of the commodities’ (p. 515). This identity of price and value is in turn only possible if the apparatus of production is assumed to be in a state o~ equilibrium. Marx makes an assumption of this sort. The same holds for credit. Credit crises are possible and do occur. But the question is, are crises necessarily connected with the. movement of credit? Hence on methodological grounds we must first exclude credit and then see whether crises are possible. Marx says:

In investigating why the general possibility of crisis turns into a real crisis, in investigating the conditions of crisis, it is therefore quite superfluous to concern oneself with the forms of crisis which arise out of money as means of payment [credit — HG]). This is precisely why economists like to suggest that this obvious form is the cause of crises. (pp. 514-5)

Once we have shown that even in a state of equilibrium, where prices and credit are ignored, crises are not only possible but inherent, then we have proved that there is no intrinsic connection between the movement of prices and credit on the one hand and crises on the other; ‘that is to say, crises are possible without credit’ (p. 514).

Bourgeois economists try to explain the movement of market prices by competition or the changing relations of supply and demand. But why does competition exist? This question they do not pose. Competition becomes some mysterious quality that one simply assumes or submits to without exploring its causes. ‘Competition exists only in industry’, Sternberg tells us, ‘because the law of rising returns is fully valid for industry, or individual entrepreneurs struggle to control the market by cheapening their commodities’ (Sternberg, 1926, p. 2). But why should they struggle to control the market, why should there not be outlets for the ‘rising returns’ of industry? This is not something logically necessary or obvious, and simply to assume it is to start off by presupposing what has to be proved. With this mystical force which has been left unexplained, he then tries to explain all other phenomena.

Marx was perfectly right in saying that ‘competition has to shoulder the responsibility of explaining all the meaningless ideas of the economists, whereas it should be the economists who explain competition’ (1959, p. 866). In fact:

a scientific analysis of competition is not possible, before we have a conception of the inner nature of capital, just as the apparent motions of the heavenly bodies are not intelligible to any but him, who is acquainted with their real motions, motions which are not directly perceptible by the senses. (Marx, 1954, p. 300)

But how do we grasp the inner nature of capital? Marx’s answer is, since individual capitalists ‘confront one another only as commodity owners, and everyone seeks to sell his commodity as dearly as possible... the inner law enforces itself only through their competition, their mutual pressure upon each other, whereby the deviations are mutually cancelled’ (1959, p. 880). So in reality the inner law of capitalism enforces itself through the mutual cancellation of deviations of supply and demand, which only means that it is through this process that the mechanism preserves its equilibrium.

The inner law only works itself out in reality through the constant deviation of prices from values. But in order to gain a theoretical perception of the law of value itself, we have to assume it as already realised, that is, we abstract from all deviations from the law. This does not mean that competition is discarded; rather it is conceived in its latent state, as a special case where its two opposing forces are in equilibrium. Only this ‘normal case’ draws out the various economic categories — value, wages, profit, ground-rent, interest — in their pure form, as independent categories. This is the starting point of Marx’s analysis. He states:

let us assume that the component value of the commodity product, which is formed in every sphere of production by the addition of a new quantity of labour ... always splits into constant proportions of wages profit and rent, so that the wage actually paid always directly coincides with the value of labour-power, the profit actually realised with the portion of the total surplus value which falls to the share of each independently functioning part of the total capital by virtue of the average rate of profit, and the actual rent is always limited by the bounds within which ground rent on this basis is normally confined. In a word, let us assume that the division of the socially produced values and the regulation of the prices of production take place on a capitalist basis, but with competition eliminated. (1959, pp. 869—70)

Starting from this methodological basis is it possible to ask - what is the impact of the accumulation of capital on the process of reproduction? Can the equilibrium which is presupposed be sustained in the long run or do new moments emerge in the course of accumulation which have a disruptive effect on it?

The equilibrium theory of the neo-harmonists

In approaching this problem I shall refrain from constructing any scheme~ of my own and demonstrate the real facts through Bauer’s reproduction scheme (see Table 2.1). In Chapter 1 we saw the neo-harmonists Hilferding, Bauer and others join the company of Tugan-Baranovsky in reproducing a version of JB Say’s old proportionality theory in order to prove that capitalism contains unlimited possibilities of development.

No doubt, as an answer to Luxemburg’s theory, the reproduction scheme constructed by Bauer represents a distinct progress over all earlier. attempts of this kind. Bauer succeeded in constructing a reproduction scheme which, apart from some mistakes, matches all the formal requirements that one could impose on a schematic model of this sort.[2]

Bauer’s scheme shows none of the defects that Luxemburg ascribed t the reproduction scheme of Marx. First it takes account of incessant technological advances and incorporates this in the form of an ever-increasing organic composition of capital. Consequently what Luxemburg calls the ‘cornerstone of Marxist theory’ is preserved. Second, it avoids Luxemburg’s criticism that ‘there is no obvious rule in this accumulation or consumption’, for Bauer’s scheme does specify rules to which accumulation must correspond — constant capital grows twice as fast as variable capital - the former by ten per cent, the latter by five per cent per annum. Third although capitalist consumption increases absolutely, increases in productivity and the mass of surplus value allow a progressively greater portion of the surplus value to be earmarked for the purposes of accumulation. Fourth, Bauer’s scheme preserves the symmetry between Departments I and II required by Luxemburg. In Marx’s scheme Department I always accumulates half its surplus value, whereas accumulation in Department II is anarchic and jerky. In Bauer’s scheme both departments annually devote the same percentage of surplus value to accumulation. Finally the rate of profit behaves according to the Marxist law of its tendential fall. No wonder Luxemburg herself preferred the cautious warning:

Naturally I shall not let myself be drawn into a discussion of Bauer’s tabulated calculations. His position and his critique of my book depend mainly on the theory of population which he counterposes to my ideas as the basis of accumulation, and which in itself really has nothing to do with any mathematical models. (1972, p. 90)

The critique that I shall make of Bauer’s scheme starts from a quite different perspective from Luxemburg’s (see Table 2.1). I shall show that Bauer’s scheme reflects and can reflect only the value side of the reproduction process. In this sense it cannot describe the real process of accumulation in terms of value and use value. Secondly Bauer’s mistake lies in his supposing that the scheme is somehow an illustration of the actual processes in capitalism, and in forgetting the simplifications that go together with it. But these shortcomings do not reduce the value of Bauer’s scheme. As long as we examine the process of reproduction initially from the value side alone.

The conditions and tasks of schematic analysis

In the following sections I propose to accept Bauer’s assumptions completely. But the problem is not simply to explain crises — the periodic expansions and contractions of the business cycle under capitalism — and their causes but also to find out what are the general tendencies of development of the accumulation of capital. Initially we make the favourable assumption that accumulation proceeds on the basis of dynamic equilibrium of the kind reflected in Bauer’s scheme.

On this assumption Luxemburg’s criticism that ‘the question of markets does not even exist for Bauer’ although periodic crises ‘obviously stem from disproportions between production, that is the supply of commodities, and market, that is demand for commodities’ (1972, p. 121) becomes meaningless and untenable. For Marx worked out the problem of accumulation and the whole analysis of Capital Volume One on the conscious assumption that commodities sell at value, which is only possible when supply and demand coincide. Marx studied the tendencies of accumulation in abstraction from all disturbances arising out of disproportions between supply and demand Such disturbances are phenomena of competition that help us to explain deviations from the ‘trend line’ of capitalism, but not this trend line itself.

For Marx these phenomena are the ‘illusory appearances of competition’ and for that reason he abstracts from the movement of competition when investigating the general tendencies. Once these general tendencies~ have been established it is an easy task to explain the periodic deviation~ from the basic line of development, or the periodic crises. In this sense the Marxist theory of accumulation and breakdown is at the same time. theory of crises.

