Falling Rate of Profit?

The April issue of Monthly Review contains an article by the contemporary German Marxist scholar Michael Heinrich titled “Failure of the Falling Rate of Profit Theory – Marx’s Studies in the 1970’s.” Marx had maintained in Volume Three of Capital that there was a tendency for the general rate of profit to fall in capitalist economies, which tendency he maintained was part of the inherent logic of capitalism. This was not a view unique to Marx, of course. Adam Smith, for example, in Book I, Chapter 9 of The Wealth of Nations maintains that the rate of profit tends to fall over time due to completive forces. John Stuart Mill also argued that there was a tendency for the rate of profit to fall over time. But Marx made this an important part of his critique of capitalism in Volume Three of Capital. Heinrich, in his article and in chapter 7 of his recently translated book, An Introduction to the Three Volumes of Karl Marx’s Capital, also published by Monthly Review Press, maintains that this “law” applies only under certain specific conditions. To understand his argument, it is helpful to develop the simple math of Marx’s argument.

In Chapter IX of Volume I of Capital Marx had defined his terms:

C  =  Total capital
c  =  Constant capital or dead labor incorporated into capital goods
v  =  Variable capital or labor wages
C  = c + v
s  =  Surplus value produced by capitalist production

In Chapter III of Volume III of Capital Marx presents the definition of profit in capitalist enterprise:

profit formulaBy dividing both the numerator and denominator by v, we get what Morishima (1973, Marx’s Economics) called “the fundamental theorem of Marxism”:

The Fundamental Theorem

What this equation clearly shows is that as relative investment (c/v in the denominator) increases, the rate of profit tends to fall, assuming a constant rate of exploitation (s/v in the numerator).

Constant Rate of Exploitation

In Chapter XIII of Volume III of Capital Marx presents his argument for “The Law of the Tendency of the Rate of Profit to Fall.” Marx starts with the example of a constant rate of exploitation. In his example the value of constant capital is varied from 50 to 400 currency units while in each case v is equal to 100 and the rate of surplus-value is 100%, or 100 currency units. He calculates the rate of profit in each case (s/C) and finds that the rate goes from 66.67 percent in the first case to 20 percent in the last case as investment is increased from 50 to 400 units. I think it is useful to see this graphically in the following figure. In this case of the “same degree of labour exploitation” the result is a falling rate of profit as relative investment, c/v, is increased.The figure illustrates this case. s/v is constant, meaning that the application of capital has not made an hour of labor more productive. This is surely not a very common situation. Why would a capitalist invest if he didn’t think that it would make labor more productive? This case results in a falling rate of profit: as the constant capital increases from 50 to 400 units, the rate of profit falls from 70% to 20%.Surplus Value and Profit Marx's Numbers_Page_1

With this background in the simple math of Marx’s model I want to illustrate the impact of several additional cases as follows:

  • Increasing c/v and Decreasing s/v
  •  Increasing c/v and Increasing s/v (s/v < c/v)
  •  Increasing c/v and Increasing s/v (s/v > c/v)
  • Increasing c/v and Decreasing v (Constant s/v)
  • Increasing c/v and Decreasing v (s/v > c/v)

Graphs similar to the case of constant exploitation are illustrated below for each of these cases.

Increasing c/v and Decreasing s/v

Surplus Value and Profit Marx's Numbers_Page_2In this case I have assumed that the rate of exploitation would decrease as investment is increased. This is not a very realistic case, either, since it would imply that the surplus per worker decreases as more investment is supplied. Not surprisingly, the rate of profit falls in this case as well and to a lower level than in the case of constant surplus exploitation.

Increasing c/v and Increasing s/v (s/v < c/v)

 Surplus Value and Profit Marx's Numbers_Page_3This is a more realistic case. Here, as investment is applied to the enterprise, the rate of extraction of surplus from an individual worker increases. For otherwise, why would the capitalist invest? In this case the rate of profit still falls, however, from an initial value of 70 percent, but in this case to only 40 percent.

