The subject of Chapter 13 is the law of the tendency of the rate of profit to fall. This law is controversial. For example, Michael Heinrich rejects the law in [Heinrich12, Heinrich13]. Amongst others¹, [KFPGC13] responded to this criticism. We will also comment on this debate insofar as it is helpful to understand the law.

The Law as Such

The starting point of [Capital, Vol. III, Chap. 13] is the observation that the profit rate has a tendency to fall.² This observation was made by political economy before Marx, but it had failed to find the “puzzle’s solution” [Capital, Vol. III, p.320], i.e. it had failed to formulate the law which would explain the observed phenomenon. In [Capital, Vol. III, Chap. 13] the following explanation is offered.

The key strategy for individual capitals in the pursuit of profit is to increase the productivity of labour in order to decrease costs per commodity. In [Capital, Vol. I, Ch. 15] it was already discussed that in the pursuit of extra surplus-value individual capitalists strive to employ means of production which allow their production to be more productive. For a commodity which is being produced more productively, the individual value decreases and extra surplus-value can be realised. That is, this individual value is lower than the social actual value, which the capitalist can realise on the market.

In [Capital, Vol. III] this is generalised, the goal is extra profit and the means is that the costs per commodity shall be reduced. If capitalists are able to produce cheaper, then they can realise an extra profit over their competitors who produce less productively. That is, when selling at the same price or even when selling below their competitors to capture market share. Others need to catch up with the new technology in order to stay in the market.

The particular techniques employed by capital to increase the productivity of labour lead to an increased outlay in constant capital relative to variable capital. The argument continues that this implies a decrease of the labour applied to each commodity relative to constant capital transferred to it.³ Thereby, the amount of surplus per advanced capital is reduced, too, and the profit rate falls.

Hence, in [Capital, Vol. III, Chap. 13] the observed fall of the general profit rate is explained by reference to the general tendency of the capitalist mode of production that the progressive development of productivity lowers the profit rate:

The progressive tendency for the general rate of profit to fall is thus simply the expression, peculiar to the capitalist mode of production, of the progressive development of the social productivity of labour. This does not mean that the rate of profit may not fall temporarily for other reasons as well, but it does prove that it is a self-evident necessity, deriving from the nature of the capitalist mode of production itself, that as it advances the general average rate of surplus-value must be expressed in a falling general rate of profit. [Capital, Vol. III, p.319]

It only falls as a tendency, because there are other causes which lead to a temporal rising rate of profit. These counteracting causes are treated separately in [Capital, Vol. III, Chapter 14].⁴ Here, the object is the law itself, i.e. the effects on the profit rate by increasing productivity.

Note that, as established previously in [Capital, Vol. III, Chapter 9], different individual rates of profit exist in different branches of industry, i.e.  labour intensive spheres of production exist. The law concerns the general rate of profit which is the average rate of profit.

Organic Composition

The law of the tendency of the rate of profit to fall is premised on rising organic composition of capital.⁵ In the pursuit of higher profits, (a typical individual) capital seeks to reduce the cost price of commodities. Besides techniques such as increased economy in the use of constant capital, this is accomplished by increases in the productivity of labour for producing commodities. Some such increases of productivity of labour come to capital essentially for free: cooperation [Capital, Vol. I, Chap. 13] and division of labour [Capital, Vol. I, Chap. 14]. These techniques have their limits, however.⁶ Hence, the main technique for increasing the productivity of labour is to employ (more) machines: new or more tools or machines are used to produce the same product faster. This, as a rule, requires additional outlays for these technologies in the first instance. At the same time, using these technologies allows to save labour, production is faster, which means less needs to be expended on wages per commodity.

If the cost price of a commodity is $k_1 = v + c$, then capital will only adopt some technological change if the new cost price $k_2 = (v - Δv) + (c + Δc)$ is smaller than before. In other words, it is required that $Δc < Δv$.⁷ Note that this means that organic composition increases even if the new machine does not cost more ($Δc=0$) since then it is only employed if $Δv>0$. Now, if we disregard value revolutions (i.e. neither $c$ or $v$ drop in value) for the moment (see below), it is implausible that, as a rule, the new machine will cost less than the previous because by assumption it “does more”, i.e. saves labour compared to the previous technology. Of course, this could be accomplished by a breakthrough in science which simply shows how to produce the same thing with less. More generally, however, simply putting a bigger machine (twice the amount of hammers, needles, soldering irons etc.) in place (while keeping the number of workers required to push buttons, pull levers and move stuff around the same) already increases productivity. If, at first, one worker operates one machine that produces one car and then one worker operates a (simply) bigger machine which produces two cars, then the second machine will cost more unless either the productivity of making these machines increased twofold or the second machine is sufficiently different such that a different, cheaper process of production suffices. Ruling those cases out, for now, the organic composition of capital rises.

