The ratios
of turned over capital to advanced capital can be manipulated in a
number of ways. So, for example, the turned over capital can be
divided by advanced capital to give number of turnovers. The
advanced capital multiplied by number of turnovers to give turned
over capital, or turned over capital multiplied by the turnover time
as a fraction of a year, e.g. 1/10, to give the advanced capital.

In the
example, the quantity of paid and unpaid labour (necessary and
surplus labour) turned over during the year, is the same for both A
and B. Because the turnover period for A is five weeks, and £100
per week is employed, A has to have a ratio of 5:1, of its advanced
capital to employed capital, whilst B a ratio of 50:1.

Marx here
makes a distinction. The rate of surplus value distinguished has
been the annual rate of surplus value. But, if we calculate the rate
of surplus value on the basis of the surplus value produced, divided
by the labour-power employed to produce it, we get a different
figure. In other words, the annual rate of surplus value for A is
£5,000 surplus value divided by £500 advanced capital. But, what
Marx calls the

*“real rate of surplus value”*is £5,000 of surplus value divided by £5,000 of labour-power employed to produce it.**NB.**This can be confusing, because in

*Volume III*, when looking at the calculation of the

*Rate of Profit*on a similar basis, Marx demonstrates that it is on this latter basis that capitalists calculate the rate of profit, and that this actually understates the actual rate of profit massively for the reasons set out above. It is actually the method of calculating the

*“annual rate”*above, that provides the basis of calculating a

*“real”*rate of profit.

*“It follows rather from what has been set forth above that the annual rate of surplus-value coincides only in one single case with the real rate of surplus-value which expresses the degree of exploitation of labour; namely in the case when the advanced capital is turned over only once a year and the capital advanced is thus equal to the capital turned over in the course of the year, when therefore the ratio of the quantity of the surplus-value produced during the year to the capital employed during the year in this production coincides and is identical with the ratio of the quantity of surplus-value produced during the year to the capital advanced during the year.” (p 308)*

The annual rate of surplus value is S/v, where S is the total surplus value produced in a year, and v is the advanced variable capital. The real rate of surplus value is S/V, where V is the variable capital employed. V is equal to v x n, where n is the number of times the variable capital is turned over.

So, the annual rate of surplus value can also be written as (S/V x v x n)/v.

So, if the variable capital is £5,000 as above, and turns over just once in a year, and the real rate of surplus value = 100%, then,

100 x £5,000 x 1/£5,000 = 100%.

Only in this case, when the advanced variable capital is turned over once a year, will the annual and real rate of surplus value be the same.

If
we call the annual rate of surplus value S

^{1}and the real rate of surplus value s^{1}then we have,
S

^{1}= s^{1}vn/v = s^{1}n
So,
S

^{1 }can only equal s^{1}where n = 1.
In
addition, n is the same as the inverted time of turnover. If the
turnover time is a tenth of a year, the number of turnovers, n, is
ten, i.e. 1/10 inverted is 10/1. So, when n is greater than 1, S

^{1 }is greater than s^{1}, and when n is less than 1, i.e. when the turnover time is greater than a year, S^{1}is less than s^{1}.
Suppose in the previous example, the turnover time is 55 weeks, rather than 50 weeks. The advanced capital, v, is now £5,500 (i.e. enough to cover 55 weeks x £100). However, in a period of 50 weeks, this advanced capital has turned over only 50/55 = 10/11 times. Then,

S

^{1}= (100% x £5,500 x 10/11)/£5,500 = 100% x 10/11 = 1000/11 = 90 10/11%.
Marx
gets another bit of this calculation wrong. He says,

*“Indeed, if the annual rate of surplus-value were 100%, then during the year 5,500 v would produce 5,500 s, whereas 10/11 years are required for that.” (p 309)*

In fact, that should read

*“whereas 11/10 years are required for that.”*In other words, 55 weeks rather than 50 weeks are required. In 50 weeks, the advanced capital, v, of £5,500 only produce £5,000 surplus value, so 5000/5500 = 10/11 = 90 10/11%.
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