Rosa Luxemburg and the tendency of the rate of profit to fall

January 2, 2014

This is a longish note that was originally part of an email discussion concerning the tendency of the rate of profit to fall (TRPF) in Marx’s own writings, and that of later Marxists. It might be of wider interest, so I’ve reproduced it here.

The evidence from Rosa Luxemburg’s principle writings does not tend to support the conclusion that she viewed the falling rate of profit as an essential part of her analysis. Her critical focus, in The Accumulation of Capital, was on the crisis of realisation: of what we might now think of as effective demand. On the basis of her updates of Marx’s volume 2 reproduction schemes, she concluded that this realisation crisis – not a profits crisis – could be resolved through the expansion of capital into the non-capitalist world; that is, through imperialism. The dynamic of her system, in other words, was not determined by a crisis of profitability emerging at the point of production (as in the orthodox, Chris Harman version of TRPF), but of crisis emerging as result of problems in the circulation of commodities.

There are a very few references to the tendency in The Accumulation of Capital. I counted no more than four. The first is very minor. Luxemburg is quoting Engels, who refers to the tendency whilst describing how he collated the notes left by Marx left that eventually became volume two of Capital. Engels mentions, pretty well as an aside, that some sections of the material on surplus value and profit he moved to what became volume three.

No further comment is made by Luxemburg on the tendency at this point.

Tugan-Baranovksy and wages

The second reference is in Luxemburg’s critique of the Russian “legal Marxist”, Tugan-Baranovsky. Tugan-Baranovsky argued (amongst other things) that capitalism could resolve its crises through an expansion of the market, and that the extent of the market would itself be determined by the extent of production. This follows because (he argued) the output of both production and consumption goods, if sold, must add up to the revenues expended in their production: so a capitalist producing, say, cars, would hire workers and machines, and both workers and the capitalist producing machines would receive revenues. They would spend these revenues on other goods, and so crises could (in theory) be overcome: expansion of production by itself would expand the market, and as long as the different parts of the economy were kept in proportion with aggregate demand. The key to this, in Tugan-Baranovsky’s view, is that production can keep its capitalist form if it is planned and organised.

Luxemburg is scathing about this, seeing it (correctly) as little more than a complication of Say’s Law – this being the belief, still dear to bourgeois economics (where it is now mathematicised into Walras’ Law), that supply creates its own demand. We might also recognise, in Tugan-Baranovsky’s belief in organised capitalism, something of the latter-day Keynesians – people like Paul Krugman – in this; they, too, believe capitalism can overcome its tendencies to crisis if aggregate demand is organised sufficiently to meet aggregate supply.

In dismissing Tugan-Baranovksy, she refers directly to the “fundamental law” of the falling rate of profit:

The opinion, that producer goods can be produced independent of consumption, is of course a mirage of Tugan Baranovski’s, typical of vulgar economics. Not so the fact cited in support of this fallacy: the quicker growth of Department I as compared with Department II is beyond dispute, not only in old industrial countries but wherever technical progress plays a decisive part in production. It is the foundation also of Marx’s fundamental law that the rate of profit tends to fall. Yet in spite of it all, or rather precisely for this reason, it is a howler if Bulgakov, Ilyin and Tugan Baranovski imagine to have discovered in this law the essential nature of capitalist economy as an economic system in which production is an end in itself and human consumption merely incidental.

This “fundamental law”, however, is described rather peculiarly: as the result, in Luxemburg’s words, of the “quicker growth” of “Department I” (capital goods) “as compared with Department II” (consumer goods).

