The rate and the mass of profit

Professor David Harvey is probably the best-known scholar of Marxist economics in the world.  Over the years, Professor Harvey and I have engaged in debate and discussion on Marx’s law of value and Marx’s law of the tendency of the rate of profit to fall.  Professor Harvey has always been sceptical of the relevance of Marx’s law of profitability in explaining regular and recurring crises of production and investment under capitalism.  He prefers alternative explanations.  In the past, I have debated with Professor Harvey on this in defence of the relevance, indeed the ultimate causal connection between crises in capitalism and Marx’s law.  You can read the substance of these debates here and also in the excellent book: The Great Financial Meltdown, systemic, conjunctural or policy created, edited by Turan Subasat.  See in particular, Part Two on Crisis and Profitability.

Now Professor Harvey kindly sent me in advance an article that has been published in the New Left ReviewThe article is entitled ‘Rate and Mass’. In this article Professor Harvey spells out again in detail his argument for considering the mass of profit over the rate of profit in the analysis of crises.  At one point, he says: “mainstream commentators are not alone in missing the import of mass. There is a long history of Marxist economists doing so, too—not least in work on the tendency for the rate of profit to fall.”  And later he comments that “Michael Roberts’ studies of the consequences of a falling rate of profit, (are) absent any concern for the importance of the rising mass”, referencing my book The Long Depression.

Well, in my book, go to p26 and you will find me saying: “The underlying contradiction between the accumulation of capital and the rate of profit (and then a falling mass of profit) is resolved by crisis.” And again, on p27 I say “on each occasion,… a fall in the mass of profit led or coincided with a slump”. Indeed, for several pages in that section of the book, I outline the role of the mass of profit in booms and slumps and quote other sources.

What is at debate here?  Marx spells it out in Volume One of Capital: “despite the enormous decline in the general rate of profit…the number of workers employed by capital i.e. the absolute mass of labour set in motion by it, hence the absolute mass of the surplus labour absorbed, appropriated by it, hence the mass of surplus value it produces, hence the absolute magnitude or mass of the profit produced by it, can therefore grow, and progressively so, despite the progressive fall in the rate of profit.”  He then adds: “this not only can, but must be the case…. The same laws “produce both a growing absolute mass of profit, which the social capital appropriates, and a falling rate of profit.” And then Marx asks:  How, then should we present this double-edged law of a decline in the rate of profit coupled with a simultaneous increase in the absolute mass of profit arising from the same causes?”

As Marx explains, his law of profitability has a double-edge.  As the rate of profit falls in a capitalist economy, it is perfectly possible, indeed likely, that the mass of profit will rise.  It’s arithmetical really: a falling rate can still imply a rising mass.  But a double-edge cuts both ways.  As Marx goes on to explain in Volume 3 of Capital (chapter 13).  The two movements not only go hand in hand, but mutually influence one another and are phenomena in which the same law expresses itself….. there would be absolute over-production of capital as soon as additional capital for purposes of capitalist production = 0.   at a point, therefore, when the increased capital produced just as much, or even less, surplus-value than it did before its increase, there would be absolute over-production of capital; i.e., the increased capital C + ΔC would produce no more, or even less, profit than capital C before its expansion by ΔC.”  So the mass of profit can and will rise as the rate of profit falls, keeping capitalist investment and production going.  But as the rate of profit falls, the increase in the mass of profit will eventually fall to the point of ‘absolute over-accumulation’, the tipping point for crises.

Nevertheless, Professor Harvey wants to argue that Marx saw the mass of profit as more important in any analyses of crises than the rate.  I think the above quote shows that they are integrally connected, in Marx’s view.  Crises erupt when the mass of profit drops, causing over-investment and overproduction, but that happens when the rate of profit falls sufficiently to cause a fall in the mass of profit.

Now in a You Tube video of a recent panel in New York entitled Anti-Capitalist Chronicles,, Professor David Harvey tells the audience of his latest views on China, imperialism and crises (see from about 50min). But then a little later, Professor Harvey makes a critical comment on the ‘rate of profit’ theorists, singling out me in particular (at about 1.08).  After supporting Paul Sweezy and Baran’s rival ‘surplus profit thesis’ over Marx’s law of profitability, Professor Harvey remarks that Michael Roberts is obsessed with the rate of profit falling all the time and went on to joke: “if it started falling in 1850, should it not have reached zero by now!”  

Amusing as this joke is, anybody that reads my material on the rate of profit knows that the world rate of profit has not fallen to zero and will not any time soon, if ever, although there is a long term secular fall in the rate.  And there are several reasons for that, as I explain in my work.  The first is that there are counteracting factors to the law of the tendency of the rate of profit to fall and these countertendencies can raise the rate of profit for whole periods, decades even, as they did from the early 1980s to the end of the 20th century.  The other main reason is that regular slumps in capitalism lead to the devaluation of capital, with companies going bankrupt, writing off fixed assets and laying off workers.  That leads to a rise in profitability possibly for several years.  So there is a cycle of profitability – again something that I explain in detail in the Long Depression, for example.  So the rate of profit does not fall in a straight line towards zero and Professor Harvey’s little joke at my expense does not hold to reality.  You can see in this graph below how that pans out.  Even if the rate of profit fell in a straight line from here, it would not reach zero before 2060 or so – and that won’t happen for the reasons above.  Indeed, there are plenty of periods when the rate of profit rises, often after major world wars or after long periods of economic depression.

A world rate of profit (%) – from the work Esteban Maito using 14 key countries.

In his presentation to the panel, Professor Harvey goes to say that he challenged me personally about why I don’t ever talk about the mass of profit.  Apparently, I replied: “oh, I talk about it, but it doesn’t really matter.”  But that’s not how I remember the discussion.  This discussion actually took place at a public session, a plenary debate between Professor Harvey and myself in front of over 200 people at the HM conference of 2019 in London, after Professor Harvey had sent me in advance a paper which follows the same arguments as in his article for the NLR above.  Now I fully documented (accurately I think) this debate between me and David here.  If you read this post closely, I think you will find the ‘challenge’ and my response was not quite as Professor Harvey portrayed it at the New York panel.

As I say in my post covering that debate with Professor Harvey back in 2019, “Indeed, we ‘falling rate of profit boys and girls’ have been well aware of Marx’s double-edge law (of rate and mass)”.  And in my presentation to that plenary, I outlined the law; and I cited various works by ‘rate of profit’ theorists like Henryk Grossman who have used Marx’s double-edge law to explain crises.  Indeed, Grossman’s whole argument is built around the view that eventually a falling rate of profit leads to a slowdown in the rise in the mass of profit to the point where there is not enough surplus value to sustain investment in production and take a share for their own living and breakdown follows. 

And I provided a batch of empirical evidence showing the close connection between the rate and the mass of profit in leading to crises.  For example, I refer to the work of Jose Tapia from Drexel University published in the book, World in Crisis, jointly edited by myself and G Carchedi, that shows the close connection between the changes in the mass of US corporate profits and investment, leading to successive crises.  Indeed, at the plenary, I also provided a careful modelling of Marx’s double-edge law and applied it to real data from the US economy to show its connection to the Great Recession.

But more important than who said what and when, is what is the best explanation of the causes of regular and recurring crises under capitalism?  In the post on the debate between DH and myself, I concluded that “I think Professor Harvey’s purpose (in his paper and now in his article) was to weaken the role of Marx’s law of profitability and its relevance to crises.  By bringing up the double-edge law, it seems to me, David was saying that a rising mass of profit or capital stock or GDP is the problem. And thus, the problem for capitalism is not insufficient profit due to a falling rate, but too much surplus due to rising mass. How are we going to absorb or cope with ‘too much’ is apparently the problem?  This connects with David’s view that crises under capitalism arise because of too much capital or profit relative to the ability of consumers to use it. Indeed, David argues that it is consumer confidence and the level of consumption that matters in triggering crises not the rate or level of profits and investment. But the evidence on that does not support David’s thesis as I have shown before.”  (See the posts identified at the end).

As readers of my blog will know, in the debates that I have had in the past with Professor Harvey, he rejects Marx’s law of profitability as the underlying cause of crises in favour of what he has called a multiplicity of causes (again see the posts below). He reckons those who focus on Marx’s rate of profit law are being ‘monocausal’. But he has had to admit that the empirical evidence of a falling rate of profit is compelling. So now he has moved the goal posts from the rate to the mass. But shifting the goal posts just leaves us with a new goal to score in.

Marx’s double edge law is not a refutation of the law of profitability as the underlying cause of crises; on the contrary, it is integrally connected. And alternative ‘multiple’ causes (like underconsumption, ‘too much surplus to absorb’, disproportion, financial fragility etc) remain unconvincing and unproven in comparison.

I leave the readers of DH’s new piece and my response to make up their own minds.

75 thoughts on “The rate and the mass of profit

  1. Normally I wouldn’t reply, but as this is about Harvey: I actually read Marx and I read Harvey’s analyses of Marx later on and I found it disorientating: either I can’t read or this is not what Marx wrote. As the years went by, I became almost allergic to it. In my opinion, Harvey did the left a disservice by presenting a reading of Marx which is, in my opinion, simply incorrect. The thing I hated the most was his almost papal presence in human geography: why read Marx now that there is Harvey? I hated it.

    1. Michael,
      Just go on!
      Only those who “improve” Marx’s capital analysis can make a name for themselves in the academic world.

  2. The problem with Robert’s analyses of profit rate is profit is assumed to be a result of exploitation of productive labor only–which must be the case if either ‘rate’ argument is to be considered a marxist analysis.