However, as shown in [Capital, Vol. I, Chap. 12], advances in the productivity of labour do lead to a reduction of the value of labour-power insofar as these productivity gains either concern the production of means of subsistence which workers consume or the production of means of production that eventually enter the production of these means of subsistence.⁸ Hence, higher productivity does eventually lead to a value revolution for the means of subsistence, which means the assumption above (“no value revolutions”) does not hold. However, a drop in the value of labour-power increases the value composition of capital further. Yet, the same advances in productivity which lower the value of labour-power also eventually lowers the value of constant capital. Hence, if the value of constant capital drops faster than the value of labour-power, this would reduce organic composition again.

[Capital, Vol. I, p.512] merely states the observation that this does not seem to be the case:

A comparative analysis of the prices of commodities produced by handicrafts or manufacture, and of the prices of the same commodities produced by machinery, shows in general that in the product of machinery the value arising out of the instrument of labour increases relatively, but decreases absolutely. In other words, its absolute amount decreases, but its amount in relation to the total value — of the product of a pound of yarn, for instance — increases.

In [MECW 33, p.287] the issue is discussed further. On machinery:

There can be no doubt that machinery becomes cheaper, and this for two reasons: [1] The application of machinery to the production of raw materials from which the machinery is made. [2] The application of machinery in the transformation of these materials into machinery. In saying this, we already say two things. Firstly, that in both these branches, compared with the instruments required in the manufacturing industry, the value of the capital laid out in machinery also grows as compared with that laid out in wages. Secondly, what becomes cheaper is the individual machine and its component parts, but a system of machinery develops; the tool is not simply replaced by a single machine, but by a whole system, and the tools which perhaps played the major part previously, the needle for example (in the case of a stocking loom or a similar machine), are now assembled in thousands.

The latter argument is simply the assertion that the machine park (per worker, say) grows more rapidly than the value of its components drops. This point is similar to the point made in [Capital, Vol. I] cited above as it derives the point from observation. The first argument is that if the value of constant capital (or variable capital for that matter) falls, then this is premised on a rising organic composition elsewhere. To this we might respond that the value of the components of $c$ might have simply fallen because the components of their $c$ has fallen, which, however, in turn simply moves the assumption that organic composition increased one further down the production chain. However, in itself, the observation that a dropping value of the components of $c$ implies a rising organic composition elsewhere does not show that the drop in value does not reduce organic composition in general. Put differently, the observation then necessitates to ask what happens if organic composition rises and prices drop everywhere.

This is discussed in [Heinrich06]. If we assume that increases in productivity offset the rise in organic composition then that also presumes that productivity in department I, producing means of production, grows faster than productivity in department IIa, producing means of subsistence for workers. Only under this assumption can we assume that the price of constant capital drops faster than the price of the means of subsistence which workers buy with their wages. This is an artificial assumption. Furthermore, productivity gains in department I also reduce the cost of means of subsistence insofar the machines produced there are used by department IIa (or by a firm in department I producing a machine which used by department IIa etc.). Hence, if productivity rises in department I this also reduces prices of means of subsistence even when productivity is not increased in department IIa. Hence, it is unrealistic to assume that prices, overall and long term, drop faster for means of production than for means of subsistence.

Similarly, if we assume a general and uniform increase in the productivity of labour, then it is clear that the value of raw materials consumed by a worker (per day, say) can at best stay constant, but cannot drop. If twice as much raw material is consumed in the process of production and all branches of industry see the same increase in productivity then the value of raw material drops by two, i.e. the two movements cancel each other out. Hence, as far as raw materials are concerned, a drop in their value cannot offset the initial increase of the organic composition.

As a consequence, productivity increases generally do increase the organic composition of capital even under value revolutions, i.e. these value revolutions do not offset the rising organic composition. Note, however, this is no verdict yet on how they affect the profit rate, which relates outlay to surplus-value and not constant capital outlay to variable capital outlay.

Relative Surplus-Value

If organic composition $c/v$ grows and the rate of surplus-value $s/v$ is unchanged, then outlay $c+v$ grows relatively to profit $s$ and the rate of profit falls.