Increasing c/v and Increasing s/v (s/v > c/v)

Surplus Value and Profit Marx's Numbers_Page_4This case is set up so that the rate of growth of s/v (the slope of the line) is just greater than the growth rate of c/v. Unlike the previous cases, this case yields an increasing rate of profit. Is this a possible case? It certainly seems to me in cases where the rate of surplus extraction is greater than the relative value of capital invested that profits would rise. In any case, it seems to illustrate the incentive that capitalists have to increase s/v, by increasing the amount of surplus achieved (by monopoly, for example). This case assumes a constant variable capital.

Increasing c/v and Decreasing v (Constant s/v)

Surplus Value and Profit Marx's Numbers_Page_5This next case illustrates the case where the variable capital following investment is driven down, either by decreasing the number of workers or by decreasing their pay, or both. In this case s/v, the rate of exploitation is constant. This turns out to be another case where the rate of profit falls, from 70% to under 20% as constant capital is increased from 50 to 400.

Increasing c/v and Decreasing v (s/v > c/v)

Surplus Value and Profit Marx's Numbers_Page_6In this last case we assume that the rate of expenditure on wages and supplies (variable capital, v) decreases, the situation that one would think the capitalist investing in an enterprise would expect, but unlike the previous case with falling v, in this case the rate growth of the rate of exploitation, s/v, is greater than the rate of increase in relative constant capital, c/v. In this case, the rate of surplus starts at 100% of wages (v) but increases to 150% as investment is applied. Here we see that the rate of profit soars from the initial rate of 70% to 120%.

So what does this seem to show? To me it seems to show that, even in Marx’s world of pure competition, it is very possible for profit rates to increase, but for this to happen the rate of exploitation needs to increase more dramatically as more investment is applied. In our age of globalization and union busting, isn’t that what we see happening?

About Randal Samstag

Randal has an undergraduate degree in political philosophy, but has a graduate degree in engineering and has earned his bread for 30 years working on municipal and community water supply and wastewater collection and treatment systems in the US, Caribbean, Latin America, and Asia.
This entry was posted in Economics. Bookmark the permalink.

8 Responses to Falling Rate of Profit?

  1. There has been some traffic on this issue; critiques of Heinrich’s article by several commenters are referenced in the Monthly Review here). Also see a post by Yanis Varoufakis that touches the question of falling rate of profit in the course of justifying his view of “What is to be done” for the Eurozone. Also see Michael Roberts’s response to Heinrich’s response to his critique here).

  2. Pingback: Piketty’s Capital | Notes from my library

  3. There has been some lively discussion of this topic on Professor Robert Paul Wolff’s blog, The Philosopher’s Stone. I will post here a comment which came up in an exchange between a poster, Chris, and myself and, subsequently, post my reply.


    I appreciate the reply.

    For some reason I don’t see any mention of Zizek in that blog post? I do empathize with the author of the post though, in that in many academic settings I waver between being reticent about my views, to ensuring I insert them. Of course given the anonymity of the internet, I do the latter more. Critical realism is a philosophy of science; quantum mechanics is a field of science. There’s an important distinction there. In general critical realists argue that the sciences are in fact getting at the nature of reality, unlike let us say Kantians who argue that there is an unbridgeable gulf between the subject and the thing in itself, or Humeans who may argue that we cannot be absolutely certain that our sciences really are correct because the future may be different from the past. A blogs comment section is certainly not the best space to give a critical realist critique of these opposing views and then offer up a reason as to why critical realism should be preferred, but if you’re interested I’d recommend reading Roy Bhaskar’s A Realist Theory of Science, and The Possibility of Naturalism. So the theory acts as an under laborer to defend the sciences from detractors, but it does not propose to do science. So by all means embrace quantum mechanics.

