Marx’s Capital, Volume 1, Chapter 11: A Critical Summary

Chapter 11 of volume 1 of Capital is called “The Rate and Mass of Surplus-Value” (Marx 1990: 417), and it deals with further aspects of surplus value.

In essence, Marx makes a number of points in this chapter as follows:

(1) the rate of surplus value is dependent on the duration of the working day and the value of labour-power;

(2) the total mass of surplus value can be measured by s/v multiplied by the value of total variable capital, and capitalists wish to maximise the mass of surplus-value;

(3) given a constant value of labour-power, the limit to the rate of surplus value is the limit to the working day (Brewer 1984: 47; Harvey 2010: 160–161).

There are also three “laws” Marx seeks to establish in this chapter as follows:

(1) the mass of surplus value S = P * (a′ (surplus labour) / a (necessary labour)) * n, where

P = value of an average labour power;
a′ / a = degree of exploitation;
n = number of workers employed.

(2) if the number of workers falls and rate of the surplus value rises, the physical limit to the working day in turn sets a limit on how far the rate of surplus value can rise by increasing the number of hours worked per day.

(3) the mass of surplus value will change in accordance with the quantity of variable capital, although this contradicts the Classical theory of a uniform, average rate of profit. That is to say, when the value of labour-power and the rate of surplus value are constant, the mass of surplus value is determined only by the mass of labour:

“The law demonstrated above now, therefore, takes this form: the masses of value and of surplus-value produced by different capitals—the value of labour-power being given and its degree of exploitation being equal—vary directly as the amounts of the variable constituents of these capitals, i.e., as their constituents transformed into living labour-power.” (Marx 1906: 335).

The critical summary follows.

Chapter 11: The Rate and Mass of Surplus-Value
Marx assumes that the value of labour-power which represents the part of the “working-day necessary for the reproduction or maintenance of that labour-power” (Marx 1906: 331) is a constant and given magnitude (Marx 1990: 417).

It is important to remember that the rate of surplus value is surplus value/variable capital (Marx 1990: 324; Brewer 1984: 43), and that surplus value/total capital is the rate of profit and is distinct from the rate of surplus value (Brewer 1984: 43). Furthermore, the rate of surplus-value is measure of degree of exploitation of labour-power (Marx 1906: 241).

A monetary value x can be attached to the value of labour power, and if the rate of surplus value, is, for example, 100%, then the monetary value of the surplus value is also x (Marx 1990: 417).

Marx goes on to say:

“But the variable capital of a capitalist is the expression in money of the total value of all the labour-powers that he employs simultaneously. Its value is, therefore, equal to the average value of one labour-power, multiplied by the number of labour-powers employed. With a given value of labour-power, therefore, the magnitude of the variable capital varies directly as the number of labourers employed simultaneously. If the daily value of one labour-power = 3s., then a capital of 300s. must be advanced in order to exploit daily 100 labour-powers, of n times 3s., in order to exploit daily n labour-powers. In the same way, if a variable capital of 3s., being the daily value of one labour-power, produce a daily surplus-value of 3s., a variable capital of 300s. will produce a daily surplus-value of 300s., and one of n times 3s. a daily surplus-value of n X 3s. The mass of the surplus-value produced is therefore equal to the surplus-value which the working-day of one labourer supplies multiplied by the number of labourers employed. But as further the mass of surplus-value which a single labourer produces, the value of labour-power being given, is determined by the rate of the surplus-value, this law follows: the mass of the surplus-value produced is equal to the amount of the variable capital advanced, multiplied by the rate of surplus-value; in other words: it is determined by the compound ratio between the number of labour-powers exploited simultaneously by the same capitalist and the degree of exploitation of each individual labour-power.” (Marx 1906: 331–332).

Marx then gives formulae for S, the mass of surplus value:

S = (s/v) * V, and
S = P * (a′ (surplus labour) / a (necessary labour)) * n, where

V = sum total of the variable capital;
P = value of an average labour power;
a′ / a = degree of exploitation;
n = number of workers employed.

(Marx 1906: 332).

Here a′ / a is the equivalent of s/v (Brewer 1984: 47).

