Various Formula for the Rate of Surplus-Value

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

      
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%.¹

NOTE 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. 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

 Surplus-
labor        Surplus-value 
———————-  or  ———————-
  Working-day         Value created