    The tendency of the rate of profit to fall by Marx clearly relates only to profits from surplus value exploitation in the process of production. It does not include profits derived from various capitalist exchange relations. Yet capitalist profits data–to which Roberts and other adherents of the ‘falling rate’ argument always refer– includes both profits from production as well as profits from capitalist exchange.

    That means capitalist profits data (profits from production and exchange) can’t be used to prove the falling rate of profits tendency (profits from exploitation in production only). Yet that’s what Roberts (and other marxist adherents to the falling rate of profits tendency) refer to in order to prove their argument that changes in the ‘rate’ of profits is what drives capitalist business cycle crises like depressions, great recessions, etc.

    Marx’s (unpublished notes) view of a tendency of the rate of profit to fall clearly refer to profits from exploitation of labor value in production–not profits from exchange.

    In short, one can’t use capitalist profits data (derived from both production and exchange) in order to ‘prove’ the falling rate of profit tendency which in Marx defines profits from production of value only.

    The ‘tendency-rate’ argument has become an economic fetish employed by some marxist economists in order to explain capitalist short run crises and business cycle instability in the short run (All business cycle contractions are short run even depressions, which historically run 5-10 yrs. in duration. There is no such thing as a decades-long ‘long depression’ unless one wants to redefine the concept of depression as a chronic stagnation, which is different from depression).

    It is also important to note that, even in Marx, it is clear the ‘tendency’ argument is a long run supply side argument of the eventual breakdown of capitalist relations and mode. It is not an argument to explain short run capitalist business cycle crises (like 2008-09 or today or even 1929-39). The ‘tendency/rate’ thesis is part of Marx’s explanation of the long run breakdown of capitalist production relations and mode–not an explanation of short run business cycle/depressions.

    I would add that Profits, however defined, are also not the primary determinant of short run capitalist crises. They are correlated with such short run contractions but don’t very well explain the crises as causation. The ‘rate’ argument is even less convincing since the rate is dependent on base period one chooses and varies accordingly. How much of a rate change is necessary to precipitate a short run contraction is never explained by its adherents.

    Another problem with the ‘rate of profits’ argument is that profits (rate or mass) is not the primary determinant of capital accumulation (or lack thereof) in contemporary capitalism. Profits (retained earnings or whatever definition) today in 21st century capitalism constitute at most a fourth of the total source for financing of real investment and capital accumulation. Other ‘sources’ of financing capital accumulation are corporate bond debt, equity (stock) financing, tax subsidization by the State, now private cryptocurrency creation, to name bu a few.

    Another point: it is impossible to estimate accurately global profits due to data definition data gathering problems across countries in 21st century global capitalism. Different countries define profits differently. Allow capitalists to avoid recording profits differently. Collect profits data poorly or not at all. Etc. For these reasons it is impossible to aggregate capitalist profits on data globally, which must be done first since capitalism is now clearly a globally integrate production and distribution system.

    Profit variables are poor data sources, in other words, for trying to explain movement and change in 21st century global capitalism.

    For all these and other reasons Marxist economists should stop treating profits as the key variable for explaining the movement and evolution of Capital. They should focus on capital accumulation, which is what Marx himself did (before his unpublished notes on the ‘tendency’ led marxist economic analyses off in a false direction. There is no single, primary causative variable of capitalist business cycle crises.

    A better approach is to explain the various, growing, myriad means by which capitalists exploit labor (both in terms of production relations and exchange relations) and how that exploitation is what drives capital accumulation. Profits from production is but a part of that bigger picture. And the ‘tendency/rate’ explanation an even smaller element in that part.

    It’s all about capital accumulation and not about profits (rate or, I suspect, ‘mass’ either).

    Jack Rasmus

    1. If prof. Rasmus has his own theory of capital (and, therefore, capitalism), then, by all means, he should publish it. I would be more than happy to read it.

      And by “theory” I mean a true theory like Marx’s, not what bourgeois economists call nowadays “theory”, which are basically a bunch of loose postulates that are circular logic disguised as a closed system.

      Economists live and make fortunes and fame by abusing the ceteris paribus fairy. I think it is unfair to treat Marx to the polar opposite.

      1. Yes, I have my own theory but it is still very much a work in progress. For an early version, read the concluding chapter of my 2016 book, ‘Systemic Fragility in the Global Economy’, Clarity Press, as well as the equation addendum at the end of the final chapter. But it’s still an early view, in progress. I am basically curious about disproportionality crises, precipitated by contradictions and imbalances between real asset investment (aka capital accumulation) and financial asset investment (aka fictitious capital). I think it is wrong to just dismiss ‘fictitious capital’ as the benign consequence of late capitalism.

    2. Dear Jack, thanks for your comments. Let me say that you are doing great work in critiquing the the US economy and the policies of its economic and monetary leaders. On your criticism of my position and the ‘rate of profit fetishists’ like me, let me just say a few things. 1) I don’t agree that profits can come from ‘exchange’ as well from the exploitation of labour. Of course, you know that Marx ruled that out in his labour theory of value. Maybe he is wrong or at least wrong for the 20th century, but I don think so. 2) profits in finance, real estate etc are profits derived from the exploitation of labour in the productive sectors and redistributed to these unproductive sectors and are derived from within these sectors, in my view. And it is perfectly possible to separate the profitability of productive sectors from those in unproductive sectors. 3) in my work and in the work of others we can provide good empirical evidence of the causal connection between profitability, profits and investment and thus output in modern capitalist economies – the evidence is strong. 4) you say that the primary source of profits is in financial assets – this Marx called fictitious capital generating fictitious profits, in effect the financial sector making profits from each other or from productive sectors. It is fictitious in that those profits cannot generate new value for accumulation in a capitalist economy. 5) sure there are statistical problems in measuring a world rate of profit (which have been much discussed by us ‘fetishists’ ) but our results do reveal general trends which seem compelling. 6) your emphasis on ‘capital accumulation’ over profit is, in my view, a misleading one, because accumulation of financial assets is not accumulation of capital in value. And a collapse in such financial asset accumulation is not a good guide to any collapse in the capitalist economy – you can have a financial crash without a slump resulting, but a collapse in productive sector accumulation is the basis of a slump in production. Lots more to argue about I’m sure, but good to hear from you, Jack

      1. Let me clarify some of your comments, which miss the point(s) I was making. You say you ‘don’t agree profits come from exchange’. Ok. But you use capitalist government data to prove your falling rate of profit tendency that includes profits from exchange. That was my point. If all profits derive from production by productive labor only, then you need to show how ‘profits in exchange’ are derived from production profits. that is, what’s the transmission mechanism? You say profits are only generated in the productive sector. Why then do you refer to data on profits that are clearly from exchange–i.e. from financial asset investment and speculation? I don’t know of any data source that estimates profits from productive labor only. And of course even Marx was not totally clear on what occupations constitute productive labor. It wasn’t just labor that made discrete things, I understand. But what are the criteria for including which service occupations that qualify as productive labor? (Obviously transport of goods, but what else?)

        Re. your point 4, I never have said the ‘primary source of profits is financial profits’. I have said that profits from large corporations, for example, as they report profits, include profits from portfolio investments. Here again we have the conflating in data of profits from production in the Marxist sense and profits from ‘exchange’. How do you separate out the two corporation by corporation? The individual corporations don’t. So they two sources of profits reported are commingled. And you use that commingled data to support the argument for the ‘tendency’ to fall.

        You acknowledge the profits in aggregating profits across countries with different systems of reporting and data gathering, and say in reply there are nonetheless “general trends that seem compelling”. Concepts like ‘trends’ and ‘compelling’ are not sufficient to make the case that the data for profits you use is satisfactory.

        Here’s another ‘profits definition’ in government (US) data for you. Obviously the falling rate tendency must include capitalist profits from proprietorships and partnerships not just from corporations. They are capitalists too. The US data calls this non-corporate profits source ‘business income’. It then underestimates the total of business income/profits by arbitrarily assuming 65% of business income is ‘wages’. That way it reduces business income/profits and artificially boosts total wages. How would you deal with that data problem in your total calculation of profits?

        Here’s another problem. Clearly capitalists underestimate inflation by magnitudes, especially when using the GDP deflator index. That gets ‘real profits’ (adjusted for inflation) over-estimated. (Just like real GDP is over-estimated). It seems to me to prove your hypothesis of falling rate tendency you’d have to come up with a more accurate estimate of inflation in order to get to a more accurate total for profits.

        As for my comment re. ‘fetishism’ adherence to the falling rate tendency, perhaps it’s too harsh. But I just have a problem with trying to find all the answers to 21st century capitalist economy by citing passages from the ‘great books’. Keynesians do it with the General Theory, as do conservatives with Smith and others. Perhaps a better term is not Marxist ‘fetishists’ but Marxist Philologists.