    “So I am still left with what Marx actually said in Volume III. And here he proposes what I would call a tiny model: p’ = s / (v + c). Surely, this is not all that is going on in a capitalist (or any other) economy.”
    I think all three volumes of capital, the grundrisse, the economic and philosophic manuscripts, plus the notes on surplus value, are definitive proof that of course Marx did not think that p = s/(v+c) was “all that is going on in a capitalist economy”, but it is the case that for Marx the extraction of surplus value is a necessary condition for the health of (a very unhealthy system) capitalism.

    “We can’t really predict what it’s inventiveness will come up with.”
    Marx would be the first to champion this sentence. Again, the EP Manuscripts would attest to this. It’s specifically because capitalism channels our creative inventiveness into labor saving technologies, and technologies that increase efficiency, instead of technologies that allow for our well rounded development, that he often damns capitalism so intensely.

    “And this seems to show that in the case that seems to be most plausible (capitalists invest in anticipation of making a given labor pool more productive) the rate of profit has a “tendency” to rise, not fall.”

    Marx says the same thing in Vol I and III. This isn’t a critique of Marx, it’s an affirmation of his theory. He’s always pressing the point that capitalist in a narrow sector of the economy can increase productivity and thus increase profit. (He was very happy with himself that he was able to answer the hotly debated issue in his day as to why capitalists would seek an increase in productivity when past theories of political economy suggested it would be bad for profit rates; this comes out strongly in Vol I) But the point is that when larger and larger sectors of the economy start to do this, the SOURCE OF VALUE (i.e., human laborers) is mitigated/fired/laid off, and thus so is surplus value. You have to remember that one can derive a profit, while adding no NEW/EXTRA/SURPLUS value to the economy (think of those do it yourself laundry services, or car washes you see – those owners can be rolling in profits and adding no new value to capitalism).
    “Why did he not see this? Was it because he linked this result to his instinct that capitalism was historically doomed? Is that what all the heat is about in this debate?”

    I think he did see it, and you’re not seeing that he saw it. Fortunately nowhere in Vol I-III is there a theory of necessary collapse, as is often attributed to Marx.

  4. Chris,

    You say, “I don’t see any mention of Zizek in that blog post?” Zizek isn’t mentioned in the blog post. Varoufakis and Zizek both spoke at the 6th Subversive Festival in Zagreb in 2013. I don’t in fact know that they met, but I think they were in a forum together. Wish I had been there! If you are unfamiliar with Varoufakis, I would encourage you to take a look at his more recent books, Modern Political Economics and The Global Minotaur. There is a new (2013) edition of The Global Minotaur published by Zed. I have reviewed the earlier editions of these here.

    “Critical realism is a philosophy of science; quantum mechanics is a field of science.” Quite true. I was running to the bus. I should have said, “Usually I more interested in science than philosophy of science.” But I will try to track down the books that you mention.

    You quote me as saying “We can’t really predict what it’s inventiveness will come up with” and then say, “Marx would be the first to champion this sentence.” You don’t mention that I also said, “Marx was aware of this, as was Proudhon . . .”

    You say, in reference to my comment “the rate of profit has a “tendency” to rise, not fall”, “This isn’t a critique of Marx, it’s an affirmation of his theory.” Now this is puzzling. The whole point of Chapter XIII of Volume III, I take it, is that, “But proceeding from the nature of the capitalist mode of production, it is thereby proved a logical necessity that in its development the general average rate of surplus-value must express itself in a falling general rate of profit.”

    So (importantly, assuming a constant rate of exploitation) Marx accepts the theory of Smith and Ricardo that there was in fact a long-term problem for capitalists: that their profits would go down. But how is what I have said an affirmation of his theory? I guess what you are saying is that Marx’s tiny model was a micro theory for the individual firm but that his overall macro theory leads to the opposite conclusion. Could you cite some references for this?

    Marx goes on to say something very profound in this chapter, “Since the mass of the employed living labour is continually on the decline as compared to the mass of materialized labour set in motion by it, i.e., to the productively consumed means of production, it follows that the portion of living labour, unpaid and congealed in surplus-value, must also be continually on the decline . . .” So he clearly sees the coming of the Matrix economy in which humans are no longer needed! But he just as clearly says that this must lead to a fall in profits. You say that “nowhere in Vol I-III is there a theory of necessary collapse” but surely you would not say that Marx didn’t hope that this would be the case.