However, a rising organic composition of capital and a rising rate of surplus-value are both expressions of the same movement under the rule of capital: they both are expressions of the rising productivity of labour. In contrast to the counteracting causes discussion in [Capital, Vol. III, Chap. 14] — other causes which counteract the effects of rising value composition on the profit rate — a rising rate of surplus-value is the result of the movement itself. The same movement both produces a fall in the rate of profit (rising organic composition) and produces a rise in the rate of profit (rising rate of relative surplus-value). This does not prevent us from abstracting away a rising rate of surplus-value at some stage of the argument (as we have done above), but we must consider it eventually to actually understand the effect of rising productivity on the average rate of profit. Put differently, given that Marx explains a falling rate of profit from increased productivity, we have to study what the effect of rising productivity on the profit rate is and cannot abstract one of its effects away.⁹

Heinrich’s Criticism of the Law

On this basis, Heinrich argues against the law of the tendency of the rate of profit to fall in [Heinrich13]. He firstly observes that we can rewrite the rate of profit as

which expresses the rate of profit as essentially a relation between the rate of surplus-value $s/v$ and the value composition of capital $c/v$.¹⁰ Heinrich then observes that the rate of profit falls if and only if $c/v$ grows faster than $s/v$ and argues that there is no a priori reason why this should be the case in general and points out that Marx did not show that $c/v$ in general must grow faster than $s/v$.

Indeed, in [Capital, Vol. III, p.318] Marx claims to have proven the law even under the assumption that the rate of surplus-value rises, but no such proof can actually be found before page 318. This might be attributed to poor editing¹¹ and hence Heinrich considers an argument that Marx makes in Chapter 15:

These two movements not only go hand in hand; they mutually condition one another, and are phenomena that express the same law. But they affect the profit rate in opposite directions. The total mass of profit is the same as the total mass of surplus-value, and the rate of profit $\frac{s}{C} = \frac{\textrm{surplus-value}}{\textrm{total capital advanced}}$. But surplus-value, in its total amount, is determined firstly by its rate and secondly by the mass of labour that is applied at this rate at any one time or, which comes to the same thing, by the magnitude of the variable capital. One of these factors, the rate of surplus-value, is rising; the other factor, the number of workers, is falling (relatively or absolutely). In so far as the development of productivity reduces the paid portion of the labour applied, it increases surplus-value by lifting its rate; but in so far as it reduces the total quantity of labour applied by a given capital, it reduces the number by which the rate of surplus-value has to be multiplied in order to arrive at its mass. Two workers working for 12 hours a day could not supply the same surplus-value as 24 workers each working 2 hours, even if they were able to live on air and hence scarcely needed to work at all for themselves. In this connection, therefore, the compensation for the reduced number of workers provided by a rise in the level of exploitation of labour has certain limits that cannot be overstepped; this can certainly check the fall in the profit rate, but it cannot cancel it out. [Capital, Vol. III, p.355]

If the number of workers per advanced capital decrease then eventually the surplus-value they will create will also decline. Assume a capital which employs 24 workers producing 48 hours of surplus-labour. If organic composition rises to such an extent that only two workers are employed, then they will at most produce 48 hours of surplus-value regardless of circumstance. Hence, any further decrease of the number of workers would necessarily reduce the amount of surplus-value produced per advanced capital, lowering the rate of profit. Heinrich argues that this only holds if the capital required to employ two workers is at least as big as that to employ 24 workers before: “However, this conclusion is only correct if the capital $(c + v)$ necessary to employ the two workers is of an amount at least as great as that required to employ twenty-four workers before.” [Heinrich13]. Indeed, if the capital required to employ two workers is smaller than the capital that was required to employ 24 workers, this would affect the profit rate positively.

In response, [KFPGC13] correctly point out that Heinrich’s argument fails if we make Marx’ assumptions explicit. That is, once we explicitly mention that we are considering 24 resp. two workers employed by the same capital. If we make this assumption by Marx explicit (that we are talking about the same advance to employ these workers), then the assertion that $C$ could also drop is not a valid response, as it would merely assert that organic composition did not rise as a fast as assumed in the example. That is, it does not argue about the example but rejects it.

The Rate of Surplus-Value and the Profit Rate

In the example discussed above, Marx assumes that organic composition rises, that the rate of surplus-value rises and that a capital of a given size employs less workers over time. This last assumption holds if we assume that the rate of surplus-value rises without the value of constant capital being (sufficiently) revolutionised by increases in productivity. That is, increases in the productivity of labour decrease the value of labour-power, but they do not decrease the value of constant capital (to such an extent to make the number of workers employed on a given capital shrink). Clearly, the assumption that there is only a mild value revolution with respect to constant capital but that there is a strong value revolution with respect to variable capital is a violent abstraction, i.e. it is unrealistic to assume that this actually holds. We will come back to this point in the next section. Here, we only point out that under this assumption — which is the assumption of Marx’s argument above — the tendency of the rate of profit to fall follows.¹²

This result can be restated by simply rescaling numerator and denominator of $p’ = s/C$ such that the rate of profit is expressed per worker. That is, we can equivalently state Marx’s result by considering one worker (per day, say), instead of one capital of a given size. Now, if the constant capital required to put one worker to work grows indefinitely absolutely, the surplus value produced by a worker will not be able to offset the drop in the rate of profit: the maximal amount of value produced by one worker is finite, say, 24 hours worth of labour-time. As a consequence, the rate of profit must eventually fall: when the outlay of constant capital per worker grows indefinitely, the profit rate falls indefinitely.