        I never said, as well, that capital accumulation included accumulation of financial assets. I agree with Marx that ‘capital accumulation’ is based on investment in real assets, not financial. But I can see that financial asset investment can destabilize real asset investment. I’ve always thought that Marxist economists would do better to expand on Marx’s idea of ‘disproportionality crises’. Not disproportion between the two ‘departments’ as he discusses. But disproportionality between real and financial asset investment since it appears to me that the latter is crowding out the former in many sectors of the economy. When Marx talks about the full circuit of capital, that circuit clearly passes through exchange relations and exchange values. It seems to me there’s an area of the total circuit to which Marxist economists have not paid sufficient attention. I think too much focus on the production of value side of the total circuit–i.e. the falling rate tendency included–has prevented analyses of how exchange relations (which include financial asset investing) in 21st century global capitalism is playing a greater role in destabilizing capitalist economies

        Another point: in my reading of Marx’s Vol. 1 (which I do every year for the past six years) it is clear to me that Marx is not talking about capitalist business cycle crises in the short run. He’s talking about the long run and is very supply side focused (i.e. production is central). This was very typical of classical economists before him, from whom he borrows much (and rightly critiques much). Given his long run supply side focus, I don’t think Marx ever intended to link the falling rate tendency to explaining short term business cycle contractions (which some advocates of it try to do). It’s about the long run breakdown of capitalism (which, by the way, only occurs in the last analysis for political and class struggle reasons, as you know).

        I appreciate your commentary on specific points I made in my first remarks, although I think you misunderstood them somewhat. What I’d hope is that others commenting would also do so with specific references and arguments, rather than generalities. Marxists need to become more rigorous in their analysis of contemporary Capitalism and its obvious drift toward a fundamental crisis. That does not necessarily mean ‘more mathematical’ (which is just another language albeit potentially more precise than ‘literary economic analysis’. Bourgeois economics is in some ways even more imprecise in its definitions, data gathering assumptions, and statistical misrepresentations (all of which are the basis of ideology in economics which most of contemporary mainstream economics is about).

        I just don’t think all the answers are in Vol. 1 of Capital, or in his notes on Vol II, III. I have a hard time fitting the idea of capitalist crises occurring (short or long run) as a result of a single causative variable like the tendency of the rate of profit to fall. Especially when what is meant by profit, difficulties in data gathering and aggregating across economies, and even related issues like the meaning of ‘rate’ and ‘tendency’ are used.

        I’ll be writing an article for the ICT recent call for papers where I’ll revisit these issues. I’d be glad to send a draft to you for comment and discussion before, if you’re interested.


    3. “It is about capital accumulation and not profit (rate or, I suspect,” mass “either)” “.
      And what is capital (fixed capital, of course) if not exclusively accumulated profit? It is a benefit on your part of savings invested in the company. Professor Rasmus talks about other sources of capital but he is only referring to other forms of FINANCING capital (basically bonds and other loans). But financing is only a process that brings “benefits of the future”. Without those possible benefits of the future that a loan applicant foresees and must guarantee with existing investments today, no financial institution would grant any loan. And, once the loan is granted, if these benefits do not exist in the future, the financed capital becomes fictitious capital, is destroyed and disappears. If you miss the basics …….
      More interesting and as a subject of debate is his concept that the benefits do not only come from the operating surplus value (of production he calls it) and that there are other sources of benefits derived from ” various capitalist exchanges ”. There is only one problem with the thesis: it does not indicate what these “various capitalist exchanges” are and how the profit is produced. Best Regards

      1. No I am not talking only about ‘financing’ of bonds, etc. as a process. There is such a thing as financial investment and profits from financial investment (i.e. cost of money capital committed and return of a greater magnitude of money capital, which is financial profits. Yes, I do not indicate what the ‘various capitalist exchanges’ are. After all, I’m only commenting to a blog entry at this point.

    4. “It’s all about capital accumulation and not about profits”– Really? Try telling that to the General Motors or Toyota or Exxon, or Intel. Try telling that to GM’s, Exxon’s, Intel’s, debt and equity holders.

      Dr. Rasmus to the contrary not withstanding, circulation only allocates, distributes the profit form of surplus value. It does not create any profits. I’m sure the ghosts of Phil Gramm (what? he’s not dead yet? A pity), and every trader who ever spent time in the pits at the Chicago Board of Trade or Merc, would be heartbroken to hear this but exchange relies upon previous production, and the previous specific production of articles as commodities. It’s amazing to me how little time all these economists of “invisible hands” and arbitrage know so little, have seen so little, of how markets actually work. Those in the pits know, or knew, what it takes or took– the willingness to slice open the pockets of your counterparties, separate them from their money, and charge them a user fee on the knife.

      What is capital accumulation if not the conversion of surplus value into the means of production, or the value that can be exchanged for an equivalent value of the means of production?

      Please, capitalism has created this myth of accumulation through the alchemy of exchange, along with unicorns, white nights, angels etc. It’s junk economics.

      1. You argue all exchange depends on profits from production, but you (and others) provide no quantitative evidence for this, are vague about the transmission mechanism, and simply ignore the fact that a mass of profits is generated from financial assets that have nothing to do with production. Please be more rigorous and not engage in just logical assertions. This isn’t 1860 and, unlike in Marx’s time, we can at least make some argument based on quantitative evidence. Too much ‘marxist economic analysis’ today is ‘literary’ and not based on quantitative evidence.

      2. I think Dr. Rasmus undermines his argument in its very defense when he issues the challenges

        “You argue all exchange depends on profits from production, but you (and others) provide no quantitative evidence for this, are vague about the transmission mechanism, and simply ignore the fact that a mass of profits is generated from financial assets that have nothing to do with production.”

        We start the commodity. What is the commodity? What makes commodities exchangeable? Remember that? The commodity is both a useful article and a value. What provides that value, what makes the commodity exchangeable? A specific relation of production; a historically situated condition of labor, where labor has to be expressed as a commodity, wage-labor, organizing but veiling the appropriation of surplus labor time, surplus value.

        If that sequence, that metamorphosis does not hold, then there is no need for labor as wage labor; there is no historical need for private ownership of the means of production to enable capital accumulation. Is this a logical assertion. Indeed, based on the historical logic of capital; its organization of means of production as exchangeable values.

        And from that we recognize that profit is derived from surplus value, from the social condition of labor.

        Dr. Rasmus would like to flip the script and ask “where are the quantitative data that prove profits depend on production, and that financial profits have nothing to do with production?” I never said that financial profits have nothing to do with production. On the contrary, they have everything to do with production, in that their origin is also in the surplus labor expressed as surplus value.

        What I do deny is that financial profits are generated sui generis; just as I dispute that finance capital is “fictitious.” Finance is by definition–derivative.

  3. I always thought the really interesting parts of “the tendency of the rate of profit to fall” were the counter-tendencies and the internal contradictions. Obviously, you can’t have the contradictions and counter-tendencies without the tendency.

    1. I thought the point of the tendency of the rate of profit to fall hypothesis is that it is THE (i.e. primary, sole, etc.) predictor of capitalist crises. Of course you can show rates (or mass) of profits growing or slowing. The point, however, is the ‘rate’ a predictor of crisis? How much of a ‘rate falling’ is historically associated with predicting an actual crisis? How do you define ‘rate’ (i.e. what’s the base period used. And why not any particular base period). And while we’re at it, what is meant by a ‘tendency’ in order for the ‘falling rate of profit’ to hold as a predictor? What’s the quantitative measure of a ‘tendency’ as used here?

      1. Marx never claims the tendency of the rate of profit is the sole predictor of capitalist crises. Never. Nowhere. Not in Capital, not in The Grundrisse, not in TSV, not in the Economic Manuscripts. In fact he distinguishes between the long-term tendency of the rate of profit to fall and the short-term nature of capitalist crisis.

        He does on occasion show that the fall in the rate of profit can cause crises, but he never claims “sole cause” status for it.

        The rest of Dr. Rasmus can be best answered by……..not “economics” but history, i.e. the actions of the bourgeoisie in the US in response to the fall in profitability after 1969; the attack on wages and living standards, the transfer of wealth of the social ladder; the shrinkage of the “domestic” auto producers and steel makers, the steady increase in “free lance,” temp, and part time employment, etc etc. That’s the tendency of the rate of profit to fall at work, made manifest.

  4. Evidently, Marx’s Capital presents capital as it really is, i.e. in abstraction, in “pure form”. It is capital analyzed at the philosophical level.

    In the real world, capitalism will obviously collapse much before the profit rate reaches zero. The zero here is merely the absolute limit possible for capitalism, a representation of its mortality, it doesn’t represent what will really happen. Economists try to read Marx with the tools and preconceptions of bourgeois economy, when in reality a much higher knowledge/education is needed (and this is the problem with the American economists in general, but that’s for another discussion).

    So, to sum it up: Marx’s TPRF is just an abstraction. What matters is not the points of singularity in it, but the path, the process. It should be used as some kind of economic Rosetta Stone to decipher (and predict, if that’s your area, and because capitalism still exists) every event that happened in capitalist history. As such, this is a unique document, without parallel in History. It is not an apocalyptic book or a crystal ball.

    1. Ah Yes, at least one commentator here (VK) understands the FRPT is just an abstraction. I agree. In fact, all of Vol. 1 is an abstraction. Marx planned 8. In Hegelian fashion, he planned to move from the general to the specific, from abstract to concrete, etc. But didn’t get there. I sometimes wonder why he stopped writing and publishing (notwithstanding his notes). Perhaps he was too busy actually doing politics. (I think his writings on politics and class conflict are profound, more so than his economics which is very much a work in progress and never finished. Ditto for the FRPT, a work in progress, unfinished, and not a final word on causes of capitalist short term crises. (By the way, in reply to the prior comment on my commentary, what I said was many contemporary marxists maintain that the FRPT DOES predict capitalist crises. That was my point).