    You say “capitalism channels our creative inventiveness into labor saving technologies, and technologies that increase efficiency, instead of technologies that allow for our well-rounded development.” Again, I think this is a very profound question. But why can’t “labor saving technologies” be part of or even essential for “well-rounded development”? Aristotle clearly didn’t see labor in a cotton mill or coal mine as essential for well-rounded development. He had slaves to support him and his aristocratic peers! Hannah Arendt didn’t either when she wrote The Human Condition. Keynes didn’t when he wrote “Economic Possibilities for our Grandchildren.” Marx didn’t spend any part of his life in a coal mine! Thanks in large part to Engels’s father’s interest in the Manchester spinning mill, he was able to live out his life in revolutionary politics and scholarly pursuits in the British Museum and “playing with his daughters on Hampstead Heath, enjoying a game of chess, regularly reading Shakespeare and the Greek dramatists” (according to Roger Caldwell in a recent article in Philosophy Now.) Our goal surely must be to END (exploited) labor, not to glorify it. Doesn’t that cause one to wonder about the “labor theory of value”?



  5. CB says:

    There’s a lot going on in this post, and I feel like I need to ask: have you read Volumes I and II? I ask because I’m quite swamped with work, and while I KNOW there are answers to the many questions in this post, I really don’t have the time to address all of them sufficiently. Many of the questions are predicated upon a very narrow reading of Marx, hence why I ask if you made it through all three volumes.

    The final paragraph of this is riddled with presumptions that are just false. I’ll go through a few of your comments quickly, due to time though.

    “So he clearly sees the coming of the Matrix economy in which humans are no longer needed! But he just as clearly says that this must lead to a fall in profits. ”

    Exploited labor – real human beings – is the source of surplus value. So humans are ALWAYS needed for the health of capitalism. Period. Capitalism cannot produce more value without humans.

    “Again, I think this is a very profound question. But why can’t “labor saving technologies” be part of or even essential for “well-rounded development”? ”

    Because people need to earn an income to survive in capitalism, and a few of those people actually get to thrive. But most don’t. Most are alienated (this is backed by copious empirical research). So if you introduce a labor saving technology, you LAY SOMEONE OFF. If you lay someone off, they aren’t earning an income. If they aren’t earning an income they most certainly aren’t thriving, let alone surviving. If I work a toll booth everyday, and one day “labor time is saved” because a machine takes the quarters and dollars from the drivers, how in god’s name would this be beneficial to me? Labor saving technology under capitalism does not mean labor saving time, i.e., more luxury time for the working class. We’ve been introducing labor saving technology for over a century, and yet the 40 hour work week has been around for decades. Finally, when you ask why this type of labor can’t be fulfilling, it presumes that the types of labor people would find fulfilling are the types of labor that lay people off. This is dubious.

    I’ve published an essay on the blending of Aristotle’s ethics with Marx’s theory of alienation. If you’re interested in it, let me know. In short though, if you think Aristotle is right, you can’t support capitalism. As a matter of fact in the opening of his ethics Aristotle is explicit that any arrangement that sees money for the sake of making money as the good, is destined to lead to an inability to flourish, and that is the MO of capitalism.

    This closing sentence is again leading me to question if you read volume I:
    “Our goal surely must be to END (exploited) labor, not to glorify it. Doesn’t that cause one to wonder about the “labor theory of value”?”

    Marx is CONSISTENT that the goal is to make the labor theory of value, i.e., the law of value, CEASE TO OPERATE (check out the Gotha Program by Marx for a good argument). It’s because labor produces value through exploitation that we need to be committed to the ending of exploitation and the operation of the law of value. So no, this doesn’t cause one to wonder about the LTV, by accepting the LTV, we can then accept that the goal should be to end exploited labor. If you don’t accept the LTV, then you can totally dodge the issue of exploitation (like the majority of mainstream economist, who think in general if I accept a contract at X corporation, I’m not exploited). If you want to accept exploitation as the bedrock of capitalism, you should embrace the LTV, not jettison it.