Note that “outlay per worker increasing” is called “capital deepening” in bourgeois economics and it is assumed to be a stable feature of the capitalist economy. For example, that outlay for capital per worker tends to increase is one of the six “Kaldor facts”, cf. Appendix: Kaldor facts.

Value Revolutions

Above, we assumed an ever increasing outlay in constant capital per worker and hence per mass of surplus-value. However, since the tendency of the rate of profit to fall is an expression of the rising productivity of labour, the elements of constant capital (and the means of subsistence) eventually become cheaper as a result of the same movement. This is effectively what Heinrich is pointing out when saying that the constant capital necessary to employ a worker can also fall.

Note that the question is not whether a drop in the value of $c$ can offset the rising organic composition $c/v$. This was dealt with in Organic Composition. Rather, the question is whether the advance on $c$ grows indefinitely per surplus-value produced (per worker, say). In other words, from rising organic composition (rising $c/v$) we cannot deduce that the profit rate must fall (falling $s/C$) when the rate of surplus-value $s/v$ also rises. If, as Heinrich points out, $s/v$ grows faster than $c/v$ then this does not hold. A decline in value of $v$ and $c$ can — mathematically speaking — always offset the increase of $c/v$.

For example, let the profit rate $p_0’ = s_0/(c_0+v_0)$ be expressed for a single worker, i.e. we assume that $s_0$ is the surplus-value produced by a single worker in a day, $v_0$ the wage for a single worker for a day and $c_0$ the constant capital necessary to employ a single worker for a day.

Now, assume the outlay for constant capital per worker is doubled. In the first instance, for the early adopters, this leads to an increase in the individual profit rate because they produce each commodity faster and cheaper than the competition, but can sell at the old price. Eventually, however, the new productivity level becomes generalised and we have a new profit rate of $p_1’ = s_0/(2c_0 + v_0)$. Since we already established that $c/v$ grows, we can assume that $v$ is much smaller than $c$. Hence, we roughly have $p_1’ ≈ p_0’/2$, i.e. the profit rate dropped roughly by a factor of two.¹³

However, the premise of that drop in the profit rate was an increase in productivity. If that increase in productivity is local to some branch of industry (in particular, if it does not affect the means of production considered here) then we are done: the profit rate fell. Hence, let’s assume this productivity increase eventually also affects the production of our means of production. Assume this doubled outlay in constant capital leads to a doubling of productivity, i.e. eventually all values drop to half. Then, for any newly invested capital, we have

Note that this relation is only an approximation as we ignore the increase in the rate of surplus-value. If $v_0$ is quite small relative to $s_0$ this does not make much of a difference, though, because $s_0 + v_0$ stays constant throughout — the value product produced by a worker per day — and $s_0$ approaches this magnitude as $v_0$ decreases. Since we are assuming a rising rate of surplus-value we can assume that this is the case.

Hence, if the outlay in constant capital is, say, doubled then the rate of profit for capital invested after prices drop — all else being equal — does not drop if and only if this leads to a drop in prices by at least two.

This begs the question if this condition is typically satisfied. As discussed in Organic Composition, a typical case of increased productivity is simply the application of bigger, but not fundamentally different, machines. A worker operates two machines instead of one. In this case, a doubled outlay in constant capital translates into buying twice as many machines and raw materials which are used to produce the same commodity in half the time. Hence, here a generalised doubled outlay in $c$ leads to the kind of price revolution which eventually produces a drop in price offsetting the increased outlay.

Of course, other cases of increased productivity through increased outlay in constant capital also take place, such as complete revolutions in how a certain commodity is produced. While for this case it is impossible to give a systematic argument about the relation of increased outlay in constant capital and increased productivity (and hence price drop), bourgeois economics maintains that the identity stated above — outlay increase by a factor of $x$, prices eventually drop by a factor of $x$ — observably holds. More precisely, it is one of the six “Kaldor facts” (cf. Appendix: Kaldor facts) that the capital-output ratio remains constant over long periods of time. The capital-output ratio is a relation of use-values: “output stuff” divided by “means of production stuff”. Assuming that the kludges used in bourgeois economics to make division of some stuff by some other stuff meaningful are sound, this would imply that a doubled outlay in constant capital in some hand-waving use-value sense typically also produces a doubled product of stuff in some equally hand-waving use-value sense.