With Bauer we shall assume a productive mechanism in which constant capital amounts to 200 000 and variable capital to 100 000. The other assumptions are that: 120 000 of this constant capital is apportioned to Department I (means of production) and 80 000 to Department II (means of consumption); that the variable capital is equally divided between both spheres; that the constant capital expands by 10 per cent a year and the variable capital by 5 per cent; that the rate of surplus value is 100 per cent and that in any given year the rate of accumulation is equal in the two departments.

Proceeding from these assumptions, Bauer has constructed a reproduction scheme which in his view manifests perfect equilibrium year after year despite annual accumulation of capital and despite the fact that there are no non-capitalist markets in which the surplus value might be realised. With this scheme Bauer thinks he has established ‘a perfect basis for tackling the problem raised by Luxemburg’ (1913, p. 838). He rejects her theory of the crucial role of the non-capitalist countries in the realisation of surplus value; surplus value can be realised entirely within capitalism. As long as the expansion of capital is proportional to the growth of population — for the given levels of productivity — the capitalist mechanism creates its own market. As for the question whether the accumulation of capital encounters insuperable limits, Bauer’s answer is no:

This condition of equilibrium between accumulation and the growth of population can only be maintained, however, if the rate of accumulation rises sufficiently fast to enable the variable capital to expand as rapidly as population despite the rising organic composition of capital. (p. 869)

But can the rate of accumulation proceed so fast? Bauer does not pose this decisive question even once. He simply took the basic point at issue as something self-evident, as if the speed with which the rate of accumulation rises depended solely on the will of the capitalists. From his position it followed that capitalism would be destroyed not through any objective limits on the growth of accumulation but by the political struggle of the working class. The masses would be drawn to socialism only through painstaking, day-to-day educational work. Socialism can only be the product of their conscious will.

Tugan-Baranovsky showed some time back that a conception of this sort means giving up the materialist conception of history. If capitalism really could develop the productive forces of society without hindrance, the discontent of the working class would lack any psychological basis. He pointed out that if we hope for the downfall of capitalism purely in terms of the political struggle of the masses trained in socialism, then ‘the centre of gravity of the entire argument is shifted from economics to consciousness’ (1904, p. 274). Rosa Luxemburg wrote in similar terms some twelve years later:

If we assume, with the ‘experts’, the economic infinity of capitalist accumulation, then the vital foundation on which socialism rests will disappear. We then take refuge in the mist of pre-Marxist systems and schools which attempted to deduce socialism solely on the basis of the ‘injustice and evils of today’s world and the revolutionary determination of the working classes. (1972, p. 76)

Why was classical economy alarmed by the fall in the rate of profit despite an expanding mass of profit?

In Bauer’s scheme the portion of surplus value reserved for the individual consumption of the capitalists (k) represents a continuously declining percentage of surplus value. But it grows absolutely despite increasing accumulation from year to year, thereby providing the motive that drives capitalists to expand production. We might imagine that Bauer’s harmonist conclusions are confirmed by his table. The percentage fall in the rate of profit is of no concern because the absolute mass of profit can and does grow as long as the total capital expands more rapidly than the rate of profit falls. As Marx states:

the same development of the social productive power of labour expresses itself with the progress of capitalist production on the one hand in a tendency of the rate of profit to fall progressively and, on the other, in a constant growth of the absolute mass of the appropriated surplus value, or profit. (1959, p. 223)

And:

The number of labourers employed by capital, hence the absolute mass of the labour set in motion by it, and therefore the absolute mass of surplus labour absorbed by it, the mass of the surplus value produced by it, and therefore the absolute mass of the profit produced by it, can consequently increase, and increase progressively, in spite of the progressive drop in the rate of profit. And this not only can be so. Aside from temporary fluctuations it must be so, on the basis of capitalist production. (1959, p. 218)

If this is so, however, the question arises — why should the capitalist be so worried if the rate of profit falls as long as the absolute mass of his profit grows? To ensure this growth all he needs to do is to accumulate industriously; accumulate at a rate that exceeds the fall in the rate of profit. Moreover why was classical economy dominated by a deep sense of disquiet, of real ‘terror’ before the falling rate of profit? Why is it a veritable ‘day of judgement’ for the bourgeoisie (Marx, 1969, p. 544), why were Ricardo’s followers in ‘dread of this pernicious tendency’ (p. 541), why does Marx say that ‘his law is of great importance to capitalist production’ (1959, p. 213), why does he say that the law of the falling rate of profit ‘hangs ominously over bourgeois production’ (1969, p. 541) when, in contrast, vulgar economists ‘pointed self-consolingly to the increasing mass of profit’ (Marx 1959, p. 223)? The existing Marxist literature has no answer to any of these questions.

In other words is the falling rate of profit a real threat to capitalism? Bauer’s scheme appears to show the opposite. By the end of year four both the fund for accumulation and the fund for capitalist consumption have grown absolutely. And yet, precisely with Bauer’s scheme it will be shown that there are economic limits on accumulation, that Bauer’s harmonist conclusions about the possibilities of unlimited development represent a banal delusion.

The views of classical economists on the future of capitalism (D Ricardo and J S Mill)

Marx’s theory represented only the final stage of a fairly long development. It was directly linked to the theory of the classical economists and absorbed specific elements from the latter in a modified and deepened form. Ricardo had already reached the conclusion that due to the rising costs of basic means of subsistence the ‘natural tendency of profits then is to fall’ (1984, p. 71). Because profit is the motive behind capital the:

motive for accumulation will diminish with every diminution of profit, and will cease altogether when their [the capitalists] profits are so low as not to afford them an adequate compensation for their trouble and the risk they must necessarily encounter in employing their capital productively. (p. 73)

Ricardo viewed the distant future of capitalism with a sense of apprehension, stating that ‘if our progress should become more slow; if we should attain the stationary state, from which I trust we are yet far distant, then will the pernicious nature of these laws become more manifest and alarming’ (p. 63).

The roots of Ricardo’s theory of breakdown are discernible in the imperfect valorisation of capital that defines advanced stages of accumulation. The actual phenomenon, the tendency for the rate of profit to fall, was correctly perceived by Ricardo but he explained it in terms of a natural process rooted in the declining productivity of agriculture. Marx had only to replace this natural basis with a social one intrinsic to the specific nature of capitalism.

The theory of breakdown acquired a more developed form in the work of J S Mill despite the several distortions produced by his false theories of wages (the wage fund theory) and ground rent, his erroneous views on the relation of fixed capital to the level of the rate of profit, and by his general lack of clarity about the decisively important role of profit for the existence of capitalism. Mill viewed the ‘stationary state’ as the general direction of the advance of modem society but, unlike Ricardo, he contemplated the tendency with a sense of equanimity: ‘I cannot regard the stationary state of capital and wealth with the unaffected aversion so generally manifested towards it by political economists of the old school’ (Mill, 1970, p. 113). His standpoint was one of a petty-bourgeois reformism that sought to appease capital with the idea that a stationary state of capital would in no sense jeopardise the general progress of ‘human improvements’. In his utopianism Mill seems to have forgotten that the accumulation of capital is an essential condition of capitalist production, that the capitalists have not the least interest in human improvements; they are interested only in the level of profitability. In this respect Ricardo and his school showed a more correct understanding of the vital conditions of capitalism than Mill himself.