      1. ”more so than his economics which is very much a work in progress and never finished.” According to J.D. White (“Marx in Russia: The Fate of a Doctrine” 2019) it was Vol. 2 that caused Marx such difficulties, as when he came to study Russian social conditions he came to the conclusion that the circulation of capital does not necessarily subsume all other modes of production. Why did Marx fail to finish Vol.2? White argues, ”that when he looked for evidence that the circulation and expanded reproduction of capital absorbed earlier types of social and economic formations, it was not to be found…Marx cursed himself for ‘judicial blindness’…he had been too carried away by the structure of his system…its Hegelian structure was no longer appropriate…. From 1868…Hegelian terms, which had previously pervaded Marx’s writings , cease to appear. In the French edition of capital all Hegelian terminology was removed. Thus capitalism was no longer to be identified as the unfolding of the concept of capital, ‘a universal system, the outward manifestation of man’s inner species being.’ So he complained of Mikhailovsky:” He feels he must absolutely metamorphose my historical sketch of the genesis of capitalism in Western Europe into a historico- philosophical theory of the universal path every people is fated to tread.” Marx came to hold that Russia might avoid the capitalist state and the peasant commune serve as a fulcrum of the socialist regeneration of society; what was destroying the peasant commune in Russia was the actions of the State rather than the development of capitalism per se. White concludes:” Could one for example do ,as Sieber had suggested, and recast the content of Das Kapital in concrete rather than in abstract terms? That Marxist thought in Russia did not develop in this way is due, in the first instance, to the activities of Friedrich Engels” (Ibid. P47). And one should add: not only in Russia and not just due to Engels!

  5. Don’t worry Michael, some of us have your back on the rate of profit. Harvey, alas is the Rolling Stone of Marxism, still touring but sounding increasingly out of tune.

    A quick point on productive and unproductive labour. It is always a pity when Marxists are less conscious than the capitalists they are criticizing. In the set of accounts for a capitalist firm three distinct sub-sets are found – the Trading Account, the Profit and Loss Account and the Balance Sheet. It is in the domain of the Trading Account that productive workers are found who generate the revenue and gross profit of the firm. The Profit and Loss Account is the domain where unproductive workers are found, nowadays called SGA workers (sales, general and administrative) whose wages are found on the loss side of the Profit and Loss Account. In other words their wages are a deduction from gross profits and their deduction together with the other costs of circulating and accounting reduces gross profit to net profit which is transferred to the balance sheet. So clearly the capitalists themselves treat productive and unproductive workers differently and so should we. I do have differences with Michael on this, because I like Marx, hold that functional unproductive (SGA) workers who circulate commodities are paid out of capital, as opposed to the personal unproductive workers who circulate the blood and lymph of the capitalists such as masseurs, who are paid out of revenue.

    Finally on one of Jack’s points. Circulation does not add to the mass of profits. Let us utilize a thought experiment. A farmer renowned for the quality of his or her milk and milk products has a farm shop as well as a distributor to sell the excess products. In his or her farm shop s/he sells the milk for $2 a liter. To his or her distributor s/he sells their milk at the discounted price of only $1.40. The 60 cents difference covers the cost of distributing the milk plus an average profit. The distributor on the other hand sees it as cost price of $1.40 plus a markup of 60 cents. Mirrors, mirrors. Thus the markup found in circulation or the realm of commerce, comprises the discounts originally provided by the producers now hidden by habit. Does this mean the rate of profit found in the realm of production, say manufacturing, is understated? Yes. Only part of the surplus value produced there is realised because of these discounts. Does it matter? No. When manufacturers decide or not to invest, they base their calculations on the discounted revenue and corresponding mass of profits and not on the original undiscounted values which are difficult to determine in any case.

    I usually base the rate of profit on non-financial corporations because these include both manufacturing and commercial corporations for these reasons. I find it satisfactory and revealing. To develop theory the pre-requisite is to understand your subject first and that requires empirical mining.

    1. My experience in working in several multinational corporations is that they deduct wages for what’s called ‘direct labor’ (manufacturing, direct sales force, etc.), like cost of goods sold, in determining gross profits but then deduct wage costs for indirect labor (administrative workers, legal, accounting, etc.) to get net profits. But differenet companies place different groups of workers in ‘direct’ vs ‘indirect’. So what’s the aggregate.

      I have a question I’ve not been able to get an answer for from corporate finance managers: where do businesses account for the ‘expense’ of stock buybacks and dividend payouts? It’s important if they do so either before determining gross or net profits. That would reduce ‘profits’ as retained earnings. And if they increased these expenses over time, it would result in a ‘falling mass’ of profits reported, wouldn’t it? How much are we in fact talking about? For the Fortune 500 companies alone, this year they are on track to ‘deduct’ $1.5 trillion in stock buybacks and dividend payouts. Under Trump, 2017-19 it averaged $1.2 trillion a year. Under Obama, it averaged $800B a year. So it’s a definite trend. Or are these ‘expenses’ paid for out of retained earnings and net profits? There are no many slush funds that management sticks away part of profits, usually in order to reduce their tax requirement.

      In short, you can’t estimate profits and the falling rate tendency unless you understand the accounting games corporations play.

      1. Share buy backs and dividends are correctly deducted from equity. They should not and are not deducted from profit. Legally, equity is what the firm owes its shareholders. Ergo every payment to shareholders reduces the liabilities of the firm in this regard.

        Agreed firms differ in their treatment of wages, but accounting rules are quite clear internationally, that clerical costs only appear after the derivation of operating income.

  6. I’ve read 4 of Harvey’s book. In one, “17 Contradictions and the End of Capitalism,” he calls himself a ‘revolutionary humanist,” not a socialist or Marxist. I do have a question. The MR school pushes ‘over-accumulation’ as one of the fuels for financialization and military Keynesianism. How does this fit in with the issue of rate and mass of profit?

    1. In brief Sweezy and Baran rejected the law of profitability in favour of a theory of excessive surplus or mass of profit as the cause of crises. This surplus was the result of monopolies. So the crisis is caused by the difficulty of absorbing the surplus either by military spending or other unproductive activities. In a way this is a version of underconsumption as the cause of crises. Professor Harvey has sympathy with this theory, as he said.

      1. I think S and B proposed that monopolization produces excess surplus value (monopoly rent) which causes stagnation, not necessarily to crises.

        Of course, competition (in the “free” market) causes the rate of profit to fall. Generalized monopolization/stagnation, stagnation was capitalism’s countervailing measure. Stagnation then was countervailed by financialization, which raised profits via a global war on labor, which in turn introduced a permanent state of crisis, war and chaos. Nevertheless, the rate of profit continues to fall.

        Both Sweezy and Baran made it clear that they were not undermining either Marx’s labor theory of value or the “tendency”. They were applying historical materialism to contemporary conditions.

        …Identifying both authors with David Harvey is unfair. Whatever one thinks of the so-called “Monthly Review School” it has remained revolutionary and anti-imperialist.

      2. Baran and Sweezy conclude: “The whole motivation of cost reduction is to increase profits, and the monopolistic structure of markets enables the corporations to appropriate the lion’s share of the fruits of increasing productivity directly in the form of higher profits. This means that under monopoly capitalism, declining costs imply continuously widening profit margins. And continuously widening profit margins in turn imply aggregate profits which rise not only absolutely but as a share of national product. If we provisionally equate aggregate profits with society’s economic surplus, we can formulate as a law of monopoly capitalism that the surplus tends to rise both absolutely and relatively as the system develops.” (Baran & Sweezy 1968, 71–72)

        By substituting the law of rising surplus for the law of falling profit, we are therefore not rejecting or revising a time-honoured theorem of political economy: we are simply taking account of the undoubted fact that the structure of the capitalist economy has undergone a fundamental change (my emphasis) since that theorem was formulated. What is most essential about the structural change from competitive to monopoly capitalism finds its theoretical expression in this substitution. (Baran & Sweezy 1968, 72)

      3. The increasing returns to monopolies thesis of Paul Baran and Paul Sweezy does not, in my opinion, contradict the average decreasing returns thesis. Why do not you do it? Because they are rates of DIFFERENT economic subjects. The Baran and Sweezy rate refers to monopoly firms and the ” fetishists ” rate of the declining rate refers to an ” average capitalist firm ”. Average company that contains monopoly companies (with an increasing rate) and the rest of non-monopoly companies (companies with a highly decreasing rate until their disappearance). The authors of the decreasing rate, including M.Roberts, repeatedly insist, and this veracity in the data honors them, that their rate is an average rate, of the whole of praise, of an average economy, etc. And the source of its data, which are the statistical samples of the Central Bank Balance Sheets, shows that it is an average data because that source only allows to obtain an average data of the capitalist companies

        If the non-mopolistic companies lose, in favor of the monopolies, every day, market share, customers, assets and employees until their disappearance, their rate of profitability must be, yes or yes, decreasing. Because the negative economies of scale of a company that reduces its size play against its profitability. Therefore, if it is very possible that the average rate is decreasing.

        And it is the average rate that really matters to assess the health of capitalism because it is the rate that affects most individuals and companies in the model. The one that affects the members of non-monopolistic companies. Let’s say, as an approximation, 80% or 90% of the subjects.
        Without a decreasing average rate, Capitalism would be eternal. Why would it collapse and an economic model with a majority of subjects in an increasing or stable rate of return would have to be changed?
        The declining (average) rate of return thesis denies this viability of capitalism. Other theses, such as the cycle of class struggle, only confirm this.

      4. The key word in the first paragraph is “provisionally”. Their provisional “law” and monopoly capitalism itself–both epiphenomonal–are determined by Marx’s law of value and its most important corollary (trpf).

  7. This just came out today. I highly recommend everybody to read the second slide of this article:

    Key points from the “The CPC: Its Mission and Contributions”, by Wu Tiantong:

    It is just three lines long.