Hence, the price development Michael Heinrich anticipates to cancel the drop in the profit rate may as well be assumed to be the typical price development.

Value Revolutions and Turnover

However, the argument above about price development and profit rate only applies to newly invested capital after prices dropped. The immediate general result of the development of the productivity of labour under the rule of capital is a reduction in the rate of profit; eventually, the profit rate is restored for newly invested capital. Capitals which invested in new technology previous to this price drop are stuck with an old, reduced profit rate.

Moreover, as pointed out in [Capital, Vol. III, Chap. 6], the process of “prices catching up” itself suppresses the profit rate of existing capitals further. As the prices for means of production sink, the means of production already employed in production transfer less value onto the products produced with them, reducing the profit rate for those capitals further.

Finally, if, by the time value-revolutions suppressed the price of constant capital sufficiently to (theoretically) restore the profit rate, technological development has already moved forward towards even bigger outlays in constant capital, then no restoration of the profit rate will take place. Hence, the longer the turnover of (fixed) capital, the quicker the advance in the productivity of labour and the stronger the pressure to adopt new technologies quickly, the less likely is it that a capital will benefit from these value revolutions to restore the profit rate.

In other words, when capital accumulation is successful, i.e. when capital proceeds at a fast pace with the development of the productivity of labour because accumulation provided it with the expanded means to do so, it — at the same time — produces the tendency of the rate of profit to fall by outrunning the turnover of (fixed) capital. The tendency of the rate of profit to fall is thus not a feature of a one-off increase in the productivity of labour which would disturb the profit rate until prices of means of production have sufficiently dropped again to restore profitability.¹⁴ Instead, it is a feature of the continuous development of the productivity of labour through the accumulation of capital:

The progressive tendency for the general rate of profit to fall is thus simply the expression, peculiar to the capitalist mode of production, of the progressive development of the social productivity of labour. [Capital, Vol. III, p.319, our emphasis]

It is not (a one-off) increased productivity which suppresses the rate of profit, but the continuous process of increasing productivity. More precisely, we have to say that the profit rate is suppressed when the progressive development of the social productivity of labour proceeds at a pace which outruns the turnover of (fixed) capital. Put differently, it is the accumulation of capital which suppresses the profit rate, not accumulated capital.

Profit Rate and Mass

A falling rate of profit does not imply a falling mass of profit, if the mass to which the rate applies increases sufficiently fast. For example, $1\%$ of $2,000 = 20$ is more than $10\%$ of $100 = 10$.

The law of a progressive fall in the rate of profit, or the relative decline in the surplus labour appropriated in comparison with the mass of objectified labour that the living labour sets in motion, in no way prevents the absolute mass of labour set in motion and exploited by the social capital from growing, and with it the absolute mass of surplus labour it appropriates; any more than it prevents the capitals under the control of individual capitalists from controlling a growing mass of labour and hence of surplus labour, this latter even if there is no increase in the number of workers under their command. [Capital, Vol. III, p.322]

Moreover, a continous fall in the rate of profit must be accompanied by a rise in the mass of profit:

The number of workers employed by capital, i.e. the absolute mass of labour it sets in motion, and hence the absolute mass of surplus labour it absorbs, the mass of surplus-value it produces, and the absolute mass of profit it produces, can therefore grow, and progressively so, despite the progressive fall in the rate of profit. This not only can but must be the case — discounting transient fluctuations – on the basis of capitalist production.

The result of the last section was that the general profit rate falls when capital accumulates sufficiently successful. As already developed in [Capital, Vol. I, Ch. 25], accumulation is the conversion of surplus-value into capital, i.e. additional capital is invested in constant and variable capital, which increases the mass of surplus-value.

The capitalist production process is essentially, and at the same time, a process of accumulation. We have shown how, with the progress of capitalist production, the mass of value that must simply be reproduced and maintained rises and grows with the rising productivity of labour, even if the labour-power applied remains constant. [Capital, Vol. III, p.324]

Moreover, productivity increases imply that means of production are produced faster. More means of production are produced and sold successfully. These additional means of production must be employed if accumulation is to take place. Now, because value revolutions decrease the price of these means of production each of them is capable of absorbing living labour at a lower price:

But as the social productivity of labour develops, so the mass of use-values produced grows still more, and the means of production form a portion of these. The additional labour, moreover, which has to be appropriated in order for this additional wealth to be transformed back into capital does not depend on the value of these means of production (including means of subsistence), since the worker is not concerned in the labour process with the value of the means of production but rather with their use-value. [Capital, Vol. III, p.324]

In a word, accelerated accumulation takes place:¹⁵

We have seen how it is that the same reasons that produce a tendential fall in the general rate of proit also bring about an accelerated accumulation of capital and hence a growth in the absolute magnitude o total mass of the surplus labour (surplus­ value, profit) appropriated by it.

