We have seen that the rate of surplus-value is represented by the following formulae.
The first two forms of Formula I express as value ratios what the third expresses as a ratio of the times in which those values are produced. The three interchangeable formulae are conceptually strict. Classical political economy therefore contains them in substance, though not as a consciously worked-out account; there we instead meet the derivative formulae that follow.
In the authorized French edition, Marx brackets Formula II's first ratio because bourgeois political economy does not express the concept of surplus-labour clearly. One and the same proportion is expressed here in turn as labour-times, as the values embodied in those times, and as the products in which those values exist. “Value of the product” is understood to mean only the value-product newly created in the working day. The constant part of the total product-value is excluded.
In all Formula II’s forms, the actual degree of exploitation of labour — the rate of surplus-value — is falsely expressed. Let the working day be twelve hours. Under the assumptions of the earlier example, the real degree of exploitation is represented by the proportions that follow.
Formula II, however, gives a very different result.
These derivative formulae do in fact express the proportion in which the working day, or its value-product, is divided between capitalist and worker. But if they are treated as direct expressions of capital’s degree of self-valorization, they yield a false law: surplus-labour or surplus-value could never reach 100%. Since surplus-labour is always an aliquot part of the working day, and surplus-value an aliquot part of the value-product, each is smaller than its whole. To stand at 100/100, numerator and denominator would have to be equal. For surplus-labour to absorb the whole day — the average day of the week or year is at issue — necessary labour would have to sink to zero. Yet if necessary labour disappears, surplus-labour disappears as well, because it is a function of it. Formula II can therefore never reach 100/100, much less exceed it. The attached note cites Rodbertus's third letter to Kirchmann: despite its false rent theory, it saw through the nature of capitalist production. Engels's addition to the third German edition qualifies Marx's praise after the later Rodbertus letters. There the capitalist's activity becomes a delegated economic and political function, profit a salary-form that may be regulated if it takes too much from wages, and Marx's book a polemic against the present form of capital supposedly confused with capital as such. Engels says Rodbertus's genuinely bold beginnings run aground in these ideological commonplaces. The rate of surplus-value, the actual degree of exploitation, can do both. Lavergne estimates that the English agricultural labourer receives one quarter and the farmer three quarters of the product or its value, whatever later division occurs among capitalist, landlord, and others. The calculation leaves out the part replacing constant capital. On this estimate surplus-labour stands to necessary labour as 3:1: exploitation is 300%. The attached note adds that Lavergne, a blind admirer of England, is likelier to have put the capitalist’s share too low than too high.
Formula II reinforced the school habit of treating the working day as a constant magnitude, because it always compares surplus-labour with a day of given size. The same is true when attention is confined to the division of the value-product: once the working day has been realized in a value-product, it necessarily appears as a day with fixed limits.
Representing surplus-value and labour-power’s value as fractions of the value-product — a form arising from capitalist production itself, whose significance is disclosed later — conceals the specific capital relation. It hides the exchange of variable capital for living labour-power and the corresponding exclusion of the worker from the product. In its place comes the false appearance of an association in which worker and capitalist divide the product according to the different factors entering its formation. The attached note shows how easily developed capitalist cooperation can be stripped of its antagonistic character and retold as free association: Laborde does so explicitly, and Carey can perform the same trick even for slavery.
Formula II can always be reconverted into Formula I. For example, take the proportion that follows.
There is a third formula, already anticipated on occasion.
The misunderstanding invited by the formula “unpaid labour / paid labour” — that the capitalist pays for labour rather than labour-power — is removed by the earlier argument. The formula is only a popular expression for “surplus-labour / necessary labour.”
The capitalist pays the value of labour-power, or its price where price diverges from value, and receives in exchange disposal over living labour-power itself. Its use divides into two periods. During one, the worker produces only a value equal to labour-power’s value: an equivalent. In return for the price advanced for labour-power, the capitalist receives a product of the same price, as if it had been bought ready-made on the market. During surplus-labour, however, use of labour-power forms value for the capitalist without costing a further value-equivalent. This expenditure of labour-power comes to him gratis. In this sense, surplus-labour may be called unpaid labour. The attached note recalls the Physiocrats’ recognition that surplus-value was a disposable wealth the possessor had not bought and yet sold.
Capital is therefore not only command over labour, as Adam Smith says. It is essentially command over unpaid labour. All surplus-value, whatever particular form it later crystallizes into — profit, interest, rent, and so on — is in substance materialized unpaid labour-time. The secret of capital’s self-valorization resolves into its disposal over a definite quantity of other people’s unpaid labour.