    There’s the tale of some king of France who commissioned from a cartographer the best map of France ever. He wanted the perfect map, one which would allow him to have full knowledge of France’s geography. The cartographer came with a map the exact size of the entire territory of France to the king.

    The moral of the story of this tale is that the human being’s gift is the power of synthesis. And this is where science is humanly useful: it creates models from which humans can make objective analysis of reality, and predict its behavior.

    That’s what Marx’s Capital is: a scientific model of capital. It is reality – but a synthesis of reality, a synthesis humans can use to analyze and make predictions over the given object. Many Western Marxists and anti-Marxists commit the serious mistake of mechanicism, that the real world must replicate exactly what’s written in Capital in order for Capital to prove or not its validity. That’s the wrong way to use it, as it presents capital in its purest form, in its essence, not as it presents to ourselves.

    But, long story short: Marx’s theory is true and is definitive. There’s no point trying to search for anything else.

  8. I agree that the rate of profit in general is falling and it is the best explanation for crisis
    My question from you is :
    This general fall of rate of profit does not say anything about specific sectors or industries or firms that might have raising rate of profit
    Is it possible for capitalist society to have two or more rate of profits with different trends ?
    What is the relationship between general rate of profit and specific rate of profit in different parts of productive capital

    1. You are right. the rate of profit is a general rate of profit or an average in the total economy. Sectors will have different rates of profit and within sectors, individual companies will have different rates of profit. But competition and the switch of investment from lower profitability sectors to higher profitability sectors is going on all the time. If you took a snapshot of profitability in different sectors you would see a wide variation, but the tendency is for these differentials to equalise and so we can establish an average rate of profit for the whole economy.

      1. Still, I’d love it if you could do a post summarising the controversy and your position on it. From what little I could understand, the equalisation of the rate of profit has something to do with the transformation problem, though I don’t quite understand the connection. I also know that you subscribe to Fred Moseley’s view that there’s no transformation problem, while Cockshott thinks that in Capital volume 3 Marx made a mistake in distancing himself from his views from volume 1 (he seems to follow Kalecki on that). But I don’t really get the issue of equalisation, and Cockshott purports to show empirical evidence that it doesn’t happen (then again, he talks about price equalisation and here you talk of rate of profit equalisation), so this seems to be the most confusing part of Marxist theory I’ve stumbled upon so far. I feel if I can overcome this confusion, I’ll feel on much firmer ground.

    2. ” Is it possible for capitalist society to have two or more rate of profits with different trends?”

      It cannot by definition. Capitalism is just one world system, one world market. There are not two, three, four etc. capitalisms.

      Now, between different sectors, of course, there are different profit rates. Indeed, any coincidence can be only accidental at this level. The process of equalization is more important than the equalization itself; it is a process, not a goal.

      1. The problem with general average rate of profit is :
        This is a mathematical calculation only
        Nobody experiences it and it is just for simplicity
        For example we can have 99 rooms with 0 degree temperature and one room with 100 degree temperature , the average rate of temperature is 1 degree but there is no room with 1 degree temperature in reality
        You might say if the heat flows freely between rooms the temperature will be 1 degree in all of them eventually
        But first of all this event didn’t happen yet so it is not materialized and might take long time to happen
        Secondly in case of capital the flow of capital from one place to another is not fast angry mainly because there is a cost to change the field of investment
        Nobody can change a cable producing company to car factory in a blink of eye

      2. In fact I am saying that although the fall of rate of profit might be the best indicator of crisis and eventual disappearance of capitalism but as long as this fall is an indicator and not a material and real economic entity that acts in materialistic way , we cannot consider it as a cause of any crisis

      3. In fact I am thinking maybe the MEAN rate of profit , the rate of profit that majority of capitalists experience might be a better indicator
        I was wondering what Michael and other comrades think

      4. The important rate of profit, the one that determines investments is the enterprise rate of profit or pre-tax rate of profit after deducting interest and depreciation. In point of fact the capitalists calculation of their expected rate of return is more accurate at a micro level than what we can achieve because their cost accountants will have worked out the cost of the new or additional fixed capital and the required working capital. The problem with most Marxist calculations at a macro level is they think the rate of profit is based on fixed capital alone and not on fixed plus circulating (working) capital which it is. Cost accountants would shake their heads at this because most firms fail due to an insufficiency of working capital.

        Look, the for the capitalists to succeed they don’t need to know what is going on under the hood. They just need to know how to steer, accelerate, brake and indicate. If they get it right they profit, if they get it wrong they lose their capital. It is one thing to be a good mechanic and not know how to drive, it is is something else to be a good driver but mechanically illiterate. However to be a Marxist one needs to be a good mechanic as well as a good driver. (Now that is a fine analogy)

    1. In reply to Ucanpolitical: ‘after deducting interest and depreciation’ you say. But what interest rate are you referring to? Some fictitious ‘average’, which of course there is no such thing. And as for ‘depreciation’, there also is no objective depreciation estimate. It is all defined by legislation. And different countries define it differently. So how to aggregate something (depreciation) across countries when it is itself a legislated concept. The USA has been ‘liberalizing’ depreciation rates since the 1980s. What capital equipment was once depreciated over 30 years can now be depreciated in one year! Again, lots of discussion using sloppy definition of terms without quantification

      1. Jack where I agree with you and it makes me quite angry towards the BEA because it degraded the quality of the data, was the 2012 revision to the National Accounts. Up to then R&D and in-house software was taken correctly as a cost. After that it was capitalised by means of an imputed sale, an invented sale, and what was a cost became depreciation.

  9. I think some mainstream economists have a point when they accuse marxists of not being “rigorous”, even if the mainstream economic theory is just bourgeois obfuscation. Marx is somewhat justified for trying to explain very simple calculus using cumbersome vocabulary and not mathematical notation because of the time he was writing and his (lack of proper) training in maths. But it is inexcusable in 2021 to still bother with evident issues like this. For example, with respect to the “double-edged sword”, Marx (and Michael) are of course correct (and Harvey is wrong) but it is astonishing how the worlds most famous “marxist” (Harvey apparently) can’t grasp a relation that a STEM freshman should, namely, the relation between a function and it’s first derivative. What took Marx 5 sentences (in the quote provided at the start) to describe as a relation between mass of profit and rate of profit can simply be described if one understands the mass of profit as a function of time, say M(t), and (then), if we posit that the rate of profit (the first derivative of M(t) wrt to t)declines, that means M can still rise, but in diminishing pace. Mainstream economics call it “diminishing returns”. So yes, they are clearly directly related and to say that it is the mass not the rate doesn’t make any sense but the way Marxists communicate these relations is, yes, not rigorous for our time.

    1. A really fascinating debate, and I hope Michael will be able to address Jack Rasmus’ forthcoming paper, as we can only benefit from such challenges. I was however somewhat surprised by the comment by saigon. First, the relation between the rate of profit and the mass of profit cannot be comprehended by simple mathematical notation. Second,”because of the time he was writing and his (lack of proper) training in maths” is decidedly baffling. When he was too ill to work Marx relaxed by studying Mathematics. Among the authors he studied were d’Alembert, Landen, Lagrange, MacLaurin, Taylor, and Hall and Hemmings ( 1852), as well as Newton’s ”Principia Mathematica”, ”De Analysi per Aequationes Numero Terminorum Infinitas” and ”Analysis per Quantitatum Series, Fluxiones et Differentias,” which like Adam Smith he read in the original Latin. His mathematical manuscripts contain much on differential calculus. Thus on Lagrange Marx writes: ”Lagrange’s great service is not only to have provided a foundation in pure algebraic analysis for the Taylor theorem and differential calculus in general, but also and in particular to have introduced the concept of derived function” (”Mathematical Manuscripts of Karl Marx” new park publications 1983).

      P.S. Saigon’s ”it’s first derivative” betrays a vulgar grammatical mistake one should not expect an elementary student, much less a freshman to make!

      1. 1) “First, the relation between the rate of profit and the mass of profit cannot be comprehended by simple mathematical notation”

        Why? Capital is an investigation of the “laws of motion of a capitalist economy”. This is a patently newtonian “slang”. Moreover, even if Marx thought it couldn’t be comprehended like that, he would be wrong. Capitalism is a system subject to change and we can study it as such, under certain assumptions (guess what, this is what Marx did). He might have studied calculus but 150 years have passed and we have way more analytical tools. Not using them has led to stagnant debates with polsci grads dominating in a field they have little to contribute.

        2) On his math studies: thanks, I know he did study a lot and I have read parts of his math manuscripts. Just because he commented on these figures doesn’t change from the fact that his exposition is severely lacking by our current standards. And this dispute between Harvey and Roberts is the perfect illustration of why. And I elaborated on that. The (mass of) profit function, seen as a function of time implies directly that its first derivate is the rate of profit. Now how one defines this function can certainly vary (and thus you can define a “Marxian” profit function, “neoclassical” one and so on). But in any case, the rate of profit is the first derivative. It doesn’t get any simpler than that.

        P.S – I am aware of the mistake. I usually do not use apostrophes when commenting on the net. I also did another mistake, did you notice that? Happens when you write fast/don’t expect the police to show up.

      2. To Saigon: “This misses out the key variables that affect the dynamic rate of profit. In a vague sense the function t/(1+t) since it is asymptotic is a model for any asymptotic process, but it misses out the specific factors relevant. The more correct formula is r’=g’t’/a where r’ is the post depreciation profit rate, g’ is the rate of growth of the working population, t’ is the rate of improvement of technology measured as physical labour productivity, and a is the share of profit accumulated. If the rate of growth of the population tends to fall to zero, tthen the profit rate falls asymptotically to zero. But the original formula you gave misses out the CAUSAL Relations” ( I owe this to Paul Cockshott -emphasis added).