Finally, as already developed in [Capital, Vol. I, Ch. 25], the development of the population is no limit to capital as it produces relative surplus-population in accordance with its needs. Hence, the increased amount of means of production find unemployed workers on the market.

Note that Marx considers the case where only surplus-value is invested. He does not consider the case where fixed capital has turned over and all capital has returned to money form. In this case, an increased outlay in $C$ (accumulation) could in principle be accompanied by an absolutely decreased outlay in $v$ such that this $v$ actually corresponds to less workers being employed. Hence, in principle, an increase in the rate of profit could be accompanied by a fall in the mass of profit. However, recall that this chapter considers the general rate of profit, i.e. total social (fixed) capital would have to turn over at the same point in time, an assumption which cannot hold as we know from the reproduction schemes in Volume 2. Furthermore, when overall new investments do not yield additional returns, then accumulation — the process which makes the rate of profit fall — breaks down. This is discussed in Chapter 15.

Insofar a falling profit rate is caused by productivity increases through accumulation, it is a sign of success of capital accumulation.

Appendix: Composition Glossary

Technical composition is the relation of machinery to labourers in technical or use-value terms: how much machinery and raw material is needed for a certain amount of workers. The technical composition changes with more machinery and less workers needed. This is a qualitative relation, so the reference made in a few commentaries on the issue to a supposedly “rising” technical composition is not adequate.¹⁶ Yet, to express it as a quantitative relation seems to be obvious. For example, if a machine is replaced by one holding 20 instead of the formerly 2 spindles — and the new machine still only needs one worker to do the spinning — then the technical composition “rose”. However, there is a problem in comparing things on the use-value side. As much as the previous example suggests that this can be done, the problem becomes apparent with a technical revolution that completely changes how production is done and hence leads to the application of entirely new machinery in the capitalist production process. This new machine is not “more” or “less”, it is different and therefore not comparable.¹⁷

Value composition ($c/v$), on the other hand, is a ratio of two magnitudes of value: value of constant capital in relation to value of variable capital. There are two reasons for why the value composition can change. Firstly, because the technical composition changes and that is reflected in the value composition. Say, new machinery is bought (more $c$) which needs relatively less workers ($v$). The second reason is that prices simply changed, but nothing technically changed in the production process in question. For example, some machine became cheaper to buy (less $c$, therefore relatively more $v$).

Organic composition is simply the first case: any change in the value composition that is caused by a change in the technical composition. Note that the technical composition can change without it affecting the value composition (e.g. technical composition rises, yet workers managed to receive more $v$) — in that case, the changed technical composition will not show value-wise.¹⁸ Heinrich’s Heinrich06 [p.315] objection against the concept of the organic composition misses the point. He argues that the cause of a changing value composition cannot necessarily be detected. Anything could change the ratio between $c$ and $v$, he argues, so the organic composition cannot be an indicator of a particular change, i.e. of a change in the technical composition. Yet, the concept of the organic composition is simply that a change of the organic composition is caused by a change in the technical composition, i.e. we only use it when we know what changed value composition. Hence, the organic composition in itself does not say much as stressed by George Geo12 [p.8]. It is only meaningful in comparison with another (perhaps, earlier) organic composition: $c/v$ rose because more machinery is applied in to relation to the outlay in $v$ and that technical change reflects in a changing value relation of $c/v$.

Appendix: More Marx on Organic Composition

Marx on raw materials:

One may ask with regard to raw material: If, for example, productive power in spinning increases tenfold, that is, 1 worker spins as much as ten did previously, why should not 1 nigger produce as much cotton as 10 did previously, that is, why should the value ratio not remain the same? The spinner uses 10 times as much cotton in the same time, but the nigger produces 10 times as much cotton in the same time. The 10 times larger amount of cotton therefore costs no more than a tenth of this amount cost previously. This means that despite the increase in the amount of the raw material, its value ratio to variable capital remains the same. In fact it was only the large fall in the price of cotton which enabled the cotton industry to develop in the way it did. The dearer the material (gold and silver, for example) the less are machinery and the division of labour applied in transforming it into articles of luxury. This is because too much capital has been advanced for the raw materials and the demand for these products is limited owing to the expensive raw materials. [MECW 33 p.291]

Hence, he firstly asserts that productivity increases are more difficult for organic processes of production, i.e. those processes which produce raw materials like cotton. Secondly, he states that the law of ground rent would increase the value of such products. Thirdly, he states that the extraction of coal, oil etc. would become cheaper with the progress of industry but that this advance would eventually be undone when sources are depleted.

