Where did all that stuff come from? Marx, surplus profit, and the seemingly inexhaustible rise in the productivity of labour in capitalist production

‘[…] [E]verything is expressed upside down in competition, and hence in the consciousness of its agents […].’



In Capital, Marx argues that, in a given sector of production producing a given class of commodity, should one capitalist production unit introduce a productive technique based on a higher level of productivity of labour than that obtaining in the rest of the sector, that production unit will be able, through lowering the per-unit value of its commodity product, to reap a surplus-profit – a rate of profit higher than the sectorally-obtaining rate. Marx strongly suggests that the ability to reap this surplus profit why capitalists introduce more productive techniques in the first place (even though, once introduced, competition between production units forces the adoption of the new technique through the sector, and the innovator’s advantage disappears). Given that Marx imputes to capitalist reproduction a constant and consistent rise in the level of labour productivity, and given that this secular rise explains the key characteristics of capitalist reproduction itself (accumulation, the tendency of the rate of profit to fall, the very unstable dynamism of capitalist reproduction), the quest for surplus profit must lie at the heart of what is constitutive to capitalist production and reproduction. It is surprising, therefore, that the literature commenting on Marx’s theory almost in its entirety attributes the drive to adopt innovative and more productive techniques to competition. I reject this argument, and insist that, for Marx, it is the quest for surplus profit that drives capitalists to adopt innovative production techniques, not competition.

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2 thoughts on “Where did all that stuff come from? Marx, surplus profit, and the seemingly inexhaustible rise in the productivity of labour in capitalist production

  1. re “Where did all that stuff come from?”

    Very stimulating piece. I especially like the exposition of why competition is not the driving force behind increased productivity but rather just generalizes it. As you say, this is a rare position among Marxist commentators. I also found the detail in your illustrative examples to be illuminating. That said, I disagree with two points in footnote 15 and would like to explain why.

    First, I think you are overly generous to Michael Heinrich in his book, “An Introduction to the Three Volumes of Marx’s Capital.” You say he argues “that a rise in the productivity of labour does not necessarily provoke a fall in the rate of profit since a rise in the productivity of labour, which will cheapen produced commodities, will also cheapen those commodities that enter into production as raw materials and instruments of labour, as well as those that make up the real wage.”

    Unless I’m missing something, I don’t see that his objection to the falling rate of profit tendency hinges on the cheapening of constant capital. His point seems to be that s/v might increase faster than c/v. And as far as I can see, Heinrich does not even take up Marx’s argument that the rise of s/v is limited while the rise of c/v is not.

    His main problem in this section is that he leaves out fixed capital entirely. He assumes that the amount of capital advanced is the same as the amount consumed in one production period. On page 151, where he begins to discuss the falling rate of profit theory specifically, he writes: “The product thus has a value of c+v+s and the rate of profit amounts to s/(c+v).” But the “c” in the rate of profit formula s/(c+v) is not the same as the “c” in the value of commodities produced, c+v+s. And the fixed capital that Heinrich ignores is heavily responsible for the rising organic composition of capital and therefore for Marx’s claim that the rate of profit tends to fall.

    Marx says as much at the beginning of Chapter 14 of Capital III: “If we consider the enormous development of the productive forces of social labour in the last 30 years alone as compared with all preceding periods; if we consider, in particular, the enormous mass of fixed capital, aside from the actual machinery, which goes into the process of social production as a whole, then the difficulty which has hitherto troubled the economist, namely to explain the falling rate of profit, gives place to its opposite, namely to explain why this fall is not greater and more rapid.”

    Ignoring fixed capital makes it a lot easier for Heinrich to say that c/v doesn’t have to increase very much. He may think that disregarding fixed capital is just a harmless simplification, but in reality that assumption cooks the books.

    Second, I do not think that you deal convincingly with the argument that you attribute to Heinrich, namely “that a rise in the productivity of labour does not necessarily provoke a fall in the rate of profit since a rise in the productivity of labour, which will cheapen produced commodities, will also cheapen those commodities that enter into production…”.