However if we ignore these obviously essential points we have to concede that Mill showed a far clearer insight into the breakdown tendency and its causes, as well as into many of its counteracting moments. Mill’s central argument is that if capital continued to accumulate at its existing rate and no circumstances intervened to raise its profits, only a short time would be needed for the latter to fall to the minimum. The expansion of capital would then soon reach its ultimate limit (pp. 94—7). A general overstocking of the market would occur. To Mill the basic difficulty was not the lack of markets but the lack of investing opportunities.

Counteracting circumstances can to some extent displace or postpone this ultimate limit. Among such circumstances Mill lists: 1) worsening conditions for workers, 2) devaluation or destruction of capital, 3) improvements in technology, 4) foreign trade that procures cheaper supplies of raw materials and means of subsistence, 5) export of capital to the colonies or to foreign countries. We shall go into these circumstances in more detail later.

A comparison between the sections in Capital Volume Three on the tendency of the rate of profit to fall and the theory of breakdown developed by Mill shows that Marx linked up his own theory to the one proposed by Mill. Even if Marx gave it a much deeper foundation and made it consistent with his law of value, Mill’s seminal role is indisputable. In its external structure it shows the same logical construction one finds in Ricardo and in Marx. Marx also tackles the problem in two stages - first the tendency towards breakdown, then the counteracting tendencies — and refers to the fact that the process of capital accumulation ‘would soon bring about the collapse of capitalist production if it were not for counteracting tendencies, which have a continuous decentralising effect alongside the centripetal one’ (1959, p. 246). Marx mentions all the counteracting tendencies adduced by Mill, even if he adds some others and to some extent ascribes a different theoretical meaning to them.

The Marxist theory of accumulation and breakdown

If we are going to discuss the tendencies of development of a system, in this case — along with Bauer — the tendency of accumulation to adjust to the growth of population, then it is not enough simply to look at one or two years. We have to view the development of the system over a much longer span of time. Bauer did not do this. He restricted his calculations to just four cycles of production. This is the source of his mistakes.[3]The problem is precisely whether accumulation under the conditions postulated by Bauer is possible in the long run. If Bauer had followed through the development of his system over a sufficiently long time-span he would have found, soon enough, that his system necessarily breaks down.

If we follow Bauer’s system into year 36, holding firm to all the conditions postulated by him, we see that the portion of surplus value reserved for capitalist consumption (k) which amounts to 86213 in the fifth year and grows over the following years, can only expand up to a definite high-point. After this it must necessarily decline because it is swallowed up by the portion of surplus value required for capitalisation.

The failure of valorisation due to overaccumulation

Despite the fall in the rate of profit accumulation proceeds at an accelerated tempo because the scope of accumulation expands not in proportion to the level of profitability, but in proportion to the weight of the already accumulated capital: ‘beyond certain limits a large capital with a small rate of profit accumulates faster than a small capital with a large rate of profit’ (Marx, 1959, pp. 250-l).[4]

We can see that after ten years the original capital expands from a value of 300 000 to 681 243, or by 227 per cent, despite a continuous fall in the rate of profit. In the second decade the rate of expansion of capital amounts to 236 per cent, although the rate of profit falls even further from 24.7 per cent to 16.4 per cent. Finally in the third decade the accumulation of capital proceeds still faster, with a decennial increase of 243 per cent, when the rate of profit is even lower. So Bauer’s scheme is a case of a declining rate of profit coupled with accelerated accumulation. The constant capital grows rapidly, it rises from 50 per cent of the total product in the first year to 82.9 per cent of the annual product by year 35. Capitalist consumption (k) reaches a peak in year 20 and from the following year on declines both relatively and absolutely. In year 34 it reaches its lowest level only to disappear completely in year 35.

It follows that the system must break down. The capitalist class has nothing left for its own personal consumption because all existing means of subsistence have to be devoted to accumulation. In spite of this there is still a deficit of 11 509 on the accumulated variable capital (a_v) required to reproduce the system for a further year. In year 35 Department Two produces consumer goods to a total value of 540 075 whereas, on Bauer’s assumption of a 5 per cent increase in population, 551 584 of variable capital is required.

Bauer’s assumptions cannot be sustained any further, the system breaks down. From year 35 on any further accumulation of capital under the conditions postulated would be quite meaningless. The capitalist would be wasting effort over the management of a productive system whose fruits are entirely absorbed by the share of workers.

If this state persisted it would mean a destruction of the capitalist mechanism, its economic end. For the class of entrepreneurs, accumulation would not only be meaningless, it would be objectively impossible because the overaccumulated capital would lie idle, would not be able to function, would fail to yield any profits: ‘there would be a steep and sudden fall in the general rate of profit’ (Marx, 1959, p. 251).

This fall in the rate of profit at the stage of overaccumulation is different from the fall at early stages of the accumulation of capital. A falling rate of profit is a permanent symptom of the progress of accumulation through all its stages, but at the initial stages of accumulation it goes together with an expanding mass of profits and expanded capitalist consumption. Beyond certain limits however, the failing rate of profit is accompanied by a fall in the surplus value earmarked for capitalist consumption (in our scheme this appears in year 21) and soon afterwards of the portions of surplus value destined for accumulation. ‘The fall in the rate of profit would then be accompanied by an absolute decrease in the mass of profit ... And the reduced mass of profit would have to be calculated on an increased total capital’ (Marx, 1959, p. 252).

This Marxist theory of the economic cycle which sees the growing valorisation of social capital as the determining cause of accumulation — of the upswing — and its imperfect valorisation as the cause of the downturn into crisis has been fully confirmed by recent empirical studies. W C Mitchell (1927) has shown for the United States, J Lescure (1910) for France, and Stamp (1918) for Great Britain, that in periods of boom profits show an uninterrupted rise, whereas in periods of crisis the level of profitability declines. However, the agreement is at a purely factual level. Lescure supposes that reductions in profitability are due to shifts in commodity prices and prime costs. He overlooks the fact that profitability depends on the magnitude of capital, that is, on the relationship between the rate of increase of profits and that of capital. Overaccumulation is possible, and at a specific stage of accumulation inevitable, even for a given level of commodity prices and a given level of prime costs. Further expansion of production can become unprofitable even if the level of profits remains the same, indeed even if it rises. To understand these complicated relationships it is not enough simply to observe the movement of prices. A more sophisticated method is required, and here the assumption of constant prices for all elements of cost is crucial to the exactness of the investigation. Variations in costs (means of production, wages, interest) only encourage or constrain phases of boom or stagnation, they do not actually produce these phases themselves.

The formation of the reserve army of labour and of idle capital due to overaccumulation

Imperfect valorisation due to overaccumulation is, however, only one side of the accumulation process; we have to look at its second side. Imperfect valorisation due to overaccumulation means that capital grows faster than the surplus value extortable from the given population, or that the working population is too small in relation to the swollen capital. But soon overaccumulation leads to the opposite tendency.

Towards the closing stages of the business cycle the mass of profits (s), and therefore also its accumulated constant (a_c) and variable (a_v) portions, contract so sharply that the additional capital is no longer sufficient to keep accumulation going on the previous basis. It is therefore no longer sufficient to enable the process of accumulation to absorb the annual increase in population. Thus in year 35 the rate of accumulation requires a level of 510 563 a_c + 26 265 a_v = 536 828. But the available mass of surplus value totals only 525 319. The rate of accumulation required to sustain the scheme is 104.6 per cent of the available surplus value; a logical contradiction and impossible in reality.

From this point onwards valorisation no longer suffices to enable accumulation to proceed in step with the growth of population. Accumulation has become too small, which means that a reserve army is inevitably formed and grows larger year by year. Given our analysis of the reproduction process in terms of a schematic model whose presupposition is dynamic equilibrium, there can, by definition, be no surplus population or reserve army of labour. The latter emerges only at an advanced stage of accumulation and as its product The assumption which is made initially can no longer be sustained and is violated. The extension of Bauer’s scheme shows that in year 35 there are 11 509 unemployed workers who form a reserve army.

