In short, Sismondi's argument fails to take account of the fact that rising productivity, whilst reducing v, not only results in rising s, but also rising c. In other words, less social labour-time is devoted to necessary labour, but more is devoted to surplus labour and the reproduction of means of production. He fails to take account of the fact that this rising productivity, in reducing the unit value of production enables consumption itself to rise, and this same reduction in unit values results in a release of capital – both constant and variable capital. This release of capital, alongside the release of labour, enables an increase in capital accumulation – as well as a rise in the rate of profit – both as an increased accumulation in existing spheres, and the development of whole new industries. As Marx writes in Capital III, Chapter 14.
“... new lines of production are opened up, especially for the production of luxuries, and it is these that take as their basis this relative over-population, often set free in other lines of production through the increase of their constant capital. These new lines start out predominantly with living labour, and by degrees pass through the same evolution as the other lines of production. In either case the variable capital makes up a considerable portion of the total capital and wages are below the average, so that both the rate and mass of surplus-value in these lines of production are unusually high.”
And, this also illustrates the error of those who misunderstand Marx's comments about the limits to the rise in the rate of surplus value offsetting the fall in the rate of profit. It assumes that the relative reduction in labour translates in an absolute reduction in labour, and so fall in surplus value. But, Marx makes clear that no such fall in the absolute mass of labour employed occurs, or, therefore, in the mass of surplus value produced. On the contrary, the opposite occurs. So, whilst its true that that 20 workers producing only 5 hours of surplus value produce more surplus value than 2 workers producing 20 hours of surplus value, 20 workers each producing 20 hours of surplus value produce more still!
The error, here, resides in viewing the limit on the rate of surplus value as being determined by the length of the individual concrete working-day. Its true that each individual concrete labour can only work 24 hours, per day, and, in fact at most, say, 18 hours, so that this sets a limit on the amount of surplus value it can produce, and so also the rate of surplus value. However, this does not apply to the collective worker, and so to the social working-day. There is no limit to the social working-day, because it is determined not only by the length of the individual working day, but also the number of workers simultaneously employed.
If there are 1 million workers each working a 10 hour day, the social working-day is 10 million hours. If half of these workers produce only the required wage goods then the necessary working day is 5 million hours, with 5 million hours of surplus labour, and a 100% rate of surplus value. But, if the workforce expands to 10 million, so that the social working-day rises to 100 million hours, whilst necessary labour rises to only 10 million hours, the surplus value rises to 90 million hours, and the rate of surplus value rises to 900%. In other words, here, capital has expanded, and along with it ten times as many workers are employed, producing ten times as much value. But, productivity has risen, the wage goods for these workers can now be produced by 1 million workers, working a 10 hour day.
As Marx puts it in Capital III, Chapter 15,
“Given the necessary means of production, i.e. , a sufficient accumulation of capital, the creation of surplus-value is only limited by the labouring population if the rate of surplus-value, i.e. , the intensity of exploitation, is given; and no other limit but the intensity of exploitation if the labouring population is given.”
This doesn't show that the rate of profit itself doesn't fall, because that would require an analysis of how much the value of c rises, as a result of this rise in productivity, and the technical composition of capital, but it does show that the rate of surplus value places no necessary limit on the degree to which the mass of surplus value can rise, and, thereby, counteract the fall in the rate of profit. In fact, as Marx demonstrates, further in Chapter 15, it is precisely the squeeze on the rate of profit from the expansion of employment, which constitutes a crisis of overproduction of capital. But, it is the measures to overcome that squeeze, via a technological revolution to introduce labour-saving equipment that leads to the rise in social productivity, and of the technical composition of capital, that creates the conditions for the long term tendency for a fall in the rate of profit.
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