“The total surplus-value too would have risen, namely from 20 to 30, by 1/3. When I appropriate one-half of 60 days, this is one-third more than when I appropriate one-sixth of 120 days.” (p 216)
There is again a minor error here, as 30 is 50% more than 20, not a third larger, as Marx states. Of course, this depends upon the conditions described above. For any one industry, this rise in productivity would simply reduce the value of the output, so that a greater quantity of it would have to be sold to replace the workers wages. Marx assumes that only the same quantity of output need be produced to reproduce the labour, without taking into consideration the inevitable fall in the value of the output.
He is right that,
“Moreover, the one-half of the total product that the capitalist gets is also greater in quantity than before. For 6 hours now produce as much product as 10 did before; 1 [hour] as much as ten-sixths of an hour [before], or 1 as much as 1 4/6=1 2/3, So the 30 surplus hours contain as much product as did previously 30 (1+2/3) = 30 + 60/3 = 50. 6 hours produce as much product as 10 did previously, that is, 30—or 5×6—produce as much as 5×10 did before.” (p 216)
provided we assume that this rise in productivity causes a proportional drop in the value of labour-power. But, if the rise in productivity is restricted to this one industry, with no effect on the value of labour-power, although the capitalist will obtain a larger surplus product, this will not translate into greater surplus value.
The fall in value of the commodity will simply mean that a greater quantity of output will have to be sold to reproduce the value of wages and surplus value.
“The surplus-value can even rise without the quantity of the total product being increased.” (p 216)
I've shown above that this can be the case for any individual industry anyway, but Marx has in mind the situation in respect of production as a whole. The basis of this rise in surplus value is an increase in relative surplus value. So, a rise in productivity in the production of wage goods means that the physical products required to reproduce the workers labour-power can be produced in less time, so the amount of surplus labour-time rises.
But, its hard to see under what conditions this would occur without the total product rising in quantity. Suppose 1000 commodity units are required to reproduce labour-power, and these are currently produced in 5 hours of a working day, with another 1000 surplus units being produced in the other 5 hours of the working day. If productivity rises by 20%, the 1000 units required for workers consumption will be produced in 4 hours, equal to 250 units per hour. But, with a 10 hour day, that means that 2500 units will be produced – an increase of 25%. Total output would only remain constant at 2000 units, if the number of workers employed fell.
But, in that case, the actual amount required as variable capital would fall further because less physical product would also be required to reproduce the employed labour-power. If previously 100 workers were employed, now only 75 will be required. Previously, each worker consumed 10 units, making 1000 units in total, and now only 750 units are required to meet the workers needs.
If 100 workers produce 250 units per hour, 75 workers produce 187.5 units per hour. The 750 units they require being produced in 4 hours, and a further 1250 surplus units being produced in the remaining 6 hours of the day. But, there are various reasons why this does not usually happen. Firstly, businesses usually are interested in increasing output, not simply producing the same output with fewer workers. It is expansion of output that facilitates other economies of scale, as well as being the means by which firms grab larger market share.
They usually introduce new, more efficient equipment as additional investment in fixed capital alongside existing equipment, not in place of it. To the extent it replaces existing equipment, during periods of intensive accumulation, it often replaces worn out equipment, so that one old machine is replaced by a new machine that is more productive. During periods of extensive accumulation, although the new equipment is relatively labour replacing, i.e. a new machine does the work of two older machines, and 2 workers, it is absolutely labour adding, because as an additional machine it still requires an additional worker. It is only as older machines wear out, and are replaced by new machines that they actually replace labour, but the extent of this will depend upon the ratio of machine replacement to machine accumulation, i.e. whether it is a period of intensive or extensive accumulation.
If a firm replaces 1 machine per year, but also accumulates 1 machine per year, and each new machine is twice as productive as the machines being replaced, there may be no reduction in employment, whilst the level of output will continually rise.
Marx explains this in Capital I.
It is only where firms are at a more mature stage of the product cycle, where a large portion of the demand for the product is satisfied, the price elasticity of demand is high, and where supply is more or less just replacing existing consumption, rather than expanding markets, that any technological innovations result in an absolute reduction in employment.
But, also for these same reasons of only potential for a slow growth of demand – usually accompanied by tight profit margins – capital accumulation in these industries tends to be slow, the need to expand the workforce is reduced, and so the need to introduce labour-saving technology is reduced, leading to investment in innovation being concentrated in areas where labour shortages do exist.
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