Capital, Volume Three: The Process of Capitalist Production as a Whole by Karl Marx

Assuming a given wage and working-day, a variable capital, for instance of 100, represents a certain number of employed labourers. It is the index of this number. Suppose £100 are the wages of 100 labourers for, say, one week. If these labourers perform equal amounts of necessary and surplus-labour, if they work daily as many hours for themselves, i.e., for the reproduction of their wage, as they do for the capitalist, i.e., for the production of surplus-value, then the value of their total product = £200, and the surplus-value they produce would amount to £100. The rate of surplus-value, s/v, would = 100%. But, as we have seen, this rate of surplus-value would nonetheless express itself in very different rates of profit, depending on the different volumes of constant capital c and consequently of the total capital C, because the rate of profit = s/C. The rate of surplus-value is 100%: If c = 50, and v = 100, then p' = 100/150 = 66 2/3 %; c = 100, and v = 100, then p' = 100/200 = 50%; c = 200, and v = 100, then p' = 100/300 = 33 1/3 %; c = 300, and v = 100, then p' = 100/400 = 25%; c = 400, and v = 100, then p' = 100/500 = 20%.

This is how the same rate of surplus-value would express itself under the same degree of labour exploitation in a falling rate of profit, because the material growth of the constant capital implies also a growth – albeit not in the same proportion – in its value, and consequently in that of the total capital.