    In response to this, you say : “The cheapening of commodities as a consequence of a rise in the productivity of labour has an indirect effect on the rate of profit, since it occurs subsequently in time to the rise in productivity that causes it. The change in the value composition of capital because of a rise in the ratio of instruments of labour and raw materials to wages is immediate: more capital is laid out as the former compared to the latter. But the cheapening of commodities that occurs as a consequence is the cheapening of the commodity product output of a more productive production process; it is only in subsequent production periods (and iteratively) that these cheaper commodities affect the value composition of capital.”

    I don’t agree with your claim that the rise in c/v is immediate while the cheapening of c (and of v) takes place later. Marx does not say much about the cheapening of c. But he does consider the cheapening of v, since he allows for an increasing rate of exploitation, s/v. He does not suggest that an increase in the rate of exploitation takes place only after an increase in the organic composition, c/v. Indeed, he allows for them to take place simultaneously, and makes the case that c/v outpaces s/v, because s + v is limited by the length of the working day and other factors. So if v can be cheapened simultaneously with the rise in the technical composition, why can’t c?

    Further, in your calculation beginning on page 3, you give the example of a firm that undertakes a rise in productivity by increasing its organic composition and is thereby able to produce its output more cheaply and undersell its competitors. At first the innovating firm gets a higher rate of profit. But when the new technique is generalized across the industry, the rate of profit in this sphere has fallen – as Marx indicates.

    However, you assume that the rise in productivity takes place solely because the firm uses more efficient machinery “which costs the same” but allows it to process more raw material. You do not allow for the possibility that the new machinery itself could have been produced more efficiently by its supplier and therefore more cheaply. Or rather, in the footnote cited, you say that this possibility can only take place subsequently, not in the same production period, so in effect the cheapening of the constant capital always lags behind and never catches up with the rise in the firm’s organic composition. But there is no reason to believe that the initial industry is able to advance its productivity before that can be done by the industry that supplies its machinery.

    With that in mind, I will work through your calculation and go one step further to allow for simultaneous advances in productivity. (I will also condense the argument a bit by combining the production equations with the rate of profit calculations.)

    Step 1

    You start with the production of 100 units of a commodity, for which 60 units of raw materials are used, with total value $60; the value of the machinery employed is $200 (of which only $20 is used up in a given year); the wage or variable capital used is $20; and the surplus-value produced and realized is $20. In order to avoid subscripts, I will use the letter f to stand for used-up fixed capital, F for the stock of fixed capital, z for circulating capital (raw materials), v for variable capital, and s for surplus-value. I will also use the dollar sign for the unit of currency, since that makes it easier for me to visualize when we are talking about money. Then, similarly to Marx’s formulas, we get the equation

    (1) $20f + $60z + $20v + $20s = $120.

    Thus the value of each of the 100 units produced is $120/100, or $1.20. Since 60 units of raw materials yield 100 commodities, the output/input ratio is 5/3. And the rate of profit, which depends on the entire invested capital (where the fixed capital, F, is worth $200), is

    π = $20s/($200F + $60z + $20v), which comes to $20/$280 or 7.14%.

    Step 2

    You then assume that an innovating capitalist is able to produce more productively: “the machinery is replaced by a new, more productive alternative, which costs the same” but which depreciates similarly and increases productivity by 25%; that is, it has the effect of working up 25% more raw material (thus 75 units) in the same period and using the same amount of labor. You also assume that the rate of exploitation remains the same. Then the resulting production equation becomes

    (2) $20f + $75z + $20v + $20s = $135.

    Now the value of each of the 100 units produced is 135/100, or 1.35. But now the 75 units of raw material yield 125 commodities, at the ratio of 5/3 as before. So each of these has the unit value of $135/125, or $1.08. The cost per unit for the innovating capitalist has been reduced, which is to be expected from a more productive operation.

    But even though the innovating capitalist has produced surplus-value of 20s, her profit will be greater, because we assume that she can sell her output at the prevailing rate of $1.20 per unit. She then realizes a total value, from her 125 units, of 125 x $1.20, or $150 – that is, $15 more than the value of what she (or rather her workers) produced. So her realized profit is not just $20 but $35. Presumably this extra profit is obtained from the surplus-value produced by the less productive capitalists she is competing with. And her rate of profit is

    π = $35s/($200f + $75z + $20v), which comes to $35/$295 or 11.86%.