In addition, because only a part of the working population now enters the process of production, only a part of the additional constant capital (510 563 a_c) is required for buying means of production. The active population of 540 075 requires a total constant capital of 5499015; the result is that 117 185 represents a surplus capital with no investment possibilities.

The scheme is a lucid exposition of the condition Marx had in mind when he called the corresponding section of Capital Volume Three ‘Excess Capital and Excess Population’ (pp. 250—9). Overaccumulation, or imperfect valorisation, ensues because the population base is too small. And yet there is overpopulation, a reserve army. We cannot speak of a logical contradiction here. ‘The so-called plethora of capital’, Marx writes:

always applies essentially to a plethora of capital for which the fall in the rate of profit is not compensated through the mass of profit ... This plethora of capital arises from the same causes as those which call forth relative overpopulation, and is, therefore, a phenomenon supplementing the latter, although they stand at opposite poles — unemployed capital at one pole, and unemployed worker population at the other. (1959, p. 251)

And a few pages later:

It is no contradiction that this overproduction of capital is accompanied by more or less considerable relative overpopulation. The circumstances which increased the productiveness of labour, augmented the mass of produced commodities, expanded markets, accelerated accumulation of capital both in terms of its mass and its value, and lowered the rate of profit — these same circumstances have also created, and continuously create, a relative overpopulation, an overpopulation of labourers not employed by the surplus capital owing to the low degree of exploitation at which alone they could be employed, or at least owing to the low rate of profit they would yield at the given degree of exploitation. (p. 256)[5]

A classic illustration is the United States today (March 1928) where, together with a superfluity of capital, shortage of investment opportunities and massive speculation in real estate and shares, there is a surplus working population of 4 million unemployed workers. This not because too much surplus value has been produced but because in relation to the accumulated mass of capital too little surplus value is available.

The fact that the means of production, and the productiveness of labour, increase more rapidly than the productive population, expresses itself, therefore, capitalistically in the inverse form that the labouring population always increases more rapidly than the conditions under which capital can employ this increase for its own self-expansion (Marx, 1954, p. 604).

We must be careful to distinguish the formation of the reserve army due to a crisis of valorisation from the ‘setting free’ of workers through machinery. The displacement of workers by machinery, which Marx describes in the empirical part of Capital Volume One (Chapter 15, ‘Machinery and Modem Industry’), is a technical fact produced by the growth of M relative to L and as such is not a specifically capitalist phenomenon. All technological advance rests on the fact that labour becomes more productive, that it is economised — or set free — in relation to a given product. That machinery sets free labour is an incontrovertible fact that needs no proof; it belongs to the very concept of machinery as a labour saving means of production. This process of the setting free of workers will occur in any mode of production, including the planned economy of socialism.

From this it follows that Marx could not possibly have deduced the breakdown of capitalism from this technical fact. In Chapter 25 of Capital Volume One, where Marx derives the general law of capitalist accumulation, the setting free of the worker through the introduction of machinery is not mentioned. Here what Marx emphasises are not the changes in the technical composition of capital (ML) but changes in the organic composition of capital (c:v): ‘The most important factor in this inquiry is the composition of capital and the changes it undergoes in the course of the process of accumulation’ (Marx, 1954, p. 574). Marx adds that: ‘Wherever I refer to the composition of capital, without further qualification, its organic composition is always understood’ (p. 574).

The technical composition forms only one aspect of the organic composition; the latter is something more. It is the value composition of capital as it is determined by, and reflects, changes in the technical composition. Consequently Marx converts the technical side of the labour process, the relation M:L, into a value relation, c.v. Under capitalism, the means of production M and L figure as components of capital, as values, and they have to be valorised, that is, yield a profit.

The valorisation process, and not the technical process of production, is the characteristic driving force of capitalism. Wherever valorisation falters the production process is interrupted, even if from the standpoint of the satisfaction of needs production as a technical process may be desirable and necessary. The existing literature has totally ignored the fact that the process of setting free labour that Marx describes in the chapter on accumulation, and which is reflected in the formation of the reserve army, is not rooted in the technical fact of the introduction of machinery, but in the imperfect valorisation of capital specific to advanced stages of accumulation. It is a cause that flows strictly from the specifically capitalist form of production. Workers are made redundant not because they are displaced by machinery, but because, at a specific level of the accumulation of capital, profits become too small and consequently it does not pay to purchase new machinery and soon. Profits are insufficient to cover these purchases anyway.

The portion of surplus value destined for accumulation as additional constant capital (a_c) increases so rapidly that it devours a progressively larger share of surplus value. It devours the portion reserved for capitalist consumption (k), swallows up a large part of the portion reserved for additional variable capital (a_v) and is still not sufficient to continue the expansion of constant capital at the postulated rate of 10 per cent a year. In year 1 the accumulated constant capital (a_c) amounts to 20 per cent of the disposable surplus value of 100 000. By year 35 it climbs to 510 563, or to over 97 per cent of the disposable surplus value. Full employment requires a residue of surplus value amounting to 26 265. But only 14 756 survives as a residue to cover wages. For the capitalists’ consumption nothing remains. The disposable mass of surplus value does not suffice to secure the valorisation of the swollen capital. Because 11 509 workers remain unemployed in the following year, the expanded capital now operates on a reduced valorisation base.

Long before this final point is reached, already from year 21 onwards when capitalist consumption begins to decline absolutely, accumulation will have lost all meaning for the capitalist. Each further advance in accumulation means a further absolute reduction in capitalist consumption. The vital importance of capitalist consumption to the continued existence of capitalism is evident only at this point. For accumulation to occur, surplus value must be deployable in a threefold direction and must be divided into three corresponding fractions:

i)         additional constant capital (a_c)

ii)        additional variable capital (a_v) or additional means of subsistence for workers

iii)       a consumption fund for the capitalists (k)

Each of these three fractions is equally essential to the further expansion of production on a capitalist basis. If the available surplus value could cover only the first two, accumulation would be impossible. For the question necessarily arises — why do capitalists accumulate? To provide additional employment to workers? From the point of view of capitalists that would make no sense once they themselves get nothing out of employing more workers.

From the point of view of the distribution of income, such a mode of production would end up losing its private capitalist character. Once the k portion of surplus value vanishes, surplus value in the specific sense of an income obtained without labour would have disappeared. The other two fractions of surplus value, the additional constant capital (a_c) and the additional variable capital (a_v), retain their character of surplus value only so long as they are means for the production of the consumption fund of the capitalist class. Once this portion disappears, not an atom of unpaid labour falls to the share of the capitalists. For the entire variable capital falls to the share of the working class, once the means of production have been replaced out of it. Surplus value in the sense of unpaid labour, of surplus labour over and above the time required to produce essential means of subsistence, would have vanished. All means of consumption would now form necessary means of consumption. So it follows that the k portion is an essential characteristic condition of the accumulation of capital.