      3. There is value literally in your formula provided a is the rate of surplus value which I presume it is because you are referring to the mass of profits share of output. But your formula excludes the growth of capital. Productivity is also a function of the growth in constant capital. So I would recast it as r’ = (g’s’)/c where s stands for the rate of surplus value and c for capital accumulation. Clearly the growth of the working population times the growth in its productivity provides the potential for future profits and I endorse that part of the formula prior its modification.

        However, the rate of surplus value brings it all together, as it incorporates productivity, turnover and exploitation. Which is why the formula which relies on results rather than trends would be r=s/rc where s stands for the rate of surplus value and rc for the rising composition of capital.

        Despite this, as a forecasting tool, one that in the absence of crisis, could predict the future rate of profit, your formula has great merit. I have not encountered a formula which combines the physical with the social before. However, I do distinguish it from r = s/rc because this formula is backward looking while yours is forward looking. Both have their place.

  10. We can argue about the components, what constitutes–empirical values, utilized-the rate of profit, and that misses the point, and by a mile. Marx focuses on the fall in the rate of profit as a tendency, an index, to both the “development” of capital, and the governing limit to that development. It’s a tendency, so……unless Jack can show us in his enhancement of Marx’s critique how that tendency does not function as that index to both, we’re just spinning our wheels in, to use an overused word, “abstractions.”

    So….various challenges have been put to Jack before, and remain unanswered, like
    1) where does Marx in Vol 3 talk about “secondary exploitation” as augmenting the actual profit in industrial capitalism? spoiler. Marx does not.
    2) where has the overall “social” rate of profit, including the profit rates of the FIRE sector, arbitrage positions, etc counteracted, in the long term, as a TENDENCY itself, the tendency for the rate of profit to decline?
    3) where has the tendency of the rate of profit to decline NOT been reflected in a parallel decline of the profitability allotted or claimed by financial and commerce sectors?
    4)given Jack’s thesis what is the source of the immanent tendency of capital to become its own obstacle to accumulation?
    5) Is there even an immanent tendency of capital to become its own obstacle to accumulation?
    6) What are the causes of “financial crisis”? Irrational exuberance? Overleveraging? Those are descriptions not causes.

  11. Here’s a layperson’s take, which you might consider a result of reading this blog over the past couple of years, plus some other casual reading of my own.

    i. The table by Esteban Maito for those 14 countries (presumably present-day advanced economies with reliable economic records going back into 19th century), which Dr Roberts often uses in his columns, does show a clear trend in the decline of the rate of profit.

    Dr Rasmus asks for a definition of “tendency”, and questions the reliability of the econometrics used by Marxists to calculate the rate of profit. Well, in mathematical terms, a tendency or trend, so far as I know, is the same as a trendline – a linear function used to describe a more complicated process (the actual rate of profit) over time that enables one to see what happens to the process going ahead.

    What draws me to Marxian economic analysis is that it looks empirically well-founded, though of course I can be mistaken. And if that’s true, then it behoves Dr Rasmus to show that the trendline is wrong – that you can generate any line you want by calculating the rate of profit differently, and as such that the TRPF is unfalsifiable; or by showing evidence that Maito and others are cherry-picking data to demonstrate a foregone conclusion.

    Otherwise, the empirically verified TRP does support the abstract TRPF of Marx’s at least to someone like me who only takes what I read here at face value. At least, for the countries where it’s been possible to study it.

    ii. About crises, I’m not qualified to say whether the TRPF by itself explains crashes, followed or not by slumps. Perhaps there are more important immediate factors for crises and TRPF has more to say about capitalism itself as a mode of production doomed to run its course and be replaced by something else, hopefully socialism.

    However, I believe from reading Mr Roberts that the gist of the TRPF argument is that crises only happen after periods of decreasing profitability. There’s a subtle difference here: the rate of profit may not “trigger” crises, but it “forecasts them” (this reminds me of the Granger causality test I discussed with Dr Roberts a couple of posts ago). Whenever a crisis happen (or one that triggers a slump, as opposed to those circumscribed to the financial sector), it’s never after a period of rising profitability. That may sound like a platitude – why would there be a crisis if the rate of profit is increasing! – but the gist of the Marxian argument here is that the rate of profit is the only forecasting metric that works: things like debt, investment, exchange rates, the rate of interest, financial wizardry, trade imbalances etc. don’t pass muster in that they don’t have trends to them that correlate temporally with crises.

    Dr Rasmus may well be right that the trend in profitability doesn’t allow us to say when a crisis will happen with certainty. It just determines periods in timeline when one can occur at any moment (as opposed to periods when it’s rising and no crisis is to be expected). It might well be that you need complex econometric analysis to forecast crises. Dr Roberts mentioned in a post last year that some mainstream economists had use AI to forecast crises several quarters ahead. And in a recent post, he comments on the Austrian study that shows an inverted bond yield curve correlates well with a recession within the year, while remarking that this is an observation without a hint at an underlying mechanism.

    That’s why empiricism is a double-edged sword: you may find curves that forecast one another, and gain some predictability, without knowing why it’s happening. For that you need a mechanism, which is why science uses empirical data, but isn’t the same as empiricism as it tries to find the underlying explanation. Otherwise you can end up with trend analysis that collapses the moment a black swan event modifies the trends in a way you couldn’t have forecast.

    Personally, I think that the TRPF’s ability to predict recession danger zones is a mighty accomplishment. It may not tell an investor when to realise profits and pull out, but it allows us to not be surprised when one happens, and to use the analytical tools we have within the Marxian framework to perform a proper post-mortem of crises after the fact. Not to mention that, if it’s true, the TRPF means one shouldn’t trust Capitalism to solve much looking ahead.

    iii. I dunno whether someone has said that before, but… doesn’t the TRPF imply that crises should become more frequent as time passes, even if we can’t use it to predict when they happen?

    The reason I ask is because I noticed in Maito’s plot that recoveries in the TRP after a crisis never bring it to the same level of the previous recovery period: it recovers relative to the preceding slump, but never matches the previous period of prosperity. I take it to mean that Capitalism needs to expand its sources of surplus value to recover: open labour and consumer markets, increase productivity by technology, and destroy less profitable enterprises by bankruptcy or even war.

    But as we reach its terminal stages, all reserve armies of labour have been tapped, technology delivers diminishing returns etc. and Capitalism finds it harder and harder to recover. In mathematical terms, it’s like an oscillator losing its momentum: the rate of profit bobs ever more quickly up and down as it loses amplitude because it cannot reach the same levels from before. The ceiling of achievable profitability comes down, making slumps longer and recoveries more anemic. In other words, production crises that wipe out non-performing companies may restore profitability a little, but unless there’s a major war or some incredible breakthrough like aneutronic nuclear fusion for energy production, instability will be the norm.

    Sorry for the long post, Dr Roberts, I was trying to put my ideas in order from this discussion.

      1. The fall in the rate of profit is also about crises, but not only. The fall in the rate of profit indicates that capitalism is not a “natural” but a historical mode of production.
        It is pointed out from many quarters today that the capitalist mode of production ruins nature and people. That’s right. At the same time, capital is ruining its very special foundation:

        “The real barrier of capitalist production is capital itself. It is that capital and its self-expansion appear as the starting and the closing point, the motive and the purpose of production; that production is only production for capital and not vice versa, the means of production are not mere means for a constant expansion of the living process of the society of producers. The limits within which the preservation and self-expansion of the value of capital resting on the expropriation and pauperisation of the great mass of producers can alone move — these limits come continually into conflict with the methods of production employed by capital for its purposes, which drive towards unlimited extension of production, towards production as an end in itself, towards unconditional development of the social productivity of labour. The means — unconditional development of the productive forces of society — comes continually into conflict with the limited purpose, the self-expansion of the existing capital. The capitalist mode of production is, for this reason, a historical means of developing the material forces of production and creating an appropriate world-market and is, at the same time, a continual conflict between this its historical task and its own corresponding relations of social production.” Carl Marx, The Capital III., Part III. The Law of the Tendency of the Rate of Profit to Fall, Chapter 15.

        Wal Buchenberg, Hannover

      2. Wal I agree. The LTRPF is both cyclical and secular; both the (underlying) cause of crises; and explaining the transient character of the capitalist mode of production. That is why it is the most important law of political economy.

  12. Some observations based on the discussion here:

    1) Marx didn’t analyze “the motion of capital”. He analyzed capital itself, capital as-it-really-is. He logically demonstrated capital is a process, not a thing. The title of his magnum opus is literal;

    2) You don’t need arithmetic to mathematically demonstrate something. Euclid’s “Elements” have no arithmetic language at all, and yet it is mathematically true. Marx’s logically demonstrated the existence of capital and its essence, it is mathematically demonstrated – we don’t need to delve into his “formulas” or eventual numerical mistakes in some tables or schemes that appear in book III;

    3) There’s a historical difference between bourgeois economy and Marx’s theory. Marx investigated capital so that the proletariat could abolish it positively, i.e. he analyzed the thing scientifically so that he could get to its true essence, in a way the proletariat could comprehend it as it really is in order to overcome it (change the world). The bourgeois economists are raised to serve and counselors and advisors of the bourgeoisie (directly or indirectly, in the form of serving the State); to the bourgeois economists, Economics is just a tool to serve the bourgeoisie to preserve capitalism and, meanwhile, to help individual capitalists to make correct investment decisions (and the State, to achieve growth and order). That’s why prof. Rasmus is so revolted with Marx’s theory: he can’t use it to predict exactly when corporation x will achieve profit y at date z, or when crisis a will happen, and by what magnitude. He can’t use it to his clients. Marx’s theory is useless as a tool of advising to the dominant classes. That’s why the capitalists themselves pay more attention to Marx than the bourgeois economists: they can use Marx as a tool of class struggle, to predict how the organized proletariat will act, and how they should act in order to counter it.