    Thus the innovating capitalist reaps her reward. Of course, as you point out, she may have to sell her product for less than $1.20 per unit, but even so, she could easily achieve a rate of profit greater than the initial 7.14 %.

    Step 3

    Here we assume that the new technique has been adopted by all capitalists in this industry. So the prevailing unit cost is 1.08. Now the value of the 125 units is $1.08 x 125, or $135. And the profit becomes $135 – $20f – $75z – $20v, or $20s. And the rate of profit is

    π = $20s/($200f + $75z + $20v), which comes to $20/$295 or 6.78%.

    So the rate of profit has fallen from its initial value.

    Step 4

    So far I have followed your calculations as you present them. However, I would like to interpret them differently. Let us assume we are dealing with a representative industry, which Step 1 depicts at some initial moment in time. Step 3 occurs some time later (not necessarily in the next production period), when productivity in this industry has increased by 25%. But why assume that the productivity increase is limited to this industry? Productivity will, as a rule, have increased in many industries if not all. For the sake of argument, I will assume that productivity has increased by the same amount, 25%, across the board – and in particular, in the industries that supply the goods purchased by the constant and variable capital of our representative industry.

    That means that the fixed capital, valued at $200 when first introduced, now can be produced more efficiently and will cost $160. Likewise the circulating raw materials will cost $60, and the labor power, $16. Since the workers will still add $40 worth of value, the surplus-value will be $24. That makes for a rate of profit of

    π = $24s/($160f + $60z + $16v), which is 24/236, or 10.2%.

    So for this numerical example, the profit rate does not fall between the two periods.

    Where does that leave the falling rate of profit tendency? As I see it, Marx does not really attempt to prove his claim that the rising organic composition will outpace the cheapening of constant capital. Several commentators like yourself have attempted to supply a mathematical argument (some using more advanced mathematics), but none that I know of have succeeded. In my view the answer requires more than a mathematical calculation; it takes an assessment of how the system’s laws of motion are modified in the epoch of imperialism. In brief, in this epoch, when capital becomes monopolized and statified, monopolies and other powerful firms can resist the depreciation of their obsolete fixed capital, so the capital-cheapening countertendency is undermined. Under these circumstances the rising organic composition is not counterbalanced by the depreciation of constant capital, and therefore “the law itself” is able to win out.

    I would be very interested in further discussion of these issues.

  2. Thanks for your comments, Walter. I’ll have to be brief here, but here goes.

    I think my comment on Heinrich is fair, in the sense that, insofar as I understand his argument (in An Introduction to the Three Volumes of Marx’s Capital), if we express the rate of profit as (s/v)/[1 + (c/v)], then, with a rise in the productivity of labour, it is not necessarily given that (s/v) will fall quicker than [1 + (c/v)]: there may be cases in which it does and there may be cases in which it does not. This is the case, because the value of labour-power (real wages) may fall (Heinrich p. 153); and this can only happen because of a fall in price of the articles of unproductive consumption that make up the real wage. (The price of articles of constant capital both can and will fall for the same reason.) This argument, as I read it, is independent of the question of fixed capital, and what Marx calls the ‘certain limits’ to the reduction in the mass of labour-power deployed ‘that cannot be overstepped’ (Capital volume 3, p. 356): one can construct arithmetical models in which the productivity of labour rises (a greater mass of constant capital is absorbed by a given mass of labour-power) but, with appropriate changes in price of both elements of constant capital and real wages the rate of profit rises.

    Nevertheless, I think the argument is logically invalid, for the reason I set out both in the footnote and in the note I wrote on the rate of profit (here: https://edgeorgesotherblog.wordpress.com/2013/07/04/but-still-it-falls-on-the-rate-of-profit/). A rise in the level of productivity in and of itself will bring about rise in the organic composition of capital and hence a fall in the rate of profit assuming constant prices. But prices are not constant, because the overall rise in the productivity of labour cheapens commodities in general. But the cheapening of commodities as a consequence of a rise in labour productivity can only enter in as a factor of production subsequent to their production. ‘Production period’ is a theoretical abstraction: actual production is constant, continuous and coterminous, and not so neatly divided, yet I think it is self-evidently the case that a given commodity cannot enter as a factor of its own production, either as raw material, instrument of labour or component of the real wage. Heinrich’s (implied) argument only works if one adopts a method of simultaneous valuation, but this is in my view itself logically invalid. It is precisely for this reason, I argue, that Marx is so precise in his definition of ‘organic composition of capital’ as the change in the value composition consequent on a change in the technical composition, as opposed to other reasons, including the cheapening of commodities. This last belongs to the category of ‘countervailing tendencies’ (of which there are more in the Grundrisse), which also includes contingencies and factors exogenous to production.