The vacuous and scholastic manner in which Luxemburg argues is apparent now. Contemptuously she dismisses this element from her analysis:

And yet, the growing consumption of the capitalists can certainly not be regarded as the ultimate purpose of accumulation; on the contrary, there is no accumulation in as much as this consumption takes place and increases; the personal consumption of the capitalists must be regarded as simple reproduction. (1968, p. 334)

Luxemburg does not bother to explain how under simple reproduction the consumption of the capitalists can actually grow in the long run. Regarding the purpose of accumulation Marx tells us that the aim of the entire process ‘does not by any means exclude increasing consumption on the part of the capitalist as his surplus value ... increases; on the contrary, it emphatically includes it’ (1956, p. 70). But to Luxemburg accumulation only seems to make sense if the consumption of capitalist commodities is left to the non-capitalist countries. This belongs completely in the tradition of mercantilism:

we find that certain exponents of the mercantile system ... deliver lengthy sermons to the effect that the individual capitalist should consume only as much as the labourer, that the nation of capitalists should leave the consumption of their own commodities, and the consumption process in general, to the other, less intelligent nations. (Marx, 1956, p. 60)

Obviously Marx had anticipated the whole of Luxemburg’s theory.

We should not suppose, however, that the capitalist simply waits passively until the entire k portion has been swallowed up. Long before any such time (at latest from in the scheme when the k portion begins to decline absolutely) he will do his utmost to halt the tendency. In order to do this he must either cut the wages of the working class or cease to observe the conditions postulated for accumulation, that is, the condition that constant capital must expand by 10 per cent annually to absorb the annual increase in the working population at the given technological level. This would mean that from now on accumulation would proceed at a slower rate, say 9.5 or 8 per cent. The tempo of accumulation would have to be slowed down, and that, too, permanently and to an increasing degree. In that case accumulation would fail to keep step with the growth of the population. Fewer machines and so on would be required or installed, and this only means that the productive forces would be constrained from developing.

It also follows that from this point in time on a growing reserve army would necessarily form. The slowing down of accumulation and the formation of the industrial reserve army must necessarily follow even if wages are assumed to be constant throughout this period. At any rate, it would not be the result of an increase in wages, as Bauer supposes.

Marx’s theory of breakdown is also a theory of crises

The Marxist theory of accumulation described here comprises not only a theory of breakdown but also a theory of crises. Previous writings on Marx could not come to terms with the essence of his theory due to their lack of understanding of the method that underlies Marx’s analysis and the structure of his magnum opus. The objection has repeatedly been made that, despite its crucial role in his system, Marx nowhere ever produced a comprehensive description of his theory of crisis, that he made scattered conflicting attempts at an explanation in various passages of the book. This objection rests on a crude misunderstanding. The object of Marx’s analysis is not crisis, but the capitalist process of reproduction in its totality. Given his method of investigation Marx examines the unending circuit of capital and its functions through all the phases of the process of reproduction. Expressed in a formula this would mean:

Circuit one:

Circuit two: etc

Analysing each of the phases of capital in its circuit as money capital, productive capital and commodity capital, Marx asks: what impact do they have on the process of production, can this process advance smoothly, or does the normal course of reproduction encounter disruptions in its various phases? If so what sort of obstacles, and what are the factors that hinder the reproduction process in a given phase?

One consequence of this method of investigation is that Marx is compelled to return to the problem of crises at various places in his work, in order to assess the specific impact of each of the individual factors that come into play in the different phases of the circuit. A systematic description of the role of all these factors will have to be reserved for my major study. Given the specific object of this investigation I shall examine the impact of one factor alone, even if it is the decisively important one - the accumulation of capital from the standpoint of crises. I shall be looking at the effects of the fact that a given capital which began its first circuit as M (money capital), opens up its second circuit as M’ (expanded money capital).

Figure 1

I have shown that as long as no counteracting or modifying tendencies intervene, the effects are such that from certain exactly determinable level of capital accumulation they have to lead to a breakdown of the system. In the coordinate system OX and OY (Figure 1), if the line OX represents a condition of ‘normal valorisation’ and OZ the line of accumulation in accordance with this equilibrium condition, then the crisis of valorisation can be expressed as a deviation of the line of accumulation in the direction ZS. This would be the tendency towards breakdown, the basic tendency of the system or its ‘trend’.

Figure 2

Let us suppose that in our coordinate system the breakdown sets in at point z₁(Figure 2) and manifests itself in the form of an enormous devaluation of capital whose overaccumulation starts at r₁(this is represented graphically by the punctuated line z₁ —  o₁). In that case the overaccumulated capital will be reduced back to the magnitude required for its normal valorisation, and the system will be brought back to a new state of equilibrium at the higher level o₁ —  z₁.

We know that in Marx’s conception crises are simply a healing process of the system, a form in which equilibrium is again re-established, even if forcibly and with huge losses. From the standpoint of capital every crisis is a ‘crisis of purification’. Soon the accumulation process picks up again, on an expanded basis, and within certain limits (for instance, o₁—r₂) it can proceed without any disruption of equilibrium. But ‘beyond certain limits’, from point r₂on, the accumulated capital again grows too large. The mass of surplus value starts to decline, valorisation begins to slacken until finally, at point z₂, it evaporates completely in the way described earlier. The breakdown sets in again and is followed by devaluation of capital, z₂—o₂, and so on.

If we can show that due to various counteracting tendencies the unfettered operation of the breakdown tendency is repeatedly constrained and interrupted (at points z₁, z₂, z₃ ... ) then the breakdown tendency will not work itself out completely and is, therefore, no longer describable in terms of an uninterrupted straight line ZS. Instead it will break up into a series of fragmented lines (O —z₁—o₁, o₁—z₂—o₂, o₂—z₃—o₃...) all tending to the same final point. In this way the breakdown tendency, as the fundamental tendency of capitalism, splits up into a series of apparently independent cycles which are only the form of its constant, periodic reassertion. Marx’s theory of breakdown is thus the necessary basis and presupposition of his theory of crisis, because according to Marx crises are only the form in which the breakdown tendency is temporarily interrupted and restrained from realising itself completely. In this sense every crisis is a passing deviation from the trend of capitalism.

Despite the periodic interruptions that repeatedly defuse the tendency towards breakdown, the mechanism as a whole tends relentlessly towards its final end with the general process of accumulation. As the accumulation of capital grows absolutely, the valorisation of this expanded capital becomes progressively more difficult. Once these countertendencies are themselves defused or simply cease to operate, the breakdown tendency gains the upper hand and asserts, itself in the absolute form as the final crisis.[6]

An anti-critical interlude

The passing of booms and the turn to depression is frequently explained in terms of a series of factors that push costs of production up, reduce profitability and dampen business activity. This is the view of G Cassel who gets stuck at the surface level and cannot grasp the deeper connections, the essence underlying the appearances. It is obvious that increases in costs of production do threaten profitability and can intensify the crisis. But this factor only accelerates the formation of a crisis, it does not produce the crisis itself.

The methodological significance of the analysis proposed here is that it forestalls any such attempt to displace the problem or to drive it into secondary issues. Interest and its fluctuations are excluded from the analysis; we are concerned with a total surplus value that has not yet split into its several portions. Rising prices are likewise excluded; by assumption commodities sell at value. The same is true of the commodity labour power; by assumption workers receive only the value of their labour power in the course of accumulation. And in spite of all this the process of capital accumulation grinds to a halt. The crisis ensues. Its formation is thus independent of the various price movements.

The real problem, the essence of the appearances, emerges in its pure form only through abstraction from all these subsidiary moments. The accumulation of capital is too large — there is absolute overaccumulation —because valorisation is insufficient. Is such a description only correct from a purely abstract logical point of view; is it reconcilable with the facts of experience? Does the accumulation process really come to an end due to overaccumulation of capital? Cassel assures us that even in the final stages of the business cycle there is never a superfluity of fixed capital (1923, p. 579). There is no overaccumulation of capital but rather a capital shortage, an insufficient supply of capital. So does our theory of accumulation contradict the facts of experience?

