Marx’s Capital, Volume 1, Chapter 18: A Critical Summary

Chapter 18 of volume 1 of Capital is called “Different Formulae for the Rate of Surplus-Value” and Marx discusses his basic formulae here.

For Marx, the rate of surplus value is represented by these formulae:

Surplus value	=	s	=	Surplus value	=	Surplus labour
——————————		——		————————————		——————————
Variable capital		v		Value of labour power		Necessary labour

The first two formulae are expressed in values, but the third is a ratio of the relevant quantities of time (Marx 1990: 669). For Marx, the value of labour-power tends to be the value of the maintenance and reproduction of labour-power, a subsistence wage, but sometimes the real wage or the value of variable capital v might be above or below the subsistence wage.

As Marx says, “[t]he two first of these formulae represent, as a ratio of values, that which, in the third, is represented as a ratio of the times during which those values are produced” (Marx 1906: 582).

We must remember too that for Marx the rate of surplus value is the rate of exploitation:

“The rate of surplus-value is therefore an exact expression for the degree of exploitation of labour-power by capital, or of the labourer by the capitalist” (Marx 1906: 241).

Marx in Chapter 9 of Capital further distinguishes between

(1) the rate of surplus value (or rate/degree of exploitation) and

(2) the magnitude/amount of exploitation in terms of surplus labour hours worked.

This difference is explained as follows:

“Although the rate of surplus-value is an exact expression for the degree of exploitation of labour-power, it is, in no sense, an expression for the absolute amount of exploitation. For example, if the necessary labour=5 hours and the surplus-labour=5 hours, the degree of exploitation is 100%. The amount of exploitation it here measured by 5 hours. If, on the other hand, the necessary labour=6 hours and the surplus-labour=6 hours, the degree of exploitation remains, as before, 100%, while the actual amount of exploitation has increased 20%, namely from five hours to six.” (Marx 1906: 241, n. 2).

Marx states that the Classical Political economists had their own formulae to calculate surplus value as follows:

Surplus labour	=	Surplus value	=	Surplus product
———————————		——————————————		————————————
Working day		Value of the product		Total product

The values in each of these formulae are labour hours, values and quantity of products respectively. Marx maintains that these formulae are flawed because “the actual degree of exploitation of labour, or the rate of surplus-value, is falsely expressed” (Marx 1906: 582).

So, for Marx, the following is true:

“These derivative formulae express, in reality, only the proportion in which the working-day, or the value produced by it, is divided between capitalist and labourer. If they are to be treated as direct expressions of the degree of self-expansion of capital, the following erroneous law would hold good: Surplus-labour or surplus-value can never reach 100 %. Since the surplus-labour is only an aliquot part of the working-day, or since surplus-value is only an aliquot part of the value created, the surplus-labour must necessarily be always less than the working-day, or the surplus-value always less than the total value created. In order, however, to attain the ratio of 100 :100 they must be equal. In order that the surplus-labour may absorb the whole day (i. e., an average day of any week or year), the necessary labour must sink to zero. But if the necessary labour vanish, so too does the surplus-labour, since it is only a function of the former.” (Marx 1906: 582–583).

“The favourite method of treating the working-day as constant in magnitude became, through the use of the formulae II., a fixed usage, because in them surplus-labour is always compared with a working-day of given length. The same holds good when the repartition of the value produced is exclusively kept in sight. The working-day that has already been realised in a given value, must necessarily be a day of given length.

The habit of representing surplus-value and value of labour-power as fractions of the value created—a habit that originates in the capitalist mode of production itself, and whose import will hereafter be disclosed—conceals the very transaction that characterises capital, namely the exchange of variable capital for living labour-power, and the consequent exclusion of the labourer from the product. Instead of the real fact, we have the false semblance of an association, in which labourer and capitalist divide the product in proportion to the different elements which they respectively contribute towards its formation.” (Marx 1906: 584).

Finally, Marx presents a third set of formulae:

Surplus value	=	Surplus labour	=	Unpaid labour
———————————————		——————————		————————
Value of labour power		Necessary labour		Paid labour

Marx explains these as follows:

“The capitalist pays the value, so far as price coincides with value, of the labour-power, and receives in exchange the disposal of the living labour-power itself. His usufruct is spread over two periods. During one the labourer produces a value that is only equal to the value of his labour-power: he produces its equivalent. Thus the capitalist receives in return for his advance of the price of the labour power, a product of the same price. It is the same as if he had bought the product ready made in the market. During the other period, the period of surplus-labour, the usufruct of the labour-power creates a value for the capitalist, that costs him no equivalent. This expenditure of labour-power comes to him gratis. In this sense it is that surplus-labour can be called unpaid labour.

Capital, therefore, is not only, as Adam Smith says, the command over labour. It is essentially the command over unpaid labour. All surplus-value, whatever particular form (profit, interest, or rent), it may subsequently crystallise into, is in substance the materialisation of unpaid labour. The secret of the self-expansion of capital resolves itself into having the disposal of a definite quantity of other people’s unpaid labour.” (Marx 1906: 585).

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

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

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.