    1. ”That’s why prof. Rasmus is so revolted with Marx’s theory: ” This is manifestly false. What he IS affirming is that Marx’s project is unfinished; and to treat Capital as a Holy Bible is decidedly unscientific.

      1. Hear, hear. I heartily agree.

        It’s strange to rhapsodise about how scientific Marxism is and at the same time disparage any attempts to build on the path-breaking advances of its founder as anathema.

        I see a good analogy with the Life Sciences here. Our theoretical framework for them is Darwin’s Theory of Evolution. All data, empirical and experimental, collected by scientists in the field must be tested against the framework. If there’s a match, we move on and both the theory and the data are strengthened. If there isn’t a match, either the theory needs to be emended or even discarded, or the data should be double-checked and reproduced for thoroughness (after Feynman’s “extraordinary assertions require extraordinary evidence”).

        So far, Evolution has held. But we no longer even need to read the Origin of the Species to understand evolution. (Though I hear it’s great reading.) It’s like the solid, invisible foundations of the beautiful edifice we’ve built. It pervades all our understanding of life and gives us clarity in our scientific endeavours.

        Ditto for Marxism, with the cautionary remark that the closer we get to Social Sciences, the more the human factor can muddy things and demand flexibility in our reasoning.

        Capital was written 150 years ago. But from my reading this blog and other sources, I’m sold on Marxism precisely because of its scientific outlook. Its theoreticians like Dr Roberts, Paul Cockshott and Brian Green (the ones I know better, remember I’m a layperson) use empirical data, debate how they fit to models, and try to USE Marxism as a theoretical framework they can build on. Capital isn’t the be-all and end-all of it, and to be scientific is the opposite of treating it as Holy Writ.

        I can’t tell whether Dr Rasmus is a Marxian or not. But I can tell that he respects Marx’s findings and is open to discussing how his own models hold against them. It’s very well possible that his own ideas fit nicely into the Marxian framework – for example, that the econometric analysis of short-term trends he pursues does not contradict pillars of the theory, like the LTV and the LTRPF, but are important to understand how finance modifies short-term outcomes, including crises, and may even create distortions like financial centres such as London and New York having so much wealth concentrated in them.

      2. No, he puts it in a very sophisticated way, but, long story short, he’s clearly stating the Marx’s theory should include every possible variable in existence in order to be useful (i.e. “complete”) – all the while it has more categories than, e.g. Keynesianism.

        In other words, he’s claiming that Marx’s theory cannot be useful for a bourgeois economist. In that sense, he’s correct: what’s Marx’s usefulness if I can’t tell the CEO of Apple if the company will grow 2.0% or 2.5% in Q3 2024? Why would a capitalist hire an economist who can either only tell the obvious (i.e. you have to intensify the exploitation rate of your employees) or tell to his face there’s no solution to his problems (i.e. capitalism will eventually collapse)?

        Marx’s theory is only “incomplete” from the point of view of an economist who sees Economy as a technician tool to assist the capitalist class. Indeed, that’s why bourgeois economy exists and thrives in the first place.

        On the other side, where the interests of the bourgeois economists and Marx’s theory overlap is precisely the crisis theory. No bourgeois economics has any conception, let alone a theory, of crisis. The most they can come up with is simply the postulate that crises are an abortion of Nature that happen in spite of, not because of, capitalism. After 2008, it became a self-evident fact that wasn’t true.

        That’s why prof. Rasmus is charging Marx’s theory of being “incomplete”: he wants to transform it into a tool to predict crises. Not only when and where, but exactly when and where, and exactly by how much. Bourgeois economists are interested in Marxism only insofar as they can use it to advise their clients and thus protect them (and, therefore, the system) from the next crisis (or, in case the client is the State, to avoid the crisis altogether).

      3. Recall that capital Vol.3 breaks off just as Marx is about to tell us what constitutes ‘class.’ Anyway, he affirms a class is not constituted by an identity of its sources of revenue; perhaps a useful theme for Michael to address in a future post

    2. 1) That’s just unintentional mystification at best, quibble at worst. Also, capital being a “process” isn’t at all contradictory with stating that Capital(the book) is about studying the laws of motion of the CMP. It is just another, “non-newtonian” and certainly marx-ish way to say the same thing. I am not interested in verbal fetishism, but with the relations, categories, the mappings and the framework of the theory. Here is what Marx says in the Preface of Vol. I:

      “And even when a society has got upon the right track for the discovery of the natural laws of its movement — and it is the ultimate aim of this work, to lay bare the economic law of motion of modern society — it can neither clear by bold leaps, nor remove by legal enactments, the obstacles offered by the successive phases of its normal development. But it can shorten and lessen the birth-pangs.”

      “The physicist either observes physical phenomena where they occur in their most typical form and most free from disturbing influence, or, wherever possible, he makes experiments under conditions that assure the occurrence of the phenomenon in its normality. In this work I have to examine the capitalist mode of production, and the conditions of production and exchange corresponding to that mode….Intrinsically, it is not a question of the higher or lower degree of development of the social antagonisms that result from the natural laws of capitalist production. It is a question of these laws themselves, of these tendencies working with iron necessity towards inevitable results. The country that is more developed industrially only shows, to the less developed, the image of its own future.”

      So he explicitly says this is about the laws of motion themselves and he even connects his effort to the physicist.

      “My standpoint, from which the evolution of the economic formation of society is viewed as a process of natural history, can less than any other make the individual responsible for relations whose creature he socially remains, however much he may subjectively raise himself above them.”

      So the premise of his analysis (and it is correct) is to assume the processes that take place as quasi-natural. If you don’t do that, you simple can’t proceed with the analysis. (But he knows human societies are not natural systems in the same sense the solar system for example)

      2) Ancient Greek math was limited for due to the time, regardless of the impressive advancements. They didn’t use arithmetic, they relied instead on geometry, which was a limiting factor. Archimedes for example would approach the concepts of differentials and infinity which underpin modern analysis using geometrical insights. Moreover, arithmetic needs to be used eventually to evaluate if your theory bears any weight versus the real, observable world (otherwise you are just doing dogma). However, there are entire math fields that are not about arithmetic: functional analysis, topology, differential geometry, calculus, differential equations, to name a few, these fields are more than adequate to fully describe the natural world (and thus, the laws of motion of a capitalist system). This is not arithmetic yet.

      3) Your epistemology isn’t quite clear here. Marx said that political economy is the last denial of the bourgeoisie. He said that because his work revealed or intended to reveal a scientific truth about the CMP, a truth that went against the interests of the bourgeoisie, in the same way early natural science went against the interests of the church. And by being true, it was necessary a service to the proletarian struggle, directly so in this case. His position wasn’t a dogmatic or ideological one. Since then a lot of effort has been thrown at discrediting and sabotaging the development of political economy as a science, putting workers worldwide at a major disadvantage. Political economy (marxism) has a lot of catch up to do, especially when it comes to the tools it is using. With marxists like harvey or the “value theorists”, who needs open enemies of marxism nowadays.

      P.S – A simple demonstration of how the mass of profit and the rate of profit would look like as functions of time, respectively, try to plot the function t/(1+t) and its first derivative for t>0. A simple instance of an increasing function with declining rate (which as t tends to infinity, the function tends to the value of 1).

      1. There’s no interpretation here. Capital – as the thing-in-itself – is literally a process. This is scientifically demonstrated (by Marx). This is a very important discovery, as it puts to rest any claim that capital is natural or part of nature. That’s no my opinion: capital literally is a process; that’s a scientifically demonstrated fact, it’s not up for any further discussion.

        Thanks to Marx, we know for a fact, as an absolute truth, that capital is a social, historically specific process. It cannot exist outside the realm of human historical society.

        Newton just observed the phenomena, not the thing-in-itself. His theorems are all debunked. Marx’s theory demonstrated the thing-in-itself – his theory will never be debunked, because his demonstration is logically (philosophically) truth. There cannot be a better demonstration than that, because humans can never be the object they’re studying. Marx’s demonstration in Capital is as close as the thing-in-itself anyone will ever get, it is as good as possible of a pure mathematics demonstration.

        Euclid’s Elements only contain mathematical truths. They’re as true today as they were true in his days. The only thing that changed is the language used to express the truths contained in his book.

        Marxism in not political economy. Das Kapital is a critique of political economy, not a book about political economy. Marx was not a political economist (or, for that matter, a “classical” economist), he was a philosopher.

      2. Somehow you managed to completely ignore all my points. Whether something is historical or not doesn’t matter on that level of analysis. Marx explicitly said he is assuming a quasi-natural system for his analysis of CMP, knowing fully that this particular mode is socio-historical and not “natural”. You can certainly use math to analyze processes that are socio-historical. And if we want to be pedantic, everything is a process since everything is subject to change. What changes is the scale and timeframe. We just impose classifications and terminology in order to analyze. It is crucial however that we don’t fetishize the categories we create.