    • Chris,

      Sorry if my post made you bad-tempered. My questions were not so intended, but were an effort to expand both of our views on the issue of the “labor theory of value.”

      First, in answer to your first question: Volume I and II of Capital rest on my shelves. I have actually read a bit of Volume I. Volume II, not so much. That said, I am not necessarily opposed to a more careful reading of, especially, Volume I, the only one of the volumes of Capital which Marx was able to see through to publication in his lifetime. That is actually why I wondered if you could point out references as to where my statement that in a (at least very) plausible application of Marx’s (actually Morishima’s) little formula for the rate of profit that the rate of profit rises was an “affirmation of his theory.” In Volume III he seems to clearly say the opposite, that it is “a logical necessity that in its development the general average rate of surplus-value must express itself in a falling general rate of profit.”

      My speculations about the labor theory of value seem to have upset you. What I was trying to get at was to step back a bit and to wonder what it means that labor is the sole source of “value.” I will quote an extended passage from Hannah Arendt’s The Human Condition where she addresses this:

      “The hope that inspired Marx and the best men of the various worker’s movement – that free time eventually will emancipate men from necessity and make the animal laborans productive – rests on the illusion of a mechanistic philosophy which assumes that labor power, like any other energy, can never be lost, so that if it is not spent and exhausted in the drudgery of life, it will automatically nourish other, “higher,” activities. The guiding model of this hope in Marx was doubtless the Athens of Pericles which, in the future, with the help of the vastly increased productivity of human labor, would need no slaves to sustain itself but would become a reality for all. A hundred years after Marx we know the fallacy of this reasoning; the spare time of animal laborans is never spent in anything but consumption, and the more time left to him, the greedier and more craving his appetites. That these appetites become more sophisticated, so that consumption is no longer restricted to the necessities but, on the contrary, mainly concentrates on the superfluities of life, does not change the character of this society, but harbors the grave danger that eventually no object of the world will be safe from consumption and anhihilation through consumption.”

      Arendt’s book goes through a number of candidates for characterization of “the human condition”. Her perspective comes from the pre-modern world, primarily Classical Greece, but also republican Rome and pre-Luther Christianity. She sees these aspects of the human as: animal laborans, man as a biological being; homo faber, man as a maker of things; the vita active, the active life which she equates with free participation in a political world; and the vita contemplative, the life of philosophy. She sees the modern world, starting with the Reformation, as a reversal of the pre-modern ordering of these aspects of the human. That pre-modern ordering had been from animal laborans to the vita contemplative. In the modern world this is reversed. In the modern (capitalist) world, as you say, “labor produces value.” This would be a completely strange thought to a Classical thinker, like Aristotle.

      In the passage from Volume III that I quoted, Marx clearly sees the dynamic of capitalism as replacing current labor with machines (past labor).The tragedy of capitalism is that this leaves humans with nothing to do, if labor is the sole source of value. Arendt says,

      “The danger that the modern age’s emancipation of labor will not only fail to usher in an age of freedom for all but will result, on the contrary, in forcing all mankind for the first time under the yoke of necessity, was already clearly perceived by Marx when he insisted that the aim of a revolution could not possibly be the already-accomplished emancipation of the laboring classes, but must consist in the emancipation of man from labor. At first glance, this aim seems utopian, and the only strictly utopian element in Marx’s teachings. Emancipation from labor, in Marx’s own terms, is emancipation from necessity, and this would ultimately mean emancipation from consumption as well, that is, from the metabolism with nature which is the very condition of human life. Yet the developments of the last decade, and especially the possibilities opened up through further development of automation, give us reason to wonder whether the utopia of yesterday will not yet turn into the reality of tomorrow, so that eventually the effort of consumption will be left of the “toil and trouble” inherent in the biological cycle to whose motor human life is bound.”