Marx sets out a second and third “law”:

“The absolute limit of the average working-day—this being by Nature always less than 24 hours—sets an absolute limit to the compensation of a reduction of variable capital by a higher rate of surplus-value, or of the decrease of the number of labourers exploited by a higher degree of exploitation of labour-power. This palpable law is of importance for the clearing up of many phenomena, arising from a tendency (to be worked out later on) of capital to reduce as much as possible the number of labourers employed by it, or its variable constituent transformed into labour-power, in contradiction to its other tendency to produce the greatest possible mass of surplus-value. On the other hand, if the mass of labour-power employed, or the amount of variable capital, increases, but not in proportion to the fall in the rate of surplus-value, the mass of the surplus-value produced, falls.

A third law results from the determination, of the mass of the surplus-value produced, by the two factors: rate of surplus-value and amount of variable capital advanced. The rate of surplus-value, or the degree of exploitation of labour-power, and the value of labour-power, or the amount of necessary working time being given, it is self-evident that the greater the variable capital, the greater would be the mass of the value produced and of the surplus-value. If the limit of the working-day is given, and also the limit of its necessary constituent, the mass of value and surplus-value that an individual capitalist produces, is clearly exclusively dependent on the mass of labour that he sets in motion. But this, under the conditions supposed above, depends on the mass of labour-power, or the number of labourers whom he exploits, and this number in its turn is determined by the amount of the variable capital advanced. With a given rate of surplus-value, and a given value of labour-power, therefore, the masses of surplus-value produced vary directly as the amounts of the variable capitals advanced.” (Marx 1906: 334).

At this point, a crucial problem arises in this passage:

“Now we know that the capitalist divides his capital into two parts. One part he lays out in means of production. This is the constant part of his capital. The other part he lays out in living labour-power. This part forms his variable capital. On the basis of the same mode of social production, the division of capital into constant and variable differs in different branches of production, and within the same branch of production, too, this relation changes with changes in the technical conditions and in the social combinations of the processes of production. But in whatever proportion a given capital breaks up into a constant and a variable part, whether the latter is to the former as 1:2 or 1:10 or 1:x, the law just laid down is not affected by this. For, according to our previous analysis, the value of the constant capital reappears in the value of the product, but does not enter into the newly produced value, the newly created value-product. To employ 1000 spinners, more raw material, spindles, &c, are, of course, required, than to employ 100. The value of these additional means of production however may rise fall, remain unaltered, be large or small; it has no influence on the process of creation of surplus-value by means of the labour-power that put them in motion. The law demonstrated above now, therefore, takes this form: the masses of value and of surplus-value produced by different capitals—the value of labour-power being given and its degree of exploitation being equal—vary directly as the amounts of the variable constituents of these capitals, i.e., as their constituents transformed into living labour-power.

This law clearly contradicts all experience based on appearance. Every one knows that a cotton spinner, who, reckoning the percentage on the whole of his applied capital, employs much constant and little variable capital, does not, on account of this, pocket less profit or surplus-value than a baker, who relatively sets in motion much variable and little constant capital. For the solution of this apparent contradiction, many intermediate terms are as yet wanted, as from the standpoint of elementary algebra many intermediate terms are wanted to understand that 0/0 may represent an actual magnitude. Classical economy, although not formulating the law, holds instinctively to it, because it is a necessary consequence of the general law of value. It tries to rescue the law from collision with contradictory phenomena by a violent abstraction. It will be seen later how the school of Ricardo has come to grief over this stumbling-block. Vulgar economy which, indeed, ‘has really learnt nothing,’ here as everywhere sticks to appearances in opposition to the law which regulates and explains them. In opposition to Spinoza, it believes that ‘ignorance is a sufficient reason.’” (Marx 1906: 335–336).

It is because Marx thinks that surplus value causes profits that his theory is struck with this damning problem. This passage is usually held to be the most important point in volume 1 of Capital where Marx raises the transformation problem (Howard and King 1989: 23–24).

But, in essence, the problem is as follows:

(1) in volume 1 of Capital Marx says that commodities tend to have prices at their true labour values, so that these prices also reflect the surplus value embodied in the commodities.

(2) in turn surplus value is what determines profits. Engels defines the problem as follows in his famous preface to volume 2 of Capital:

“2. According to the Ricardian law of value, two capitals employing the same and equally paid labor, all other conditions being equal, produce the same value and surplus value, or profit, in the same time. But if they employ unequal quantities of actual labor, they cannot produce equal surplus-values, or, as the Ricardians say, equal profits. Now in reality, the exact opposite takes place. As a matter of fact, equal capitals, regardless of the quantity of actual labor employed by them, produce equal average profits in equal times. Here we have, therefore, a clash with the law of value ... . (Engels 1907 [1885]: 27–29).