This is a peculiarity, relative to the interpretation of the falling rate of profit those like Chris Harman have offered. Harman argues that the rate of profit falls because of the growth of investment in constant as opposed to variable capital causes a rise in the organic composition of capital, and, therefore, a diminution of the source of surplus value, labour power, relative to total investment over time, causing a drag on profits. But note that this effect is independent of whether the investment occurs in Department I or Department II: Harman argues, in Explaining the Crisis and elsewhere, that the fall in the rate of profit will occur irrespective of whichever sector of the economy (Department I or Department II) is making the investment, since he argues that the outputs of both sectors flow eventually back into the production process as inputs for future rounds of production. This contrasts with Department III, “waste” or luxury goods production, in which the products are simply consumed by the capitalists and form no further part in the production process. Investment in Department III therefore has no impact on the rate of profit overall – an important result that provides the key argument behind the theory of the Permanent Arms Economy, with military expenditure as the ultimate “waste” production.

To restate: Harman, and the standard interpretation of the tendency of the rate of profit to fall, depends on how capitalists invest over time. They are driven, through competition, to invest in greater and greater amounts of capital goods, thus squeezing out as proportion of their investment the amount they spend on labour power. It is a story about investment and production.

Luxemburg is arguing for something different. Her story of the falling rate of profit is about consumption. She continues, from the paragraph just cited:

The growth of the constant at the expense of the variable capital is only the capitalist expression of the general effects of increasing labour productivity. The formula c greater than v (c > v), translated from the language of capitalism into that of the social labour process, means only that the higher the productivity of human labour, the shorter the time needed to change a given quantity of means of production into finished products.

This is a universal law of human labour. It has been valid in all pre-capitalist forms of production and will also be valid in the future in a socialist order of society. In terms of the material use-form of society’s aggregate product, this law must manifest itself by more and more social labour time being employed in the manufacture of producer than of consumer goods… the capitalist becomes interested in a machine only when the costs of its production – assuming the same level of performance – amount to less than the wages of the workers it replaces. From the point of view of the social labour process which is the only one to matter in a socialist society, the machine competes not with the labour that is necessary to maintain the worker but with the labour he actually performs.

The last sentence is critical. First, Luxemburg believes that the tendency to invest in means of production ahead of means of consumption is a universal law. Second, this universal law conflicts with capitalist relations of production only to the extent that the wages paid to workers are a barrier to its operation. A very low-wage, low-consumption economy will not introduce more machinery; a high-wage, high-consumption economy will provide the capitalists with a reason to introduce machinery, which (in turn) undermines the creation of surplus value. Low wages restrict the operations of the falling rate of profit; high wages lead to its operation.

This is not the same as Harman’s story. In his case, the incentive to introduce the machine is always there because of competitive pressures amongst capitalists, with new machinery allowing the first capitalist to introduce it to maximise their profits (even if eventually profits for all capitalists are reduced). In Luxemburg’s case, the incentive to introduce machinery is determined by wage pressure. And the problem capitalists face, as she says in her original paragraph, is in the disproportion amongst the different sectors of production leading to a weakness in demand for the products of capitalist society. One story, Harman’s, is about competition between capitalists only; another, Luxemburg’s, is about completion between capitalists and workers. Her complete theory is, in Harman’s terms, underconsmptionist, since it hinges on the inability of workers to consume the entirety of the product that is offered for sale to them.

In other words, there is more than one interpretation of the falling rate of profit. And these interpretations are not limited to the two given here. Robert Brenner’s influential study, The Economics of Global Turbulence, published by the New Left Review in 1998, has a theory of crisis based on falling rates of profit. Here, however, it is falling rates of profit as a result of increased competition: older capitalist producers are challenged by newer, more efficient producers, which undercuts their own profits. This, in turn, forces them to invest in more productive equipment, cut costs, squeeze wages, and so on. (Robert Hoveman, back in the day, wrote a pretty good critique and account of this in the International Socialism Journal.) More recently, the eminent bourgeois economist Robert Gordon has offered a theory of declining growth and profitability predicated on a fundamental decline in the rate of innovation. And of course, it was in critiquing the falling profit rates theories of Smith (to whom Brenner’s theory is probably closest), Ricardo and others that Marx developed his own economic system.

