Marx describes the limits on the increase in the mass of profit in a similar way to that set out in Capital III.
“It is physically impossible that the surplus labour-time of, say, two men who displace twenty, can, by any conceivable increase of the absolute or relative [surplus] labour-time, equal that of the twenty. If each of the twenty men only work 2 hours of surplus labour a day, the total will be 40 hours of surplus labour, whereas the total life span of the two men amounts only to 48 hours in one day.” (p 300)
But, herein lies the logical fallacy referred to earlier. This assumes that the relevant working-day is that of the individual worker rather than the social working-day, and that the rise in social productivity is manifest not just in relatively less labour employed, but absolutely less labour, i.e. 2 workers rather than 20.
If £10,000 of capital employs 10 workers working a 12 hour day of which 10 hours is necessary labour (£1,000), and 2 hours surplus labour (£200) the rate of surplus value is 20%, and rate of profit 2%. But, if we take this to relate to the whole economy what we have is a social working-day of 10 x 12 hours = 120 hours, necessary labour of 10 x 10 hours = 100 hours, and surplus labour of 10 x 2 hours = 20 hours.
As Marx points out, the law of the tendency for the rate of profit to fall is predicated on rising social productivity, a rising rate of surplus value, and a rising mass of capital employed, rising mass of labour employed, and rising mass of profit. So, if now the working day remains constant, at 12 hours, but an increased social capital of £20,000 employs 18 workers, the actual social working day rises from 10 x 12 hours – 120 hours, to 18 x 12 hours = 216 hours. But, viewed in terms of the social capital, and social working day, its quite clear that the same rise in social productivity that leads to relatively less labour being employed, also leads to less necessary labour. Suppose previously, of the workforce of 10, 8.33 workers worked solely producing wage goods = 8.33 x 12 = 100 hours. But, as a result of the rise in productivity, the wage goods required for the 18 workers can be produced in 156 hours. In other words it requires 13 workers, each working a 12 hour day. So, now the 18 workers have produced a new value of 216 hours, and the necessary labour is 156 hours, leaving 60 hours of surplus labour.
In money terms, £20,000 of capital now employs 18 workers, 13 of whom are engaged wholly in necessary labour, producing the wage goods for all 18. That amounts to £1,560 for wages, and £600 profit. The rate of surplus value rises from 20% to 38.46%, and the rate of profit rises from 2% to 3%. There is no theoretical reason why, as capital accumulates, the absolute mass of labour should not continue to rise, and along with it, the mass of new value produced. Indeed, Marx insists this must be the case. That is just another way of saying that the social working-day continues to increase, and its upper bound is only set by the normal working-day, and the mass of employed, and employable labour. And, that is exactly what Marx says, and it forms a central aspect of his theory of overproduction of capital.
"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. And the capitalist process of production consists essentially of the production of surplus-value, represented in the surplus-product or that aliquot portion of the produced commodities materialising unpaid labour."
(Capital III, Chapter 15)
Moreover, whilst there is no upper limit to the social working-day, theoretically, the only lower limit to the necessary working-day is zero. Rising social productivity means that fewer workers are required to produce the mass of wage goods, so that both the rate of surplus value and mass of profit can continue to rise.
Suppose, for example we assume that £100,000 of capital now employs 50 workers. At the original technical composition it would have employed 100. The social working-day is then 50 x 12 = 600 hours = £6,000 of new value. If the wage goods for these 50 workers can now be produced by 20 workers, working a 12 hour day = 240 hours necessary labour = £2,400, then the surplus social working day is 360 hours = £3,600, and the rate of profit rises to 3.6%.
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