    This the mistake that I think you make in your ‘Step 4’. Step 1 is, as you say, the initial conditions in a given sector of production. Step 2, the situation of the innovating production unit (reaping an above average rate of profit). Step 3 is the conditions in the original sector once a productivity of labour innovation has been generalised through by competition. For your step 4, which is really an alternative step 3, you assume an economy-wide increase in the productivity of labour of 25 % , simultaneous with that occurring in the sector I use as an example. This is not unreasonable, but it is not legitimate to include the cheapened commodity product produced outside my sector as inputs at this stage, for if the rise in labour productivity occurs simultaneously in the sector and throughout the wider economy, then the cheapened commodity product will appear as inputs subsequently to my step 3 and your step 4: during my step 3 and your step 4 they are still only being produced. And when they are incorporated as inputs then it is reasonable to assume a further rise in productivity in the sector. The reduced price of inputs will offset the rise in the value composition in the sector as a result of the rise in the organic composition, but only offset it, for the organic composition will continue to rise as a consequence of a continuous rise in the productivity of labour. Including the cheapened commodity products as inputs only at the start of the stage where the productivity raising innovation first becomes generalised is an example of simultaneous valuation, in my opinion.

    In addition, you overestimate the cheapening occasioned by the rise in productivity. As I point out in my post (p. 3), the ‘fall in per-unit value [occasioned by a rise in productivity of labour] […] is not directly proportional to the rise in productivity, for it is also dependent on the ratio between means of production and labour-power in production.’ You assume a 25 % fall in price as a consequence of a 25 % rise in productivity. This would assume a production process with no constant capital.

    Third. In your step 4 you calculate the rate of profit on the basis of the cheapened price of the fixed capital. But, even after taking my comments above into account, even when cheapened fixed capital does come onto the market, precisely because it is ‘fixed’, only a minority of capitalist producing units will be able to benefit from it, because the majority will not be in a position where the depreciation of the old fixed capital is complete and it needs to be replaced. In the case you cite in your example, a capitalist who has laid out $200 on a piece of fixed capital finds that it now costs $160. But this in and of itself has no effect on the rate of profit. It is not as if someone will give her the balance of $40 back. The $200 has been spent and is someone else’s pocket. Her rate of profit needs to be calculated on what was actually laid out, not what would be. (It is true that actual capitalist firms do write down or even write off capital stock value in circumstances such as these, but this is really only an accounting exercise designed to make operating profits appear higher than they really are.)

    In fact, what happens in this case is that, with the fall in value of the fixed capital, the labour time socially necessary for the production of the commodity product for which the fixed capital is deployed has fallen. Those producing units lucky enough to be able to benefit from the cheapened fixed capital are now effectively innovators, able to undercut those producing units still forced to use the fixed capital at the previous higher price; these latter may, indeed, have to write off this capital before its depreciation is reached. Both these facts will themselves have negative consequences for the rate of profit.

    In addition to this, even though I make the assumption in my post that the new, more efficient fixed capital cost no more than the old, this was just a simplifying assumption to emphasise the point that, given conditions of price stability, more productive production techniques themselves automatically lead to a rise in the organic composition of capital. In reality, of course, more productive fixed capital, being either/or bigger, more complex and involving more R&D for its production will, all else being equal, be more expensive than what it is replacing (even though it will, as all commodities will be, be subject to subsequent cheapening.

    All these issues are explored in more detail in my note on the rate of profit in any case, here: https://edgeorgesotherblog.wordpress.com/2013/07/04/but-still-it-falls-on-the-rate-of-profit/.

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