Marx then examines a further situation combining both a change in the technical and value composition of capital.
“Here one change may neutralise the other, for example, when the amount of constant capital grows while its value falls or remains the same (i.e., it falls pro tanto, per £100) or when its amount falls but its value rises in the same proportion or remains the same (i.e., it rises pro tanto). In this case there would be no change at all in the organic composition. The rate of profit would remain unchanged. But it can never happen—except in the case of agricultural capital—that the amount of the constant capital falls as compared with the variable capital, while its value rises.” (p 381)
If social productivity rises, so that a given amount of variable-capital processes twice as much cotton into yarn as previously, the technical composition of capital doubles, but if this same rise in social productivity causes the value of cotton to halve, the value of cotton processed would thereby remain the same, i.e. 100 kilos of cotton at £2 per kilo = £200, just as 200 kilos of cotton at £1 per kilo = £200. The organic composition of capital would remain the same provided the rate of surplus value remained constant, so that the value of v remains constant.
If the same rise in social productivity caused the value of labour-power to fall, the rate of surplus value would rise, the mass of surplus value would also thereby rise, causing the rate of profit to rise. If the rise in productivity caused the value of cotton to fall, to £0.75 per kilo, the value of processed cotton would fall to 200 x £0.75 = £150, so that c + v would fall, so that the rate of profit would rise. If the rise in productivity only causes the value of cotton to fall to £1.50 per kilo, the value of processed cotton would rise to 200 x £1.50 = £300, so the organic composition of capital would rise, and the rate of profit would fall.
Marx's comment that, “...it can never happen—except in the case of agricultural capital—that the amount of the constant capital falls as compared with the variable capital, while its value rises.” (p 381) is based on the assumption that productivity in industry constantly rises. In other words, as Marx says, elsewhere, capitalists never choose to introduce less efficient machines or techniques. If the level of productivity is constant, and a rise in cotton prices leads to less cotton being processed, less labour will be employed to process it. Marx exempts agricultural capital from this rule because of the effects of soil fertility, and the consequences of crop failures. So, for example, in a year where agricultural output, in the shape of seeds, is adversely affected by weather, the amount of constant capital, in the shape of seeds, remains constant, because they have already been planted, and that may also apply to manure etc. But, more labour may be required for irrigation, in a dry season, etc., so that the quantity of variable-capital rises relative to the quantity of constant capital. But, the poor harvest also raises the value of the constant capital (seeds) consumed, because as Marx sets out, in determining the value of the constant capital, for the purpose of calculating the rate of profit, it is not the historic cost of the seeds that were planted that is significant, but their current reproduction cost. The crop failure raises the current reproduction cost (value) of the planted seeds, consumed in this year's production. So, the quantity of constant capital consumed may fall, relative to the variable-capital required to process it, but the value of the constant capital itself may have risen.
“This type of nullification cannot possibly apply to variable capital (while the real wage remains unchanged).” (p 381)
In other words, if productivity rises, so that the value of labour-power falls, the rate of surplus value rises, if the real wage, i.e. the physical quantity of wage goods remains the same. Consequently, the rate of profit rises. If the value of labour-power falls, in this way, by half, but the variable-capital remains constant, because twice as many workers are employed (or workers are employed for twice as long) this will automatically cause the mass of surplus value to double, but it will rise by more than that, because of the rise in the rate of surplus-value. So, if we have 1,000 kilos of cotton, with a value of £1 per kilo, processed by 10 workers, paid £10 each, with a rate of surplus value of 100%,
c 1000 + v 100 + s 100, s' = 100%, r' = 9.99%.
If the value of labour-power halves, and twice as many workers are employed, they process twice as much cotton, so:
c 2000 + v 100 + s 300, s' = 300%, r' = 14.29%.
In other words, 10 workers produced 200 of new value divided 100 v and 100 s, so 20 workers produce 400 of new value, now divided 100 v and 300 s.
“Except for this one case, it is therefore only possible for the value and amount of the constant capital to fall or rise simultaneously in relation to the variable capital, its value therefore rises or falls absolutely as compared with the variable capital. This case has already been considered. Or they may fall or rise simultaneously but in unequal proportion. On the assumption made, this possibility always reduces itself to the case in which the value of the constant capital rises or falls relatively to the variable.
This also includes the other case. For if the amount of the constant capital rises, then the amount of the variable capital falls relatively, and vice versa. Similarly with the value.” (p 382)
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