Cassel argues that the origin of crises lies in a ‘wrong calculation’ by businessmen of the future state of the capital market or of the supply of savings that will be forthcoming to match their investment schedules. Apart from the purely psychological character of this theory, it simply obscures matters. The supply of capital is too small. But what capital is Cassel talking about? Obviously not about the already accumulated and functioning capital. Since he refers to a future supply of savings, he can only be meaning the additional capital that has still to be accumulated and which is symbolised in the scheme by the magnitudes a_c and a_v.

What is the source of the supply of this capital? Why is there a shortage of this capital? Instead of pursuing the formation of this capital to its birthplace — the sphere of production — Cassel gets bogged down in the sphere of circulation. Before it is saved it has to be produced. It is produced by the workers and appropriated by the capitalist as surplus value. This future capital forms only a portion of the surplus value, the portion that is not consumed but destined for accumulation. To say that this additional capital is increasingly in short supply as accumulation progresses only means that in the course of accumulation the primordial source of this capital, surplus value, becomes progressively more scarce, too small, in relation to the already accumulated mass of capital. If the mass of surplus value is too small then so is the portion destined for purposes of accumulation.

Cassel simply mixes up concepts. He speaks of a capital shortage, an insufficient supply of capital. In the language of the banker everything is capital. But Cassel is not talking about capital, but about a part of surplus value that still has to be accumulated, a part that represents capital only potentially and becomes capital only through its function in the valorisation process. So really there is not a shortage of capital, but a shortage of surplus value. In contrast, there is an overaccumulation of the already functioning capital. Overproduction of capital and imperfect valorisation are correlative concepts each of which determines the other.

A capital that fails to fulfil its function of valorisation ceases to be capital; hence its devaluation. The devaluation of capital is here a necessary, logical consequence of its insufficient valorisation. it is otherwise with Cassel. He too refers to a ‘sudden devaluation of fixed capital’ due to capital shortage. He speaks of devaluation because in reality such a phenomenon exists, and theory must take some stand in relation to it. But Cassel cannot account for the fact of devaluation in terms of his theory. It bears no logically necessary connection with it. From Cassel’s theory of crises it is in fact impossible to derive an explanation of the devaluation of capital. Given his subjective theory of prices how can capital be ‘devalued’ if it is in short supply? On the other hand, in Marx’s theory imperfect valorisation and devaluation of the original capital stand in a close logical connection.

A definitive answer to the question raised by Diehl is also possible only now. He asked if there was any necessary relationship between Marx’s theory of value and surplus value and socialism. He argued no, despite conceding that profit, ground-rent, etc. are rooted in the surplus value extorted from workers. But no socialist conclusions necessarily follow as long as we suppose that surplus value is indispensable to technical and economic progress.

What a fantastic misunderstanding. Surely it is not a question of moral assessment of surplus value but of the variations in its magnitude that decide what civilising role it plays. As the possibility of valorisation disappears surplus value ceases to play any such role; it ceases to develop the productive forces of society and capitalism must necessarily make way for a higher form of production. Marx showed that given its dynamic basis in the law of value, capital accumulation runs up against definite limits, that is, it bears a transitory character because in the long run the surplus value does not suffice for the valorisation of c and v.

Oppenheimer is one of the sharpest and best known recent critics of Marx’s law of accumulation. He says: ‘Honestly speaking it can no longer be disputed that ... Marx’s law of capitalist accumulation and his deduction of the reserve army are logically erroneous and that therefore his definition of the tendency of capitalist development is false’ (1923, p. 1098). But Oppenheimer’s mistakes are strikingly obvious when we compare what he means by the Marxist theory of accumulation with the one presented here. The elegant deductions characteristic of a sharp thinker fail completely here.

He vacillates in his characterisation of the theory of accumulation. Sometimes he sees it purely as a product of Hegel’s dialectic of contradiction: ‘The solution Marx proposed flowed from his application of the “dialectical method” (Oppenheimer, 1919, p. 115). According to him the theory of breakdown, which he agrees is the ‘pillar of Marx’s whole economics and sociology’ (p. 137), flows not from an analysis of capitalism but from an application of Hegel’s dialectical method. But elsewhere Oppenheimer states that the problem Marx was concerned with was not resolvable purely by deduction. Marx’s theory of the inevitable growth of a reserve army was, according to Oppenheimer, based on a purely empirical ‘impression’ that he gained from a study of British capitalism (Oppenheimer, 1903, p. 56). Yet the Marxist theory of accumulation was established by way of a deduction which he calls ‘an imposing deduction’ (1919, p. 144), a ‘gigantic effort’ (p. 146), a ‘solution attempted in the grand style’ (p. 135). All of this only shows that Oppenheimer has overlooked the real content of Marx’s theory.

The imperfect valorisation of the accumulated capital, in Marx the decisive phenomenon that destroys the capitalist mechanism from the inside, is not mentioned by Oppenheimer even once. Instead Oppenheimer brings in two elements that have nothing to do with Marx’s theory of accumulation.[7]

The first is ‘that machinery sets free workers’ (1919, p. 137). 1 have already drawn out the difference between the displacement of workers by machinery and their being set free in the very process of accumulation. Oppenheimer confuses these phenomena. Machinery displaces the worker. Hence Marx supposedly argues that the productive process creates ‘a chronic relative overpopulation’, which leads to a permanent oversupply of labour power that pins wages down to the minimum.

The process of setting free that Marx discusses in the chapter on accumulation is something quite different from displacement by machinery. Its cause is the accumulation of capital; that is, insufficient valorisation at a definite, advanced stage of accumulation. Down to this point the number of workers grows absolutely: ‘With the growth of the total capital, its variable constituent or the labour incorporated in it, also does increase’ (Marx, 1954, p. 590). But with accumulation it increases ‘in a constantly diminishing proportion’ (p. 590) until at a specific level of accumulation its growth ceases completely and turns into ‘a relatively redundant working population, i.e., a population of a greater extent than suffices for the average needs of the self expansion of capital, and therefore of surplus population’ (p. 590).

Oppenheimer misses the point completely because he ignores the basic difference between the technical labour process and the capitalist valorisation process. Machinery in relation to labour power (M:L) and constant capital in relation to variable (c:v) represent two absolutely different categories and to confuse them is to end up in serious mistakes. It was from the ‘social form’ and not from the technical application of the real means of production that Marx deduced the necessary end of the accumulation process.

Oppenheimer’s interpretation of the theory of the reserve army in the sense of a chronic overpopulation is quite false. What prevails instead is the law of the alternative attraction and repulsion of workers, so that the absolute number of workers who find employment and are later thrown off can, and does, increase: ‘in all spheres, the increase of the variable part of capital, and therefore of the number of labourers employed by it, is always connected with violent fluctuations and transitory production of a surplus population’ (Marx, 1954, pp. 590—1). So it is not a question of chronic overpopulation, as Oppenheimer supposes, but of the periodic reforming and reabsorption of the reserve army within the production cycle: ‘The course characteristic of modern industry, namely, a decennial cycle depends on the constant formation, the greater or less absorption, and the re-formation of the industrial reserve army or surplus population’ (Marx, 1954, pp. 592—3). It follows that the absolute number of workers can grow and indeed must grow if accumulation or expanded reproduction is to occur.

The second so-called premise of Marx’s deduction is the classical wages fund theory (Oppenheimer, 1919, p. 138). According to Oppenheimer, Marx ‘took over this theory in its decisive aspects’ (p. 141). ‘The classical theory derived all prices from supply—demand relations, and resolved the problem of wages, i.e., of the price of labour on the same basis’ (p. 138).

So Marx is supposed to have resolved the problem of wages in terms of supply and demand. I have shown the complete untenability of this view elsewhere (Grossmann, 1926, p. 180). Marx’s theory of wages is only a special case of the theory of value applied to the commodity labour power. Just as in value theory the determination of the magnitude of value proceeds quite independently of competition, or supply and demand, the same is true for Marx’s theory of wages.

