1) s' and C Constant, v variable.
In terms of the constraints Marx has established, this is impossible if considered as changes for a single capital. If wages etc. are constant then any change in “v” is a consequence of more or less labour-power being employed. But, with constant productivity, that would mean more or less material being processed by that labour etc., in the same direction. The only way that could be possible is if the value of C changed so that the changed physical amount of c employed, was automatically compensated by the change in value. Besides the fact that such a change is highly improbable, it also requires that productivity in the production of c changes to bring about that change in value, thereby breaking that condition.
Bearing that in mind, the following examples should be seen as solely illustrating the effects of changes in v as highlighting its role. As stated earlier, the easiest way of doing that is to consider these examples as comparisons between different capitals within the same economy, rather than changes within the same capital. Marx does this, in part, but also tries to relate it to the same capital or capital in the same industry. In doing so, to be honest, he gets himself into a terrible muddle. But, it should be remembered that these were only his working notes. It could be argued that Engels should really have sorted the muddle out before publishing, but he has given his reasons for not doing so.
Obviously, for C to remain constant whilst v changes, c must change by an equal and opposite amount. If we have C as a constant 100, then if v is 20, c must be 80. If v falls to 10, c must rise to 90.
If the rate of surplus value, s', remains constant, whilst v changes, then the amount of surplus value, s, must change in proportion to v, because s = s'v. The rate of surplus value multiplied by the variable capital.
Because the rate of surplus value, and the total capital, C, remain constant, we can formulate another equation:-
p1' = s' v'/C.
To put it another way, the original equation was p' = s' v/C, but s' and C are constant, so if v becomes v', then p' must change too, i.e. p1'.
We can then calculate the proportion of this new rate of profit to the previous rate of profit, brought about by changes in v. The proportions are:
p':p1' = s' v/C:s' v'/C = v:v'.
In other words, the new rate of profit changes, in relation to the old rate of profit, in the same proportion as the variable capital changes as a percentage of the total capital.
“If the original capital was, as above:
I. 15,000 C = 12,000c + 3,000v ( + 3,000s), and if it is now:
II. 15,000 C = 13,000c + 2,000v ( + 2,000s), then C = 15,000 and s' = 100% in either case, and the rate of profit of I, 20%, is to that of II, 13⅓%, as the variable capital of I, 3,000, is to that of II, 2,000, i. e., 20% : 13⅓% = 3,000 : 2,000.” (p 56)
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