C A P I T A L, vol. I
PART V -- THE PRODUCTION OF ABSOLUTE AND
OF RELATIVE SURPLUS-VALUE
Capital, Part Five
VARIOUS FORMULAE FOR THE RATE
We have seen that the rate of surplus-value is represented by the
Surplus-value (s) Surplus-value Surplus-labor
I. -------------------- == -------------------- == ---------------
Variable Capital (v) Value of labor-power Necessary labor
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.
Surplus-labor Surplus-value Surplus-product
II. --------------- == -------------------- == -----------------
Working-day Value of the Product Total Product
One and the same ratio is here expressed as a ratio of labor-times, of
the values in which those labor-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
labor, 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-labor Surplus-value of 3 sh.
----------------------- == --------------------------- == 100%.
6 hours necessary labor Variable Capital of 3 sh.
From formulae II. we get very differently,
6 hours surplus-labor Surplus-value of 3 sh.
----------------------- == --------------------------- == 50%.
Working-day of 12 hours Value created of 6 sh.
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 laborer. 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-labor or surplus-value can never reach 100%.
Since the surplus-labor is only an aliquot part of the working-day, or
since surplus-value is only an aliquot part of the value created, the
surplus-labor 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-labor may absorb the whole day (i.e., an average dy of
any week or year), the necessary labor must sink to zero. But if the
necessary labor vanish, so too does the surplus-labor, since it is only
a function of the former. The ratio
--------------- or ---------------
Working-day Value created
can therefore never reach the limit 100/100, still less rise to
100+x/100. But not so the rate of surplus-value, the real degree of
exploitation of labor. Take, e.g., the estimate of L. de Lavergne,
according to which the English agricultural laborer gets only 1/4, the
capitalist (farmer) on the other hand 3/4 of the product  or its
value, apart from the question of how the booty is subsequently divided
between the capitalist, the landlord, and others. According to this,
this surplus-labor of the English agricultural laborer is to his
necessary labor as 3:1, which gives a rate of exploitation of 300%.
The favorite method of treating the working-day as constant in magnitude
became, through the use of formulae II., a fixed usage, because in them
surplus-labor is always compared with a working-day of given length.
The same holds good when the repartition of the value produced is
exclusively kept insight. The working-day that has already been
realized in given value, must necessarily be a day of given length.
The habit of representing surplus-value and value of labor-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 characterizes capital,
namely the exchange of variable capital for living labor-power, and the
consequent exclusion of the laborer from the product. Instead of the real
fact, we have false semblance of an association, in which laborer and
capitalist divide the product in proportion to the different elements
which they respectively contribute towards its formation.
Moreover, the formulae II. can at any time be reconverted into formulae
I. If, for instance, we have
Surplus-labor of 6 hours
Working-day of 12 hours
then the necessary labor-time being 12 hours less the surplus-labor of 6
hours, we get the following result,
Surplus-labor of 6 hours 100
---------------------------- == ---.
Necessary labor of 6 hours 100
There is a third formula which I have occassionally already anticipated;
Surplus-value Surplus-labor Unpaid labor
III. -------------------- == ----------------- == --------------.
Value of labor-power Necessary labor Paid labor
After the investigations we have given above, it is no longer possible to
be misled, by the formula
into concluding, that the capitalist pays for labor and not for
labor-power. This formula is only a popular expression for
The capitalist pays the value, so far as price coincides with value, of
the labor-power, and receives in exchange the disposal of the living
labor-power itself. His usufruct is spread over two periods. During
one the laborer produces a value that is only equal to the value of his
labor-power; he produces its equivalent. This the capitalist receives
in return for his advance of the price of the labor-power, a product
ready made in the market. During the other period, the period of
surplus-labor, the usufruct of the labor-power creates a value for the
capitalist, that costs him no equivalent. This expenditure of
labor-power comes to him gratis. In this sense it is that surplus-labor
can be called unpaid labor.
Capital, therefore, it not only, as Adam Smith says, the command over
labor. It is essentially the command over unpaid labor. All
surplus-value, whatever particular form (profit, interest, or rent), it
may subsequently crystallize into, is in substance the materialization
of unpaid labor. The secret of the self-expansion of capital resolves
itself into having the disposal of a definite quantity of other people's
 Thus, e.g., in "Dritter Brief an v. Kirchmann von Rodbertus.
Widerlegung der Ricardo'schen Lehre 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.
[added in the 3rd German edition]
It may be seen from this how favorably Marx judged his predecessors,
whenever he found in them real progress, or new and sound ideas.
The subsequent publications of Robertus' letters to Rud. Meyer has
shown that the above acknowledgement by Marx wants restricting to
some extent. In those letters this passage occurs:
"Capital must be rescued not only from labor, but from itself,
and that will be best effected, by treating the acts of the
industrial capitalist as economic 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 organization. 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. Robertus-Jagetzow, herausgg. von Dr. Rud.
Meyer", Berlin, 1881, I, Bd. P.111, 46. Breif von Rodbertus.) To
such ideological commonplaces did the bold attack by Robertus in
his "social letters" finally dwindle down. -- F.E.
 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.
 All well-developed forms of capitalist production being forms of
cooperation, 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'Espirit d'Association dans tout les interets de la
communaute". Paris 1818. H. Carey, the Yankee, occassionally
performs this conjuring trick with like success, even with the
relations resulting from slavery.
 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.)
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