Marx seems to consider it unlikely that productivity increases are uniform across branches of industry: “With the exception of isolated cases (e.g. when the productivity of labour cheapens all the elements of both constant and variable capital to the same extent), …” [Capital, Vol. III, p.333].

This is clearly true for any particular increase, e.g. some new way of making plastic. It is another question of what happens over a longer period involving productivity increases in different sectors. There is no reason why this should favour the elements of constant capital over those of variable capital.

Appendix: Marx on Relative Surplus-Value

Heinrich [Heinrich12] considers a rising rate of relative surplus-value as part of the law as such, not as a counteracting cause, and also points out that Marx himself considered the law as such proven even when the rate of relative surplus-value rises. For example, Marx writes:

With the progressive decline in the variable capital in relation to the constant capital, this tendency leads to a rising organic composition of the total capital, and the direct result of this is that the rate of surplus-value, with the level of exploitation of labour remaining the same or even rising, is expressed in a steadily falling general rate of profit. [Capital, Vol. III, p.318, our emphasis]

In contrast, [KFPGC13] claim that Marx considered rising organic composition and rising relative surplus-value separately, the latter being a counteracting cause. For this they rely on the following passage from Chap. 14 (where they omitted the part we emphasised).

It has already been shown, moreover, and this forms the real secret of the tendential fall in the rate of profit, that the procedures for producing relative surplus-value are based, by and large, either on transforming as much as possible of a given amount of labour into surplus-value or on spending as little as possible labour in general in relation to the capital advanced; so that the same reasons that permit the level of exploitation of labour to increase make it impossible to exploit as much labour as before with the same total capital. These are the counteracting tendencies which, while they act to bring about a rise in the rate of surplus-value, simultaneously lead to a fall in the mass of surplus-value produced by a given capital, hence a fall in the rate of profit. [Capital, Vol. III, p.340, our emphasis]

However, in this passage Marx is explicitly making a backward reference claiming that it was already shown that in general the production of relative surplus-value leads to fall of the general rate of profit. This is emphasised by his assertion that this was the “real secret” of the law itself. Hence, this passage, too, suggests that Marx did realise that the law itself must be considered under the assumption that the rate of surplus-value rises because of the techniques of the production of relative surplus-value. In the passage above, Marx also speaks of “counteracting tendencies” which of [KFPGC13] take as confirmation of their reading that a rise in the rate of relative surplus-value is a counteracting factor. This, however, is a misreading. Firstly, Marx is talking of a tendency here and not of a factor. Secondly, Marx is talking of tendencies (plural) and not of one tendency. That is, he is describing that the same development contains within itself two opposing tendencies: it increases the rate of surplus-value which raises the profit rate and it increases organic composition which suppresses the profit rate.¹⁹

A rising rate of relative surplus-value must be considered when discussing the law of the tendency of the rate of profit to fall and Marx did realise this necessity.

Appendix: Krisis Criticism of Heinrich

Peter Samol, writing for the journal “krisis”, aims to show that once a certain rate of surplus-value is reached ($v=s$), this rate would need to grow exponentially in order to make up for even a small change in the rate of profit [Samol13]. Hence, according to Samol, with an increase in the rate of surplus-value, it becomes ever harder for it to cancel out the fall of the rate of profit.

However, Samol makes the mistake to take a wrong reference point in his calculation: he relates an absolute number to a relation instead of the relations rate of surplus-value $s/v$ to organic composition $c/v$. Samol considers a change in the organic composition — say from $98c/2v$ changing to $99c/1v$ — and says, there was a “minor” change in $c$ (absolute number), which would call for a “major” change in the rate of surplus-value in order to cancel out a falling rate of profit.

Comparing both rates instead, we come to a different conclusion: it is indeed the same factor by which the organic composition rises, that needs to be the growth of the rate of surplus-value in order for the profit rate to stay the same. Expressed mathematically, with Heinrich’s conversion of the formula:

We rearrange to express $s/v$ in $c/v$ and $p’$. That is, we isolate the rate of surplus-value on one side of the equation to be able to see what then happens on the other side with the organic composition and the profit rate:

Hence, $s/v$ grows linearly in $c/v$. By assumption, $p’$ is to stay constant in order to find out what increase in $s/v$ is needed to cancel out the rise in $c/v$. If $c/v$ then is doubled, then $s/v$ must also be multiplied roughly by $2/p’$ in order to keep $p’$ constant. Since $p’$ is likely $< 1$ (i.e. a profit rate of less than 100%), the multiplier will be larger than $2$ (e.g. $2/0.1 = 2⋅10 = 20$). Yet, this does not imply at all that the demand against $s/v$ grows ever more. The factor stays the same, no matter how large $c/v$ becomes. Therefore, no exponential growth of $s/v$ is needed in order to cancel out a falling rate of profit.

