So, technological development, which brings about a rise in productivity, cheapens wage goods, and, thereby, reduces the value of labour-power. Setting aside any other effects, this raises the rate of surplus value, and thereby increases the mass of surplus value, and rate of profit.
“Secondly, however, the rate of profit is determined by the ratio of variable capital to the total capital, by v/c+v. The total amount of surplus-value, where its rate is given, depends of course only on the size of the variable capital, which, on the assumption made, is determined by, or simply expresses, the number of working-days worked simultaneously, that is, the total amount of labour-time employed. But the rate of profit depends on the ratio of this absolute magnitude of surplus-value, which is determined by the variable capital, to the total capital, that is, on the ratio between variable capital and total capital, on v/c+v.” (p 232)
If the rate of surplus value is given, the mass of surplus value depends on the mass of labour employed, or “the number of working-days worked simultaneously.” (p 232). If the mass of labour is given, then any variation in v/(c+v) must be due to a change in c. Consequently, if s/v is constant and v is constant, the mass of surplus value remains constant, whilst the rate of profit, s/C, changes, as a result of changes in c. Because c comprises only a part of C, the rate of profit will, thereby, change with every change in C, but not by the same proportion as the change in c.
If the rate of surplus value is 20%, and v = £1,000, surplus value will be £200. If c is also £1,000, so that C (c + v) = £2,000, v/(c + v) = 50%. So, the rate of profit is 50% of 20% = 10%, i.e. 10% of £2,000 = £200. If c rises by 100%, it's clear that the rate of profit does not fall by an equivalent amount, because c comprises only part of C. So, if c rises to £2,000 it now comprises ⅔ of C, and v comprises ⅓. So, now, the rate of profit, represented by s is £200, and 33.3% of 20% = 6.66%. In other words, surplus value is 6.66% of £3,000.
“How the growth or decline in the constant capital affects the ratio v/c+v depends evidently on the proportion in which c and v originally constitute parts of the whole capital C (consisting of c+v).” (p 233)
But, this value of the constant capital can vary for different reasons. If productivity rises, a given mass of labour (v), will process a greater mass of material. So, whilst the unit value of this material remains the same (i.e. no change in the value composition of capital) or may even fall, the total value of c, relative to v may rise. So, if 100 workers process 1,000 kilos of yarn, costing £1 per kilo, a 20% rise in productivity will mean that the same labour now processes 1200 kilos. If wages are £1,000 the ratio of c:v rises from 1:1 to 1.2:1. Even if the price of yarn falls to £0.90 per kilo, c is still £1,080, so c:v still rises to 1.08:1. Here, c:v rises due to a rise in the technical composition of capital, even where the value composition falls.
But, c may rise because the value of yarn rises itself, i.e. a rise in the value composition of capital, even if the technical composition remains constant or falls. So, 100 workers may continue to process 1,000 kilos of yarn, but, if the price of yarn rises to £1.20 per kilo, c rises to £1200, and c:v rises to 1.2:1. This is a rise in the value composition of capital. Where Marx's law of the tendency for the rate of profit to fall is based upon rising productivity, this rise in the value composition is a result of a fall in productivity, which increases the value of commodities that comprise constant capital.
“In this case therefore, the variations in constant capital are not determined by the conditions of production prevailing in the industrial process into which it enters as constant capital, but are independent of them. Whatever the causes bringing about the change in value may be, they always influence the rate of profit. In this case, the same amount of raw material, machinery, etc., has more or less value than it did previously, because more or less labour-time was required to produce them. The variations, then, are determined by the conditions of production of the processes from which the component parts of constant capital emerge as products.” (p 233)
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