In Marx the wage is determined by the reproduction costs or value of labour power which is independent of competition. Because Oppenheimer fails to understand this determination of wages in terms of value, the factor which, according to Marx, exerts an upward pressure on real wages in the course of capitalist development — namely, the growing intensity of labour - likewise escapes him. This is why he can arrive at the patently false conclusion that in the Marxist system wages ‘can never rise above their lowest point’ (1919, p. 149).

Since Oppenheimer’s description of Marx’s theory of wages as a wage fund theory is absolutely false, the criticisms he develops of Marx’s theory of accumulation from this particular aspect also crumble. To demonstrate the inevitable formation of a reserve army Marx hardly needed to refer to supply and demand relations. In his system the reserve army of labour is a result of the process of reproduction at a late stage of accumulation not, as Oppenheimer supposes, a permanent precondition for the reproduction of the capital relationship. Given the nature of Marx’s simplifying assumptions, the reserve army can be deduced as a necessary consequence of ‘accumulation or of the development of wealth on a capitalist basis’ (1954, p. 592). Once it has come into being this surplus population ‘becomes, conversely, the lever of capitalist accumulation, nay, a condition of existence of the capitalist mode of production’ (p. 592).

The existence of the reserve army is a vital condition for empirically given capitalism, but not by way of reproducing the capital relationship so much as to make possible sudden expansions of production, because: ‘In all such cases, there must be the possibility of throwing great masses of men suddenly on the decisive points without injury to the scale of production in other spheres. Overpopulation supplies these masses’ (p. 592). Initially, however, Marx takes as the object of his analysis not this empirically real capitalism with its sudden expansions, but the ideal trajectory of capitalist production, and so he is perfectly justified in excluding the reserve army from his analysis in the initial stages.

Now we come to Oppenheimer’s description of Marx’s ‘proof procedure’. What is the basic meaning of Chapter 25 of Capital Volume One on ‘the general law of capitalist accumulation’? Oppenheimer takes it to mean that the existence of a reserve army is a crucial precondition of the reproduction of the capitalist relationship. This is completely wrong. The existence of capital itself — of the separation of the worker from the means of production — is quite sufficient for the reproduction of the capitalist relationship. A reserve army is not crucial in this respect.

Oppenheimer is preoccupied with the problem of the setting free of workers through machinery and misses the basic point in Chapter 25. His myopic concentration on machinery precludes him from ever tackling the problem of insufficient valorisation due to accumulation. He deals with the latter only in passing, and even then entirely from the standpoint of the subjective experience of the individual capitalist. Again Oppenheimer overlooks the fact that Marx does not directly analyse empirical reality; in the chapter on accumulation the object of his analysis is surplus value and its variations of magnitude, whereas reality only confronts us with the individual parts into which surplus value splits up (interest, profit, rent, commercial profit, etc). Surplus value is only a theoretical form of totalising these individual parts that confront us in reality.

Marx’s proof procedure has the character of a deduction. With respect to deductions of this nature Oppenheimer makes an excellent comment ‘Any appeal to experience is quite inadmissible. A deduction is not validated because its results conform to experience’ (1919, p. 150). But in his critique of Marx’s deduction Oppenheimer appeals precisely to experience. Marx has to deduce a specific phenomenon, the imperfect valorisation of the total social capital, from the very conditions of accumulation. Against Marx’s demonstration that in the course of accumulation the shortage of surplus value brings accumulation to a standstill, Oppenheimer replies that ‘experience teaches us that as interest declines accumulation proceeds all the more vehemently’ (p. 149). Oppenheimer equates the shortage of surplus value, or imperfect valorisation, with a declining rate of interest. The rate of interest may decline to any level, but not surplus value. Interest is only an individualised portion of profit. Thus if interest falls, the entrepreneur’s profit rises.

Suppose interest were to fall due to an oversupply of loan capital. What would be the result? Loan capital would flow into production, and the money capitalist would be transformed into an industrial capitalist. All that would result is a redistribution of capital. The matter is quite different when we look at the total surplus value, and total social capital. Once surplus value declines below certain exactly calculable limits capital accumulation necessarily breaks down, due to the defective valorisation of capital. The result would be an extraordinary devaluation of capital. Oppenheimer presents matters as if accumulation and its scale depend solely on the good will and psychology of the saver. He ignores the objective conditions — the magnitude of the disposable surplus value — which determine the limits of the scale of accumulation. Oppenheimer knows no such limits to the accumulation of capital. He supposes that workers displaced by machinery can be reabsorbed as long as accumulation is sufficiently rapid.

Oppenheimer overlooks the essential question — that for a given size of population and rate of surplus value is the requisite scale and tempo of accumulation possible in the long run? I would say ‘no’ and I have tried to demonstrate this exactly as is possible within the limits of deduction. Oppenheimer cites three possible forms through which the accumulation of capital can compensate for the retrenchments.

i)         Partial compensation where there is more retrenchment in certain industries than redeployment in others.

ii)        Full compensation where retrenchment and redeployment are equal.

iii)       Overcompensation where redeployment is greater.

Oppenheimer then asks:

Which of these three cases is the actual one? This problem cannot be resolved through more deduction: it is an equation with several unknowns. It can only be solved with figures: one would have to compare the number of unemployed at different points in time. (1903, p. 56)

He adds that there was hardly any statistical data available to Marx to decide the question. As neither deduction nor empirical proof was possible he was left with an impression that the reserve army tends to increase.

So according to Oppenheimer the fundamental law of the Marxist system was an illicit generalisation of vague empirical impressions. The entire argument is untenable. Marx’s theory of breakdown was neither a generalisation from purely empirical observations nor an elaboration of Hegel’s dialectic of contradiction. It was derived through deduction as a self-evident consequence of the accumulation of capital on the basis of the law of value. Oppenheimer’s statement that the problem is not soluble by deduction is contradicted by the fact that I have used a concrete numerical example to provide an actual solution and, as we shall see, this is also possible mathematically. As far as empirical relationships are concerned there may very well be a difficulty of an equation with several unknowns. But no such difficulty exists for theory. Through the simple procedure of making certain assumptions theory can transform all unknown variables into known quantities which are also measurable.

The scheme developed earlier proceeds from a state of equilibrium where despite a rising organic composition of capital, the retrenchment of workers is cancelled by their redeployment. And yet this state is only possible for a certain period of time. At a certain point accumulation becomes impossible on the basis assumed because it runs up against limits to valorisation; Oppenheimer’s second case is transformed into his first case. At this late stage of accumulation the retrenchment of workers dominates over their redeployment not due to the action of machinery, but due to imperfect valorisation. The available surplus value does not suffice to keep accumulation going on the necessary scale.

Oppenheimer abstains from presenting any deductive counterproof against Marx and relies purely on empirical facts. But Oppenheimer himself knows that we cannot arrive at a theory through simple experience. Marx could quite easily agree that from time to time overcompensation has occurred in industry. But this would not in the least affect the Marxist law of accumulation and breakdown. Indeed additional labour power is a necessary constitutive part of the very concept of accumulation. The entire system is constructed on the notion of surplus value, on the greatest possible intensive and extensive exploitation of labour power. By its very nature capital strives to employ the largest number of workers. Marx himself notes that, on the whole, the number of workers employed in industry grows not only absolutely but as a ratio of the total population. As the population base expands the upper limits of capital accumulation are pushed back. This is one form in which the breakdown tendency is defused and postponed to the future (See Chapter 3, section 13). Nevertheless it follows from the law of accumulation that for a given size of working population capital accumulation encounters insuperable limits, beyond which any further accumulation is pointless.