      I don’t quite know what she meant by “the already-accomplished emancipation of the laboring classes” but I hope this makes more clear what I was getting at when I suggested that “labor saving” might well be appropriate or even necessary for the good life. Robert Skidelsky and his son, Edward, outline seven features of that “good life” in their book How Much is Enough?. Much of this discussion derives from Aristotle. The book starts with a review of Keynes’s article “Economic Possibilities for our Grandchildren (1930)” in which Keynes predicts that “the standard of life in progressive countries one hundred years hence will be between four and eight times as high as it is to-day.” Keynes asks why at least part of this increase in productivity could not be applied to reduce working hours from an average of fifty or sixty hours per week in Keynes’s time to “three hour shifts or a fifteen hour week” today? This has not occurred. Why not? The Skidelskies answer that as we have become more productive, modern capitalism encourages waste and insatiability to take up the slack. And we could add, in order to maintain the profits of the capitalist class. Your statement that “if you introduce a labor saving technology, you LAY SOMEONE OFF” is certainly true in the current capitalist system. But need it always be so? Clearly we need a change to that system. What I wonder is whether defining animal laborens as the highest standard of value is the right preparation for that world in which we pursue “our well rounded development.”

      A main focus of Marx’s theory was on the central contradiction of capitalism, that an individual contract with a laborer enables the capitalist to reap the sole reward from the cooperative benefit produced by the division of labor. This observation is not unique to Marx, of course. Proudhon also pointed this out. Marx focuses on the manifest unfairness of this contract. But what happens after the revolution? We have a glimpse of that in the history of the Soviet Union. We have an aping of the capitalist West in its acquisition of armaments and the evolution of a sinister bureaucracy which would be quite familiar to Polybius or Herodutus describing the tyrannies of Siracusa or Persia. Why didn’t this evolve into “well-rounded development.” Well, the opposition of the capitalist West is certainly part of the answer, but one wonders about that re-ordering of the qualities of the human condition that Arendt describes. Marx, himself, clearly lived a life of philosophy, political action, and scholarly work. Labor, not so much. Why is labor such a crucial feature of his writing? Well, of course, because the capitalism of his day and ours is dominated by animal laborans. I just ask the question, though, if your theory is dominated by glorifying animal laborans how can you hope to lead us to “well-rounded development?” How do you make the switch from animal laborans to the vita active?

      I would be delighted to see your comparison of Aristotle and Marx. Arendt says something to the effect that Marx was more influenced by Aristotle than by Hegel. I would be very interested to see that developed.


  6. CB says:

    My intentions were not to come across as rude or upset, if I did I apologize. I hope I come across as pressed for time, which is what’s causing me to write curtly and in a matter-of-fact tone.

    I cannot stress enough that much of the problems you’re catching in Marx are due to not having read Vol I. I wish I had the time to go over Vol I with you and clarify the murkiness of your problems with Marx, but I simply don’t (David Harvey has an online class at davidharvey.org – or .com? – that you could watch for help. Or i STRONGLY recommend the videos by the blogger at kapitalism101 – just google kapitalism101, they are fantastic). At my old university we had a Capital Vol I reading group, it took us two whole semesters to finish the text. I’m good at teaching Marx, and succinct, but I presently lack the time. Vol II isn’t as crucial as Vol I, please read Vol I.

    As far as Arendt, I really don’t have the time to address those claims either, but I will say this, no one, not even Arendt, doubts the fact that Arendt had an overly fastidious reading of Marx’s theory.

    I do think to some degree Marx is more of a Aristotelian than a Hegelian, but at the same, I sometimes wary of reading Marx through other thinkers (as Arendt did), instead we should read Marx on Marx’s own terms. I only read Marx through Aristotle for normative force, that’s all.

    I’m sorry I can’t be of more help. If you have narrow and specific questions I’m happy to help, but I unfortunately can’t help you with broader and robust questions (which your entire reply is).


  7. Pingback: Thoughts on the Labor Theory of Value | Notes from my library

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s