The broad point is that theories of the tendency of the rate of the profit to fall can differ. Even those explicitly based on Marx, given the somewhat partial notes he left us, can differ. Neil’s piece is weakened in that it assumes the orthodox interpretation of the TRPF is the only one available, even with Marxist economics. The orthodox interpretation – that of Harman, and the one claiming the closest fidelity to Marx’s own writings – is probably a minority opinion. This is not the same as “incorrect” (far from it!), but it is a point to note.

Rising productivity and the Okishio Theorem

Back to Luxemburg. Her next reference to the falling rate of profit in The Accumulation of Capital occurs in chapter 25. This, interestingly, is to highlight one of the “countervailing tendencies”, and stress its central importance in undermining the falling rate of profit. It occurs in her discussion of the problems faced by capitalism under conditions of “expanded reproduction” (ie with economic growth occurring). She notes:

The increasing productivity of labour ensures that the means of production grow faster in bulk than in value, in other words: means of production become cheaper. As it is use value, i.e. the material elements of capital, which is relevant for technical improvements of production, we may assume that the quantity of means of production, in spite of their lower value, will suffice for progressive accumulation up to a certain point. This phenomenon amongst others also checks the actual decline of the rate of profit and modifies it to a mere tendency, though our example shows [just above, in her text] that the decline of the profit rate would not only be retarded but rather completely arrested.

Note the last sentence: the increase in productivity reduces the “actual decline” in the rate of profit to a “mere tendency” and that, under specific conditions, can halt it entirely. This is an identical point to the one made by Neil, I think – that improvements in productivity, given that they reduce the cost of the means of production, will reduce in turn the tendency of the rate of profit to fall, simply because capitalists’ costs are reduced.

Now, Harman has an answer to this, presented in Explaining the Crisis. (I don’t have my copy in front of me, and it’s not online, so this is from memory. I think I’ve got it down.) He says that even if the technical improvements, resulting in improved productivity of machinery lead to cost reductions in output, capitalists still have to produce with older equipment. The new stuff might be available to buy, but production now takes place with older equipment. In other words, some producers will still feel the pinch of competition from producers able to use the newer, more productive equipment, but have to produce on the older, less cost-effective equipment. Only once they install the newer machinery will they ease this pressure – but that installation of new machinery, of course, is what leads to the decline in the general rate of profit.

In other words, Harman points out that production takes place over time. It’s not good enough to presume that the introduction of new equipment leads simply to reduction of costs of output and therefore to an increase in the rate of profit. Harman is here critiquing the Okishio Theorem, which is a mathematical representation of the argument Luxemburg uses above. Okishio used a method of “simultaneous equations” to show how new, more productive techniques lead to an increase in profits, not a decrease.

I think this much is true, and self-evidently so. The economy is a dynamic system. However, this is not adequate. If we are using a dynamic setting – in other words, if we presume production takes place over time – the question to ask is not just “what is the rate of profit?”. It is “what is the rate of profit at a given point in time?” If time is a factor – Harman says it is – this has to be the question to ask. But his descriptive account of production cannot tell you. He argues that input prices will differ from output prices, because different producers are using different techniques at any given point in time. If there are different techniques being used at different points in time we cannot establish an economy-wide rate of profit. We have to be able to do this, because Marx makes the equalisation of profit amongst different branches of industry central to his law of value – it’s a fundamental part of how his economic system operates. But Harman’s account leaves us with two different rates of profit – one prevailing in the firms with the new technique, and one prevailing in the old. He has not shown us what the economy-wide rate of profit is, which means his system is not closed and the law of value is not operating fully.

This matters a great deal. It is absolutely true that production takes place over time and that the prices of inputs at the start of production will differ from prices of output at the end. However, capitalism does not produce once and just stop. It produces continuously, so that the outputs from one period of production form the inputs into the next. So to calculate the economy-wide rate of profit in Harman’s system, we can take the output volumes and prices, and use them as inputs into another round of production. If we do this for successive rounds, we should find (as Marx and Luxemburg demonstrated) that a stable, economy-wide rate of profit has been formed. The system is closed and therefore analysable.

