Productivity and The Rate of Profit
Suppose that the new value produced by current labour resolves into wages 5, and profit 5, i.e. a 100% rate of surplus value. In scenario (1), the rate of profit is 5/(10+5) = 33.3%, whereas in scenario (2) it is 5/(20+5) = 20%, and that is due to the fact that the rise in productivity means that in (1) constant capital (cotton) (congealed value preserved and transferred) accounts for 50% of the value of output, whereas in (2) it accounts for 66.6% of the value of output, and assuming that there is no equivalent rise in productivity in cotton production, this continued rise in productivity, must result in constant capital (raw materials/cotton) forming an ever larger proportion of the value of output, and revenues (wages and profit (v + s)) a continually declining proportion. In that case, this tendency could only be offset by s rising relative to v, i.e. by the rate of surplus value rising.
However, as Marx sets out in Theories of Surplus Value, Chapter 23, this also depends, as in this example, on there being no equivalent change in productivity in the cotton or fixed capital production. As Marx sets out, if productivity rises equally across all spheres, then this tendency for raw materials and wear and tear to rise as a proportion of output value, also does not occur, and so this tendency of the rate of profit to fall, also does not occur. In fact, as Marx sets out, improvements in technology, mean that productivity in fixed capital production, and greater durability of fixed capital, itself seen in a greater productivity of that fixed capital, i.e. much greater output per machine, and so less and less wear and tear per unit of output, causes fixed capital to also form an ever declining proportion of output value.
“If one worker can spin as much cotton as 100 [workers spun previously], then the supply of raw material must be increased a hundredfold, and this is moreover brought about only by the spinning-machine which enables one worker to control 100 spindles. But if simultaneously, one worker produces as much cotton as 100 workers did previously and one worker produces a spinning-machine whereas previously he produced only a spindle, then the ratio of value remains the same, that is, the labour expended in the spinning, [in the production of] the cotton and the spinning-machine remains the same as that expended previously in spinning, the cotton and the spindle.”
(Theories of Surplus Value, Chapter 23)
So, taking the scenarios above, we would have:
c 10 + v 5 + s 5 = 20 = 100 metres = 0.20 per metre, r` = 33.3%
c 10 = v 5 + s 5 = 20 = 200 metres = 0.10 per metre, r` = 33.3%
In fact, if this rise in productivity was uniform across the economy, then the rate of profit would rise, because, the rate of surplus value would rise, as a result of a rise in relative surplus value. The reproduction of labour-power is a function of the quantity of use values that the worker must consume, not the value of those wage goods. So, if the value of the wage goods that workers must consume is halved, as shown above, then, whilst the amount of new value created by the worker remains 10, the amount of necessary labour falls to 2.5, meaning that surplus labour rises to 7.5, causing the rate of surplus value to rise to 300%. So, now, we would have:
c 10 + v 2.5 + s 7.5 = 20 = 200 metres = 0.10 per metre, r` = 60%.
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