Naturally the internal consequences of accumulation are always interrupted and neutralised by modifying circumstances. Hence the periodic, cyclical alteration of phases of expansion and breakdown. However if we abstract from the alternating attraction and repulsion of workers in the course of the industrial cycle, and follow through only the secular tendency of development, we shall have to conclude that in the initial stage of capital accumulation population was, on the whole, too large in relation to the existing scale of accumulation. Hence Malthus and Malthusianism. In the late stage of accumulation the inverse relationship dominates. In relation to the enormous accumulation of capital, population — the base for valorisation — becomes increasingly smaller. Hence the sharpening tensions in the advanced capitalist countries in the course of accumulation, the increasing role of capital exports, the ever more brutal expansionist tendencies of capital to secure the largest possible reserves of human labour power. But here capitalism runs into obstacles. The world is already divided up. The economic displacement of large masses of people encounters difficulties. And so the very tendencies that defuse the breakdown are themselves defused, and the breakdown intensifies.

K Muhs’s critique of Marx (1927) shows not the slightest trace of originality. He simply draws together the arguments developed by others. Like them he ignores the decisively important passages of Capital Volume Three on the falling rate of profit. With Oppenheimer he agrees that Marx’s theory of accumulation has an empirical basis. This is then criticised empirically. The superficiality of this method is perfectly obvious. Totally incapable of mobilising a single theoretical argument to launch a frontal attack on the law of accumulation, Muhs tries to finish off the theory through an empirico-statistical detour. The expansion of population in industrialised countries is supposed to refute the theory that workers are set free in the course of accumulation. But theory? There is not the least trace of any theory in Muhs.

On the other hand the process of breakdown described above should not be confused either with the limits to accumulation that Bauer talks about. So as not to be taken for an apologist of capital, Bauer claims that he has discovered a limit to the accumulation of capital. This limit is set by: (i) the proportionality between the two departments of the reproduction scheme and (ii) the rate of growth of population at a given level of productivity. Variable capital has to be accumulated in a specific proportion to increases in population. This prescribes the limits to the growth of constant capital since there is likewise a specific proportionality between constant and variable capital. The proportionality c:v is the limit Bauer discusses. If the constant capital expands at a faster rate than that required in terms of its proportional relation to variable capital the result will be overaccumulation of capital. A slower rate means underaccumulation.

Crises arise only because the necessary proportionality between accumulation and population is not maintained. As long as accumulation proceeds within these limits, it can advance indefinitely under the assumptions made. Bauer speaks of ‘overaccumulation’. But this occurs only because the conditions specified by him are violated. In fact he argues that these conditions can be maintained even in the long run and the very mechanism of capital ensures that all disturbances of equilibrium are automatically corrected: ‘Like underaccumulation, overaccumulation is only a passing phase of the industrial cycle’ (Bauer, 1913, p. 870).

In my description the process is totally different. I have shown that even if all conditions of proportionality are maintained and accumulation occurs within the limits imposed by population, the further preservation of these limits is objectively impossible. The system of production described in Bauer’s own scheme has to breakdown or the conditions specified for the system have to be violated. Beyond a definite point of time the system cannot survive at the postulated rate of surplus value of 100 per cent. There is a growing shortage of surplus value and, under the given conditions, a continuous overaccumulation. the only alternative is to violate the conditions postulated. Wages have to be cut in order to push the rate of surplus value even higher. This cut in wages would not be a purely temporary phenomenon that vanishes once equilibrium is re-established; it will have to be continuous. After year 36 either wages have to be cut continually and periodically or a reserve army must come into being.

This would not be one of those periodic crises within the system that Bauer refers to, for a crisis of this sort could always be surmounted by adjusting the scale of the productive apparatus to the available population. Here there is no more room for adjustments. The proportionality conditions required by Bauer have been preserved throughout and still after year 35 a crisis, a tendency towards breakdown, sets in. The real dynamic of the capitalist system is quite different from what Bauer supposes. He maintains that capitalism is characterised by a ‘tendency for the accumulation of capital to adjust to the growth of population’ (p. 871). I have shown the opposite — there is a tendency towards an absolute overaccumulation of capital that outstrips the limits imposed by population.

The same hold for Tugan-Baranovsky. He believes that

If social production were organised according to a plan, if those in charge of it had a perfect knowledge of demand and the power to shift labour and capital freely from one branch of production to another, the supply of commodities would never exceed the demand (Tugan-Baranovsky, 1901, p. 33).

Bauer’s scheme represents precisely this kind of planned, organised production in which the managers know all they need to about demand and have the power to adapt production to demand. In spite of this a tendency towards breakdown emerges, valorisation declines absolutely and a reserve army forms. This only shows that the problem is not whether there is a surplus of commodities or not. In fact we have assumed a state of equilibrium where, by definition, there can be no unsaleable residue of commodities. Yet still the system must break down. The real problem lies in the valorisation of capital; there is not enough surplus value to continue accumulation at the postulated rate. Hence the catastrophe.

Obviously, as Lenin correctly remarks, there are no absolutely hopeless situations. In the description I have proposed the breakdown does not necessarily have to work itself out directly. Its absolute realisation may be interrupted by counteracting tendencies. In that case the absolute breakdown would be converted into a temporary crisis, after which the accumulation process picks up again on a new basis. In other words the valorisation of the overaccumulated capital can be met through capital exports to countries at a lower stage of accumulation. Or a sharp devaluation of the constant capital during the crisis might improve the prospects for valorisation. Or wage cuts could have the same effect in terms of warding off the catastrophe. But quite apart from the fact that all these situations violate the assumptions postulated in Bauer’s scheme, these solutions would have a purely temporary impact. Restored accumulation will again generate the very same phenomena of overaccumulation and imperfect valorisation.

The logical and mathematical basis of the law of breakdown

In year 1 of Bauer’s reproduction scheme the amount due for capitalisation constitutes 25 per cent of a surplus value of 100 000 (20 000 a_c + 5 000 a_v, = 25 000). In year 2 the capitalised component increases to 25.95 per cent of an expanded surplus value of 105 000(22 000 a_c + 5 250 a_j, = 27 250). [The actual ratio should be 25.95 per cent — J Banaji]. Under these conditions the reservoir of surplus value is progressively exhausted and the accumulated capital can only be valorised at an increasingly unfavourable rate. After some time the reservoir dries up completely — the quotas due for capitalisation turn out to be far in excess of the available mass of surplus value even though notionally they are only fractions of this surplus value. This is the contradiction; at the hypothesised rate of accumulation the mass of surplus value is no longer sufficient. The breakdown of the system is the inevitable consequence.

Apart from the arithmetical and logical proofs that we have been given already, mathematicians may prefer the following more general form of presentation which avoids the purely arbitrary values of a concrete numerical example.

Meaning of the symbols

c = constant capital. Initial value = c₀.Value after j years = c_j.

v = variable capital. Initial value = v₀. Value after j years = v_j

s = rate of surplus value (written as a percentage of v)

a_c = rate of accumulation of constant capital c

a_v = rate of accumulation of variable capital v

k = consumption share of the capitalists

S =mass of surplus value =

Ω = organic composition of capital, or c:v

j = number of years

Further let ;

The formula

After j years, at the assumed rate of accumulation a_c, the constant capital c reaches the level c_j=c₀.r^j. At the assumed rate of accumulation a_v, the variable capital vreaches the level v_j=v₀.w^j. The year after (j + 1) accumulation is continued as usual, according to the formula:

whence

For k to be greater than 0, it is necessary that