      3. For the unsound nature of Saigon’s reasoning, consider the following analogy: With an ambient temperature of 38 degrees C and humidity at 20%, the wet bulb temperature is 22degrees C.;but with humidity at 75%, the wet bulb temperature equals 34 degrees C., thus reaching the limit at which human life is sustainable. So if one were to plot on a graph rising temperatures and increasing humidity, and to affirm that the point they meet to give a wet bulb temperature of 35 degrees C. causes death, one can readily comprehend how unsound such a mathematical illustration is; for it is devoid of rationality to advance as an explanation in itself the claim that a wet bulb temperature of 22 degrees C does not cause death, but one of 35 C does. For the causes of death or not, one has to examine the various physiological stresses that human beings are subject to; the causes of death cannot be explained by a graph, though such a graph may illustrate the point, 35 degrees C wet bulb temperature, that trigger the actual physiological causes that result in death.

      4. @jlowrie

        ” for it is devoid of rationality to advance as an explanation in itself the claim that a wet bulb temperature of 22 degrees C does not cause death, but one of 35 C does. For the causes of death or not, one has to examine the various physiological stresses that human beings are subject to; the causes of death cannot be explained by a graph,”

        Now this is just sophistry. It is not that I disagree with that, and I don’t really. But what point are you trying to make here? An empirical study of what combination of these factors and their intensity sustains (or not) human life is a concrete question and in fact can be answered, as you said, by looking at that graph. Now, as with everything, you can always keep asking “why?” but I suspect this is where your sophistry kicks in. Well sir, it seems that some people wont be satisfied until we elaborate on the exact position and velocity of each particle of the human body(irony intended) under the conditions you just described to fully explain the “causes of death”.

        Can you now explain what is not sound with my initial argument? I repeat here that my argument was: the rate of profit is simply the first derivative of the profit with respect to time and for everyone who has elementary knowledge of calculus, a declining first derivative by no means restricts the function to increase. Are there other factors that come into play here? I am sure there are. But there is nothing wrong fundamentally with what I said. Moreover, I am not aware of any empirical data on this issue, but I would expect the graph of the “mass of profit” function (profit of productive capital) to be a monotonically increasing function. That is, it is reasonable to expect wealth generated to accumulate. Of course, graphs over longer periods might include “loss of wealth”, such as periods of war, but it is reasonable to expect that the profit function would have some “intrinsic” properties.

  13. This has been one of the most thoughtful and comprehensive debates on this site. One of the questions asked here repeatedly, is can the rate of profit be measured and if so, is it representative of the economy over time? To answer this essential if not intriguing question, I have prepared a post to show that it can be done and that the results yielded are powerful.

    I hope it satisfies many of the questions raised. The rate presented is based not only on fixed capital but fixed and circulating capital. Traditionally the rate of profit has been confused with the rate of return because it has been based only on fixed capital.

    1. The start dates of a data series determine the trend displayed.
      In your graph 8, the data from 1980 are given as the starting time. I find that problematic.
      Current capitalism developed from the post-war period (1945-1949), not from 1980. The year 1980 is not a historic turning point.

      1. If you check out my site you will find the rate of profit going back as far as 1950. I am more focused on the period pre and post 2014 as this is what is shaping current inter-imperialist rivalries and will shape the future class struggle.

    2. To Saigon:”” Can you explain what is not sound in my initial argument?” The more correct formula is r’=g’t’/a as I have posted above.

  14. Dear all
    I spend some valuable time to read this new intellectual fruit by Harvey. And I certainly regret the time spent.
    It is another gibberish piece by Harvey which shows his immense ignorance of Marxist Political Economy.
    Let me pinpoint only a few issues.
    First, he makes a lot of bruhaha about economists of all persuasions (Marxists included) neglecting the role of absolute size in favour of rates of change. This is totally stupid and exhibits an amazing lack of knowledge. All economic approaches pay attention to both measures.
    Second, regarding the operation of the Law of the Rate of Profit to Fall (LRPF) the crucial question is if and how the falling rate of profit impacts on the mass of profit. Harvey ignores all the relevant literature (e.g. Shaikh). Marx, and Marxist economists (Grossmann among them), are aware that over the capitalist cycle – and particularly before the onset of a profitability crisis – there is, usually, an increase of the mass of profit. But ultimately the falling rate tendency bites into the mass of profit. This has been shown both mathematically and also tested empirically. Harvey is totally ignorant of this. If this was a peer-reviewed article it would have been rejected outright.
    Third, Harvey hides his ignorance and blatant contradictions behind his misuse of dialectics. Dialectical contradiction does not mean incoherence, chaos and indeterminacy. The previous point highlights this. A flagrant example is how he messes up population growth with labour productivity, capitalist accumulation and crisis. An averagely erudite postgrad student of growth theory would do much better.
    Fourth, his analysis of interest bearing capital (IBC) is totally stupid – to say it politely. Harvey references Fine but in fact Harvey’s analysis is in obvious contediction with that of Ben. The latter (particularly in the debate with Panico) has differentiated IBC from money-dealing capital (MDC) and showed that this differentiates Marxist monetary theory from Keynesianism and Sraffianism. Harvey follows – probably without even knowing – the second path. A typical example:
    ‘Interest-bearing capital flows through two distinctive channels. Some of it flows from financial institutions and wealthy individuals seeking a rate of return (interest) on the money they lend out. The second intermingles with the circulation of state revenues as governments raise money, either directly or in the bond market, to build long-term projects of various kinds’
    But the best of all is the following idiocy:
    ‘The circulation of interest-bearing capital is not of course confined to production. Credit is extended to consumers, to buy housing, cars, consumer durables.’
    Last but not the least, Harvey’s text is full of incoherent and erroneous expressions (for example ‘fixed capital is not itself in motion).
    The motives behind this recent Harveyism can be easily discerned. Voicing M.Heinrich he attempts to reject the LRPF by contrasting it to the rise of the mass of profit. An irrelevant point that has been answered long ago..
    In toto, this is another example of the immense damage that Harvey is doing to Marxism.

    1. ”It is another gibberish piece by Harvey which shows his immense ignorance of Marxist Political Economy.” Harvey may be mistaken. I am not clever enough to feel so exalted as to pronounce such papal excommunication of Harvey from the holy priesthood of latter -day marxising saints; but gibberish is a sin of which he is innocent.

  15. It is apparently required that any visitor who has commented must join this discussion?

    I thought that by and large individual capitalist, however they choose to measure their profits, when they do, compares the money amount of profit on hand (literally, in bank accounts or in imaginary revenues from sales of financial assets at the moment’s market price,) to the money amount put into the process. That is, for the individuals, profit is basically the mass of money they would deem to be their gain if they were finished, how much they won. Since every individual capitalist began at different times, the rate is arbitrary.

    This may sound like Dr. Rasmus objections to averaging profits. But these difficulties in averaging apply to pretty much all economic phenomena, don’t they? There are difficulties in averaging wage rates, in averaging employment, in averaging marginal revenue. Probably Dr. Rasmus doesn’t mean to go nuclear with a skepticism that dissolves everything, but it is entirely unclear to me what he does accept as valid measuring in the economy.

    It seems to me that the rising mass of profits means most capitalists can calculate *they* are making profits and may continue production, even though the overall rate of profit is declining. There is no coordinated way for them to know this, after all. The result is that at some point, there can be a general glut of commodities, resulting in losses on continued production (or decreased production at the older prices?) I do not understand how Dr. Rasmus’ profits from other sources wouldn’t, when profits from production in one line decline, be used by some capitalist, to invest in other, more profitable lines. That, in short, Dr. Rasmus’ story is that there is no such thing as a general glut of commodities, only financial chicanery that prevents finance from fulfilling its function in re-allocating credit for capital accumulation in more profitable areas. To put it another way, I can’t tell how Dr. Rasmus is different from Friedrich von Hayek. Or for that matter whether he accepts or rejects Say’s Law.

    To repeat, the possibility of a general glut of commodities is conditional upon a systemic error on the part of capitalists, who are not misled by animal spirits or financial fictions, but by the concrete experience of profits in hand, something that happens because the mass of profit is rising throughout the economy. I don’t understand how Dr. Rasmus explains how there can be any periodicity in the economy, nor how there can be a general crisis, especially when on an economy-wide scale, every profit seems to match up with somebody else’s loss…or opportunity cost, at any rate.

    I am also under the impression that profits in Marx’s labor theory of value, whether considered in the form of a rate or a mass, are generated in the production process, which is why businessmen don’t worry about inflation of real estate or stocks but do worry about wage rates, regardless of their formal calculability. And that the capitalist division of labor must include an industrial reserve army of labor. And that there is a ceaseless struggle to lower the wages of the property-less which is essential to the normal operation of the capitalist system. I don’t understand how Dr. Rasmus accepts any of this.

    I have to add that even if Dr. Marx was a credentialed philosopher whose dissertation was on Democritean and Epicurean materialsim, I can’t agree that Capital is scientific precisely because it is logically/philosophically proven. Even if I didn’t think such an idea was the opposite of dialectical, Ludwig von Mises’ Human Action purports to do the same. How do you tell which speculative philosopher sits ex cathedra, not merely in their armchair?

    In the end, to me it seems that even the thesis of absolute immiseration of the proletariat has not been refuted, not on a world scale over any significant period of historical time. Nor does it seem to me that alternative theories of profit have earned complacent acceptance. It is entirely fashionable to seem Marxism as a moral critique and Marxian economics that actually takes the labor theory of value and surplus value and planning and so on and so forth as some sort of passe fashion. But then, I suppose the above has already exposed my ignorance.

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