Alexander Gray also summed up the problem as follows:

“If profit springs only from the labour employed, and in no wise from the constant capital, then the rate of profit in different industries will vary according as the proportion of variable capital is high or low. When there is much variable capital (i.e., in more primitive and undeveloped industries) the rate of profit will be high; in industries which have had extensive resort to machinery, the rate of profit will be low. Marx admitted with praiseworthy frankness that the observed facts were in glaring contradiction with the law so ascertained ... .” (Gray 1956: 319).

However, Marx offers no solution to the paradox in volume 1.

With a given total labour force and set average working day, capitalism has an aggregate “social working day” (Marx 1990: 422). If the working day cannot be increased, then the mass of surplus value can only be increased by increasing the total labour force (Marx 1990: 422).

The increase of wealth is “implied in capitalist production” (Marx 1906: 337), and so there is a tendency to greater exploitation.

Marx now turns to historical analysis. Capitalism develops as individual capitalists increase their private wealth and can thus finance investment:

“The minimum of the sum of value that the individual possessor of money or commodities must command, in order to metamorphose himself into a capitalist, changes with the different stages of development of capitalist production, and is at given stages different in different spheres of production, according to their special and technical conditions. Certain spheres of production demand; even at the very outset of capitalist production, a minimum of capital that is not as yet found in the hands of single individuals. This gives rise partly to state subsidies to private persons, as in France in the time of Colbert, and as in many German states up to our own epoch; partly to the formation of societies with legal monopoly for the exploitation of certain branches of industry and commerce, the fore-runners of our own modern joint-stock companies.

Within the process of production, as we have seen, capital acquired the command over labour, i. e., over functioning labouring-power or the labourer himself. Personified capital, the capitalist takes care that the labourer does his work regularly and with the proper degree of intensity. Capital further developed into a coercive relation, which compels the working class to do more work than the narrow round of its own life-wants prescribes. As a producer of the activity of others, as a pumper-out of surplus-labour and exploiter of labour-power, it surpasses in energy, disregard of bounds, recklessness and efficiency, all earlier systems of production based on directly compulsory labour.” (Marx 1906: 338–339).

The extension of the working day by capitalists happened before the revolution in technologies used in production (Marx 1990: 425).

Capitalism subordinates workers and strips previously independent handicraft workers of their own capital and makes them subordinate to the constant capital employed by factories and businesses (Marx 1990: 425).

Dead capital in the form of constant capital needs living labour to function and to continue to be transfer its fixed labour value into new output commodities:

“Furnaces and workshops that stand idle by night, and absorb no living labour, are ‘a mere loss’ to the capitalist. Hence, furnaces and workshops constitute lawful claims upon the night-labour of the workpeople. The simple transformation of money into the material factors of the process of production, into means of production, transforms the latter into a title and a right to the labour and surplus-labour of others.” (Marx 1906: 339).

But this image of dead capital as vampire-like and only made alive by the blood of surplus labour of human workers is a caricature of capitalism, only fit for Marxist mythology.

What is totally missing here is the fact that a factory might be completely or almost fully automated and still earn significant money profits. We have real world examples now: see here and the plans for such a factory here

Or we can see a nearly full automated factory in the video below.



In actuality, capitalists are not seeking labour per se or Marx’s mystical surplus value, but money profits and greater productivity, which can rise even as the amount of labour falls or when labour is totally eliminated. Surplus value is a redundant and incoherent concept, derived from the equally incoherent and empirically-falsified concept of homogeneous units of socially necessary labour time.

Further Reading
“Engels’ Famous Challenge in the Preface to Volume 2 of Capital on the Transformation Problem,” December 22, 2015.

BIBLIOGRAPHY
Brewer, Anthony. 1984. A Guide to Marx’s Capital. Cambridge University Press, Cambridge.

Gray, Alexander. 1956. The Development of Economic Doctrine: An Introductory Survey. Longmans, Green and Co., London.

Harvey, David. 2010. A Companion to Marx’s Capital. Verso, London and New York.

Howard, Michael Charles and John E. King. 1989. A History of Marxian Economics. Volume I, 1883–1929. Princeton University Press, Princeton, NJ.

Marx, Karl. 1906. Capital. A Critique of Political Economy (vol. 1; rev. trans. by Ernest Untermann from 4th German edn.). The Modern Library, New York.

Marx, Karl. 1990. Capital. A Critique of Political Economy. Volume One (trans. Ben Fowkes). Penguin Books, London.