## Thursday, 30 April 2015

### Capital III, Chapter 3 - Part 2

There are a number of minor mathematical and methodological errors, in some of the examples Marx gives. I will use his examples and give the corrected version where appropriate. Later, however, the constraints at the beginning here make the examples untenable, if considered as changes in a single capital, and it all descends into a bit of a muddle that I will deal with when we come to it.

Marx starts with an example:

c 80 + v 20 + s 20; s' = 100%, p' = 20%.

He then assumes the working day is increased by 50% from 10 to 15 hours. The total new value created by the workers will then rise also by 50%, from 40 (20 v + 20 s) to 60, now made up v 20 + s 40. So,

c 80 + v 20 + s 40; s' = 200%, p' = 40%.

In fact, there is an error here, because if the quantity of labour-power employed rises by 50%, the amount of constant capital employed should have risen in proportion because they would process more material etc. It should actually be:-

c (80 + 40) + v 20 + s 40; s' = 200%, p' = 28.57%.

If the working day remains the same, but wages fall, we have, for example,

c 80 + v 12 + s 28; s' = 233.33%, p' = 30.43%

“Hence, we see that a prolonged working-day (or a corresponding increase in the intensity of labour) and a fall in wages both increase the amount, and thus the rate, of surplus-value. Conversely, a rise in wages, other things being equal, would lower the rate of surplus-value. Hence, if v rises through a rise in wages, it does not express a greater, but only a dearer quantity of labour, in which case s' and p' do not rise, but fall.” (p 52)

So, changes in wages or in the length or intensity of the working-day would result in changes in v and s, and consequently in the rate of surplus value and rate of profit. But, similarly, a change in the ratio of v to s implies a change in at least one of the three elements above.

“Precisely this reveals the specific organic relationship of variable capital to the movement of the total capital and to its self-expansion, and also its difference from constant capital. So far as generation of value is concerned, the constant capital is important only for the value it has. And it is immaterial to the generation of value whether a constant capital of £1,500 represents 1,500 tons of iron at, say, £1, or 500 tons of iron at £3. The quantity of actual material, in which the value of the constant capital is incorporated, is altogether irrelevant to the formation of value and the rate of profit, which varies inversely to this value no matter what the ratio of the increase or decrease of the value of constant capital to the mass of material use-value which it represents.” (p 52)

Its important not to misunderstand what Marx is saying here, because this seems to be completely at variance with his earlier comment,

“In itself, the magnitude of value of total capital has no inner relationship to the magnitude of surplus-value, at least not directly”,

and pointing out that it is the quantity not value of the constant capital that is relevant,

“Hence there is also to that extent a definite relation between the quantity of surplus-value, or surplus-labour, and the quantity of means of production.” (Chapter 2)

In Volume I, he made clear that, in terms of his conception of the expansion of capital, it is the relation between capital and wage labour that is decisive. The value of the constant capital is irrelevant here, because it only transfers its value to the end product. In this respect, what is then determinant is the quantity not the value of the constant capital, because the technical composition of capital determines how much labour is required to process a given amount of material and vice versa. But, in respect of the rate of profit, it is the value of the constant capital, not its quantity that is relevant, precisely because it is against this value that the surplus value is measured.

“It is different with variable capital. It is not the value it has, not the labour incorporated in it, that matter at this point, but this value as a mere index of the total labour that it sets in motion and which is not expressed in it — the total labour, whose difference from the labour expressed in that value, hence the paid labour, i.e., that portion of the total labour which produces surplus-value, is all the greater, the less labour is contained in that value itself.” (p 52)

In other words, the value the constant capital passes on is the value of the labour-time required to produce it. But, it is not the value of labour-power, the value of the labour-time required to produce it, that is passed on to the end product. Rather it is the new value created by that labour.

If we have a ten hour day, and the value of 10 hours = £10, then if the necessary labour, required to reproduce labour-power, equals 5 hours, which equals £5, and the surplus value £5, if necessary labour falls to 4 hours, variable capital falls to £4, and surplus value rises to £6, because the worker still works for 10 hours and produces 10 hours of new value.

“Hence, as soon as the value of the variable capital ceases to be an index of the quantity of labour set in motion by it, and, moreover, the measure of this index is altered, the rate of surplus-value will change in the opposite direction and inversely.” (p 53)