The value of the product is £1,000, hence 500s/500v = 100%. Just the same as with capital A. The fact that, in the case of capital A, the surplus-value is realised together with the advanced capital, while in the case of B it is not, does not concern us here, where it is only a question of the production of surplus-value and of its ratio to the variable capital advanced during its production. But if on the contrary we calculate the ration of surplus-value in B, not to that portion of the advanced capital of £5,000 which has been employed and hence consumed during its production, but to this total advanced capital itself, we find that it is 500s/5,500v of 1/10, or 10%. Hence it is 10% for capital B and 100% for capital A, i.e., ten-fold. If it were said: this difference in the rate of surplus-value for equal capitals, which have set in motion equal quantities of labour equally divided at that into paid and unpaid labour, is contrary to the laws of the production of surplus-value, the answer would be simple and prompted by a mere glance at the actual relations: In the case of A, the actual rate of surplus-value is expressed, i.e., the relation of a surplus-value produced in 5 weeks by a variable capital of £500, to the variable capital of £500. In the case of B on the other hand the calculation is of a kind which has nothing to do either with the production of surplus-value or with the determination of its corresponding rate of surplus-value. For the £500 of surplus-value produced by a variable capital of £500of variable capital advanced during their production, but with reference to a capital of £5,000, nine-tenths of which, or £4,500, have nothing whatever to do with the production of this surplus-value of £500, but are on the contrary intended to function gradually in the course of the following 45 weeks, so that they do not exist at all so far as the production of the first 5 weeks is concerned, which alone is at issue in this instance. Hence in this case the difference in the rates of surplus-value of A and B presents no problem at all.
Let us now compare the annual rates of surplus-value for capitals B and A. For capital B it is 500s/500v = 100%; for capital A it is 5,000s/500v = 1,000%. But the ratio of the rates of surplus-value is the same as before.
There we had Rate of Surplus-Value of Capital B10% ---------------------------------- ---- Rate of Surplus-Value of Capital A = 100%Now we have Annual Rate of Surplus-Value of Capital B100% ----------------------------------------- ------ Annual Rate of Surplus-Value of Capital A = 1,000%But 10% : 100% = 100% : 1,000%, so that the proportion is the same.
But now the problem has changed. The annual rate of capital B, 5,000s/5,500v = 100%, offers not the slightest deviation -- not even the semblance of a deviation -- from the laws of production known to us and of the rate of surplus-value corresponding to this production. During the year 5,000v have been advanced and productively consumed, and they have produced 5,000s. The rate of surplus-value therefore equals the above fraction, 5,000s/5,500v = 100%. The annual rate agrees with the actual rate of surplus-value.
In this case it is therefore not capital B but capital A which presents the anomaly that has to be explained.
We have here the rate of surplus-value 5,000s/500v = 1,000%. But while in the first case 500s, the product of 5 weeks, was calculated for an advanced capital of £5,000, nine-tenths of which were not employed by its production, we have now 5,000s calculated for 500v, i.e., for only one-tenth of the variable capital actually employed in the production of 5,000s; for the 5,000s are the product of a variable capital of £5,000productively consumed during 50 weeks, not that of a capital of £500consumed in one single period of 5 weeks. In the first case the surplus-value produced in 5 weeks had been calculated for a capital advanced for 50 weeks, a capital ten times as large as the one consumed during the 5 weeks. Now the surplus-value produced in 50 weeks is calculated for a capital advanced for 5 weeks, a capital ten times smaller than the one consumed in 50 weeks.
Capital A, of £500, is never advanced for more than 5 weeks.
At the end of this time it returns and can renew the same process in the course of the year ten times, as it makes ten turnovers. Two conclusions follow from this:
Firstly : The capital advanced in the case of A is only five times larger than that portion of capital which is constantly employed in the productive process of one week. On the other hand capital B which is turned over only once in 50 weeks and must therefore be advanced for 50 weeks, is fifty times larger than that one of its portions which can constantly be employed for one week. The turnover therefore modifies the relation between the capital advanced during the year for the process of production and the capital constantly employable for a definite period of production, say, a week. Here we have, then the first case, in which the surplus-value of 5 weeks is not calculated for the capital employed during these 5 weeks, but for a capital ten times larger, employed for 50 weeks.
Secondly : The 5-week period of turnover of capital A comprises only one-tenth of the year, so that one year contains ten such turnover periods, in which capital A of £500 is successively re-invested.