Capital Volume 1
by Karl Marx

Chapter 18

Various Formulae for the Rate of Surplus-Value

    We have seen that the rate of surplus-value is represented by
the following formulae. 

I. (s/v) = (surplus value)/Variable Capital) = (Surplus
value)/(value of labour power) = (Surplus labour)/(Necessary
Labour)

The 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. These formulae,
supplementary the one to the other, are rigorously definite and
correct. We therefore find them substantially, but not
consciously, worked out in classical political economy. There we
meet with the following derivative formulae.

II. (Surplus labour)/(Working day) = (Surplus Value)/(Value of
the product) = (Surplus product)/(Total Product)

One and the same ratio is here expressed as a ratio of
labour-times, of the values in which those labour-times are
embodied, and of the products in which those values exist. It is
of course understood that, by "Value of the Product," is meant
only the value newly created in a working-day, the constant part
of the value of the product being excluded. 
    In all of these formulae (II), the actual degree of
exploitation of labour, or the rate of surplus-value, is falsely
expressed. Let the working-day be 12 hours. Then, making the same
assumptions as in former instances, the real degree of
exploitation of labor will be represented in the following
proportions.

(6 hours surplus labour)/(6 hours necessary labour) = (Surplus
value of 2 sh.)/(Variable capital of 3 sh.) = 100%

    From formula II we get very differently,

(6 hours surplus labour)/(Working day of 12 hours) = (Surplus
value of 3 sh.)/(value created of 6 sh.) = 50%.

    These derivative formulae express, in reality, on 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%.(1*) 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. The ratio (surplus labour)/(working day)
or (surplus value)/(value created) can therefore never reach the
limit of 100/100, still less rise to (100 + x)/100. But not so
the rate of surplus-value, the real degree of exploitation of
labour. Take, e.g., the estimate of L. de Lavergue, according to
which the English agricultural labourer gets only 1/4, the
capitalist (farmer) on the other hand 3/4 of the product (2*) or
of its value, apart from the question of how the booty is
subsequently divided between the capitalist, the landlord and
others. According to this, the surplus-labour of the English
agricultural labourer is to his necessary labour as 3:1, which
gives a rate of exploitation of 300%. 
    The favourite method of treating the working-day as constant
in magnitude became, through the use of the formula 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 characterise 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.(3*)
    Moreover, the formula II can at any time be reconverted into
formula I. If, for instance, we have (surplus labour of 6
hours)/(Working day of 12 hours) the necessary labour-time being
12 hours less the surplus-labour of 6 hours, we get the following
result,

(surplus labour of 6 hours)/(necessary labour of 6 hours) =
100/100

    There is a third formula which I have occasionally already
anticipated; it is

III. (Surplus value)/(Value of labour power) = (Surplus
labour)/(necessary labour) = (unpaid labour)/(paid labour)

    After the investigations we have given above, it is no longer
possible to be misled, by the formula (Unpaid labour)/(paid
labour), into concluding, that the capitalist pays for labour and
not for labour-power. This formula is only a popular expression
for (surplus labour)/(necessary labour). The capitalist pays the
value, so far as price co-incides 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.(4*) 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. 


NOTES:

1. Thus, e.g., in "Dritter Brief an v. Kirchmann von Rodbertus.
Widerlegung der Ricardo'schen Theorie von der Grundrente und
Begrundung einer neuen Rententheorie. Berlin, 1851." I shall
return to this letter later on; in spite of its erroneous theory
of rent, it sees through the nature of capitalist production. 
    Note by the Editor of the 3rd Edition. It may be seen from
this how favourably Marx judged his predecessors, whenever he
found in them real progress, or new and sound ideas. The
subsequent publication of Rodbertus' letters to Rud. Meyer has
shown that the above acknowledgment by Marx wants restricting to
some extent. In those letters this passage occurs: "Capital must
be rescued not only from labour, but from itself, and that will
be best effected, by treating the acts of the industrial
capitalist as economical and political functions, that have been
delegated to him with his capital, and by treating his profit as
a form of salary, because we still know no other social
organisation. But salaries may be regulated, and may also be
reduced if they take too much from wages. The irruption of Marx
into Society, as I may call his book, must be warded off...
Altogether, Marx's book is not so much an investigation into
capital, as a polemic against the present form of capital, a form
which he confounds with the concept itself of capital." (Briefe,
&c., von Dr Rodbertus-Jagetzow, herausgg. von Dr Rud. Meyer,
Berlin, 1881, I. Bd. p. 111., 48. Brief von Rodbertus.). To such
ideological commonplaces did the bold attack by Rodbertus in his
"social letters" finally dwindle down. 

2. That part of the product which merely replaces the constant
capital advanced, is of course left out in this calculation. Mr.
L. de Lavergne, a blind admirer of England, is inclined to
estimate the share of the capitalist too low, rather than too
high.

3. All well-developed forms of capitalist production being forms
of co-operation, nothing is, of course, easier, than to make
abstraction from their antagonistic character, and to transform
them by a word into some form of free association, as is done by
A. de Laborde in "De l'Esprit de l'Association dans tous les
interets de la communaute." Paris 1818. H. Carey, the Yankee,
occasionally performs this conjuring trick with like success,
even with the relations resulting from slavery.

4. Although the Physiocrats could not penetrate the mystery of
surplus-value, yet this much was clear to them, viz., that it is
"une richesse independante et disponible qu'il (the possessor)
n'a point achetee et qu'il vend." (Turgot: "Reflexions sur la
Formation et la Distribution des Richesses," p. 11)