But this takes us right back to where we started. The method we have applied, following Harman’s own economic logic, gets us to a stable economy-wide rate of profit. But this method is identical to solving a simultaneous equations problem, and gets us to an identical outcome! All we have done is apply a recursive technique to finding the solution. Harman’s “critique” of simultaneous equations methods is nothing of the sort – it is simply the first step in finding the solution to a simultaneous equation. (I have blogged on this earlier.)

In other words, Harman has not demonstrated that the Okishio Theorem does not hold and that, therefore, the effect of increasing productivity highlighted by the Theorem and by Rosa Luxemburg must apply.

Internal and external markets

Luxemburg again refers to the falling rate of profit in her description of internal and external markets, and the relationship between capitalist development and the search for a non-capitalist world to “absorb the products of capitalism”. She describes how the limits to the capitalisation of surplus value are set by the extent of “renewal” of constant and variable capital, and that, as capitalism goes, the conditions for this “capitalisation” of surplus value become more and more precarious. It is in this context that she makes a passing reference to the contradiction between the expansion of capital and its difficulties in realising the surplus value it produces as being a part of the tendency towards the falling rate of profit.

Again, this makes sense if she treats the falling rate of profit as a problem of realisation of profits, not as a problem in the production of profits as such; otherwise, the relationship between an expanding mass of capital and its need to find markets, and the falling rate of profit, does not seem (to me) to be logical. The orthodox theory of the falling rate of profit applies even in conditions where supply is necessarily equal to demand – that is, where no realisation problems occur. Harman is quite clear on this. But if it applies where no realisation problems occur, it is not clear why there should be a relationship between the difficulties capital faces in securing markets for its products, as its own size increases, and the orthodox tendency of the rate of profit to fall. It would seem that Luxemburg is treating the falling rate of profit in the manner I described above – as an issue of disproportionality and realisation.

Cliff and Bauer

Luxemburg’s work was met with a certain amount of hostility on its publication. She responded, somewhat forcefully, to some of those critics in a subsequent work, the Antikritik, focusing in particular on Otto Bauer. Bauer argued, in Malthusian style, that the limits to capital accumulation were set by the extent of the population. Luxemburg responds that the situation is quite the reverse – the accumulation of capital itself creates a “surplus population”. Luxemburg, as John says, does indeed refer to the falling rate of profit bursting into Bauer’s formal analysis like a “fox in a chicken run”. This would appear to be, however, her only reference to the tendency in her entire response. It is fair to say she thought the law was important, but, on this basis she clearly did not view it as the foundation of value theory and a central part of Marx’s scheme. Both the Accumulation  and the Antikritik suggest she thought realisation crises were a more important focus for study.

Tony Cliff’s chapter on Rosa Luxemburg’s Accumulation of Capital is a part of his important early pamphlet on her work more generally. It is a clear and well-informed account of her economic system that, correctly, highlights her concern with the realisation problem. Cliff notes, also correctly, that Rosa Luxemburg abstracts from the rising organic composition of capital in her original presentation; but that therefore means that she abstracts from the conditions that give rise to the falling rate of profit. Cliff suggests that her conclusions would be strengthened if the rising organic composition of capital is included, which I think is also correct, but the falling rate of profit, as such, is barely mentioned by him. (Of course not: the simplified reproduction schemes he presents, following Luxemburg, are an abstraction away from it.)


So, in summary:

1. The evidence from the text suggests that Luxemburg did not view the falling rate of profit as such as essential to her economic system. It was important, but not key to understanding capitalism;

2. Her interpretation of the tendency was different from that of Harman and the orthodoxy, since it was based on competition between workers and capitalists, not amongst capitalists alone, and that this competition is, in turn, placed in an “underconsumptionist” setting.

3. She held that increases in productivity would undermine the falling rate of profit, and could certainly arrest its decline.

4. The falling rate of profit was not treated as a central part of her work by later commentators.


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