We have seen that the rate of surplus-value is represented by the following formulae.
The first two forms of Formula I express as value ratios what the third expresses as a ratio of the times in which those values are produced. The three interchangeable formulae are conceptually strict. Classical political economy therefore contains them in substance, though not as a consciously worked-out account; there we instead meet the derivative formulae that follow.
In the authorized French edition, Marx brackets Formula II's first ratio because bourgeois political economy does not express the concept of surplus-labour clearly. One and the same proportion is expressed here in turn as labour-times, as the values embodied in those times, and as the products in which those values exist. “Value of the product” is understood to mean only the value-product newly created in the working day. The constant part of the total product-value is excluded.
In all Formula II’s forms, the actual degree of exploitation of labour — the rate of surplus-value — is falsely expressed. Let the working day be twelve hours. Under the assumptions of the earlier example, the real degree of exploitation is represented by the proportions that follow.
Formula II, however, gives a very different result.
These derivative formulae do in fact express the proportion in which the working day, or its value-product, is divided between capitalist and worker. But if they are treated as direct expressions of capital’s degree of self-valorization, they yield a false law: surplus-labour or surplus-value could never reach 100%. Since surplus-labour is always an aliquot part of the working day, and surplus-value an aliquot part of the value-product, each is smaller than its whole. To stand at 100/100, numerator and denominator would have to be equal. For surplus-labour to absorb the whole day — the average day of the week or year is at issue — necessary labour would have to sink to zero. Yet if necessary labour disappears, surplus-labour disappears as well, because it is a function of it. Formula II can therefore never reach 100/100, much less exceed it. The attached note cites Rodbertus's third letter to Kirchmann: despite its false rent theory, it saw through the nature of capitalist production. Engels's addition to the third German edition qualifies Marx's praise after the later Rodbertus letters. There the capitalist's activity becomes a delegated economic and political function, profit a salary-form that may be regulated if it takes too much from wages, and Marx's book a polemic against the present form of capital supposedly confused with capital as such. Engels says Rodbertus's genuinely bold beginnings run aground in these ideological commonplaces. The rate of surplus-value, the actual degree of exploitation, can do both. Lavergne estimates that the English agricultural labourer receives one quarter and the farmer three quarters of the product or its value, whatever later division occurs among capitalist, landlord, and others. The calculation leaves out the part replacing constant capital. On this estimate surplus-labour stands to necessary labour as 3:1: exploitation is 300%. The attached note adds that Lavergne, a blind admirer of England, is likelier to have put the capitalist’s share too low than too high.
Formula II reinforced the school habit of treating the working day as a constant magnitude, because it always compares surplus-labour with a day of given size. The same is true when attention is confined to the division of the value-product: once the working day has been realized in a value-product, it necessarily appears as a day with fixed limits.
Representing surplus-value and labour-power’s value as fractions of the value-product — a form arising from capitalist production itself, whose significance is disclosed later — conceals the specific capital relation. It hides the exchange of variable capital for living labour-power and the corresponding exclusion of the worker from the product. In its place comes the false appearance of an association in which worker and capitalist divide the product according to the different factors entering its formation. The attached note shows how easily developed capitalist cooperation can be stripped of its antagonistic character and retold as free association: Laborde does so explicitly, and Carey can perform the same trick even for slavery.
Formula II can always be reconverted into Formula I. For example, take the proportion that follows.
There is a third formula, already anticipated on occasion.
The misunderstanding invited by the formula “unpaid labour / paid labour” — that the capitalist pays for labour rather than labour-power — is removed by the earlier argument. The formula is only a popular expression for “surplus-labour / necessary labour.”
The capitalist pays the value of labour-power, or its price where price diverges from value, and receives in exchange disposal over living labour-power itself. Its use divides into two periods. During one, the worker produces only a value equal to labour-power’s value: an equivalent. In return for the price advanced for labour-power, the capitalist receives a product of the same price, as if it had been bought ready-made on the market. During surplus-labour, however, use of labour-power forms value for the capitalist without costing a further value-equivalent. This expenditure of labour-power comes to him gratis. In this sense, surplus-labour may be called unpaid labour. The attached note recalls the Physiocrats’ recognition that surplus-value was a disposable wealth the possessor had not bought and yet sold.
Capital is therefore not only command over labour, as Adam Smith says. It is essentially command over unpaid labour. All surplus-value, whatever particular form it later crystallizes into — profit, interest, rent, and so on — is in substance materialized unpaid labour-time. The secret of capital’s self-valorization resolves into its disposal over a definite quantity of other people’s unpaid labour.