Appendix: Kaldor Facts

In [Kaldor61] six “stylized facts” are put forward for economics to chew on. These “facts” have since been reportedly verified by many bourgeois economists and are widely considered to be true statements. They might hence provide some guidance what can be observed as a staple of the capitalist economy over the last few decades. The six “facts” are:

As regards the process of economic change and development in capitalist societies, I suggest the following “stylized facts” as a startingpoint for the construction of theoretical models:

1. The continued growth in the aggregate volume of production and in the productivity of labour at a steady trend rate; no recorded tendency for a falling rate of growth of productivity.

2. A continued increase in the amount of capital per worker, whatever statistical measure of ‘capital’ is chosen in this connection.

3. A steady rate of profit on capital, at least in the “developed” capitalist societies; this rate of profit being substantially higher than the “pure” long-term rate of interest as shown by the yield of giltedged bonds. […]

4. Steady capital-output ratios over long periods; at least there are no clear long-term trends, either rising or falling, if differences in the degree of utilization of capacity are allowed for. This implies, or reflects, the near-identity in the percentage rates of growth of production and of the capital stock — i.e. that for the economy as a whole, and over longer periods, income and capital tend to grow at the same rate.

5. A high correlation between the share of profits in income and the share of investment in output; a steady share of profits (and of wages) in societies and/or in periods in which the investment coefficient (the share of investment in output) is constant. […]

6. Finally, there are appreciable differences in the rate of growth of labour productivity and of total output in different societies, the range of variation (in the fast-growing economies) being of the order of 2-5 per cent. These are associated with corresponding variations in the investment coefficient, and in the profit share, but the above propositions concerning the constancy of relative shares and of the capital-output ratio are applicable to countries with differing rates of growth.

The third “fact” can be read as contradicting the starting point of [Capital, Vol. III, Chap. 13]. However, it is not clear what rate of profit these facts are actually referring to.

The second “fact” asserts the conditions under which — in the long term — the profit rate must fall (see Relative surplus-value).

Finally, “fact” four implies that prices do eventually drop to cancel a fall in the profit rate for newly invested capital if productivity does not increase further.

References

[Capital, Vol. I] Karl Marx. Capital Volume I. Penguin, 1982.
[Capital, Vol. III] Karl Marx. Capital: Volume III. Penguin Classics, 1991.
[CR13] Guglielmo Carchedi and Michael Roberts. A Critique of Heinrich’s, ‘Crisis Theory, the Law of the Tendency of the Profit Rate to Fall, and Marx’s Studies in the 1870s’. In: Monthly Review (2013).
[Georg12] Ed George. Chapter 13: The Law Itself. 2012.
[Heinrich06] Michael Heinrich. Die Wissenschaft vom Wert. Westfälisches Dampfboot, 2006.
[Heinrich12] Michael Heinrich. An Introduction to the Three Volumes of Karl Marx’s Capital. Monthly Review Press, 2012.
[Heinrich13a] Michael Heinrich. Crisis Theory, the Law of the Tendency of the Profit Rate to Fall, and Marx’s Studies in the 1870s. In: Monthly Review 64.11 (2013).
[Heinrich13b] Michael Heinrich. Heinrich Answers Critics. Dec. 2013.
[Kaldor61] Nicholas Kaldor. Capital accumulation and economic growth. Macmillan, 1961.
[KFPGC13] Andrew Kliman, Alan Freeman, Nick Potts, Alexey Gusev and Brendan Cooney. The Unmaking of Marx’s Capital: Heinrich’s Attempt to Eliminate Marx’s Crisis Theory. 2013.
[Kliman11] Andrew Kliman. The Failure of Capitalist Production: Underlying Causes of the Great Recession. United Kingdom: Pluto Press, 2011. isbn: 9781849646239.
[Kliman96] Andrew Kliman. A value-theoretic critique of the Okishio theorem. In: Marx and non-equilibrium economics (1996), pp. 206–224.
[MECW 33] Karl Marx. 1861-63, Economic Manuscripts. Marx/Engels Collected Works (MECW) 33. Lawrence & Wishart, 1991.
[Samol13] Peter Samol. Michael Heinrichs Fehlkalkulationen der Profitrate. In: Krisis (Jan. 2013).