3) s', v and C variable.
“This case offers no new aspects and is solved by the general formula given under II, in which s' is variable.” (p 67)
The following cases are set out.
1) p' increases or decreases in the same proportion as s' if v/C is constant.
2) p' rises or falls at a faster rate than s' if v/C moves in the same direction as s', that is, if it increases or decreases when s' increases or decreases.
3) p' rises or falls at a slower rate than s' if v/C changes inversely to s', but at a slower rate.
4) p' rises while s' falls, or falls while s' rises if v/C changes inversely to, and at, a faster rate than, s'.
5) The same rate of profit can arise where the rate of surplus value varies, provided the values of v and C change accordingly.
Marx writes,
“In the case of one and the same capital, or in that of two capitals in one and the same country this is possible but in exceptional cases.” (p 68)
He begins with:
c 80 + v 20 + s 20; C = 100, s' = 100%, p' = 20%.
He assumes the wages fall so the same labour-power is available for 16 v.
c 80 + v 16 + s 24; C = 96, s' = 150%, p' = 25%.
For the rate of profit to equal 20% as originally, c must rise to 104 so that:
c 104 + v 16 + s 24; C = 120, s' = 150%, p' = 20%
“This would only be possible if the fall in wages were attended simultaneously by a change in the productivity of labour which required such a change in the composition of capital. Or, if the value in money of the constant capital increased from 80 to 104. In short, it would require an accidental coincidence of conditions such as occurs in exceptional cases. In fact, a variation of s' that does not call for the simultaneous variation of v, and thus of v/C, is conceivable only under very definite conditions, namely in such branches of industry in which only fixed capital and labour are employed, while the materials of labour are supplied by Nature.” (p 68)
The various examples provided show that the rate of profit can vary in numerous ways as a result of different compositions of capital and different rates of surplus value. The formulations provided by Marx in this section are generally muddled. They can logically only be understood, in most cases, if they are taken as relating to different capitals operating within the same country.
For an analysis of changes to the same capital, it is necessary to drop the constraints over the constancy of C and v. A series of analyses for these cases could then have been undertaken, taking into consideration changes in productivity relating to the particular commodity, to labour as a whole etc, as well as the effects on wages, the value of constant capital and so on.
“The rates of profit of two different capitals, or of one and the same capital in two successive different conditions,
are equal
1) if the per cent composition of the capitals is the same and their rates of surplus-value are equal;
2) if their per cent composition is not the same, and the rates of surplus-value are unequal, provided the products of the rates of surplus-value by the percentages of the variable portions of capitals (s' by v) are the same, i.e., if the masses of surplus-value (s = s'v) calculated in per cent of the total capital are equal; in other words, if the factors s' and v are inversely proportional to one another in both cases.
They are unequal
1) if the per cent composition is equal and the rates of surplus-value are unequal, in which case they are related as the rates of surplus-value;
2) if the rates of surplus-value are the same and the per cent composition is unequal, in which case they are related as the variable portions of the capitals;
3) if the rates of surplus-value are unequal and the per cent composition not the same, in which case they are related as the products s'v, i.e., as the quantities of surplus-value calculated in per cent of the total capital.” (p 69)
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