1) 100 c + 20 v + 10 s; C = 120, s' = 50%, p' = 8.33%
2) 90 c + 30 v + 15 s; C = 120, s' = 50%, p' = 12.5%
If wages and the rate of surplus value are unchanged, then the length and intensity of the working-day must be unchanged, so the increase in v from 20 to 30, means 50% more labour-power is being employed. But, as stated earlier, is this increase compatible with the decrease in the value of constant capital employed? If it was a change for the same capital, then, given the other constraints Marx has imposed, no. But, if we consider these as two separate capitals, that problem disappears. We are then just looking at a comparative example, showing the specific role of a change in v.
“But at the same time, with the increase in the number of labourers, the constant capital, the value of the means of production, has fallen from 100 to 90. We have, then, a case of decreasing productivity of labour combined with a simultaneous shrinkage of constant capital. Is such a case economically possible?
In agriculture and the extractive industries, in which a decrease in labour productivity and, therefore, an increase in the number of employed labourers is quite comprehensible, this process is on the basis and within the scope of capitalist production attended by an increase, instead of a decrease, of constant capital. Even if the above fall of c were due merely to a fall in prices, an individual capital would be able to accomplish the transition from I to II only under very exceptional circumstances. But in the case of two independent capitals invested in different countries, or in different branches of agriculture or extractive industry, it would be nothing out of the ordinary if in one of the cases more labourers (and therefore more variable capital) were employed and worked with less valuable or scantier means of production than in the other case.” (p 57)
That can be the case, for example, in comparing a more developed country, that uses more machines and fewer workers, to process a large amount of material, as opposed to a less developed economy that employs a lot of workers and less machines, to process a smaller amount of material. But, again, this breaches Marx's original constraint that all production takes place under the same average conditions of productivity.
Instead, then, Marx breaks one of the other constraints, to consider the situation where v changes as a result of a change in wages. So, here, wages would have risen by 50%. Of course, to be pedantic, this also implies a change in productivity, because it implies a change in the value of labour-power. Setting that aside, if these say 20 workers work with a reduced amount of means of production, which again implies a reduction in productivity, then the new value created remains 30, but as wages now also equal 30, there is no surplus value.
Marx says,
“We have assumed, however, that the rate of surplus-value should remain constant, that is, the same as in I, at 50%. This is possible only if the working-day is prolonged by one-half to 15 hours. Then the 20 labourers would produce a total value of 45 in 15 hours, and all conditions would be satisfied:” (p 57)
But, of course, they would not, and he's in a bit of a muddle again, because, if the working day is prolonged by 50%, that would require the workers to have 50% more material to process again etc., which means the constant capital would have to rise not fall, so the total capital could not remain constant.
Marx goes on,
“In this case, the 20 labourers do not require any more means of labour, tools, machines, etc., than in case I. Only the raw materials or auxiliary materials would have to be increased by one-half. In the event of a fall in the prices of these materials, the transition from I to II might be more possible economically, even for an individual capital in keeping with our assumption. And the capitalist would be somewhat compensated by increased profits for any loss incurred through the depreciation of his constant capital.” (p 57-8)
This is a fudge, and a poor one. True, no more tools etc. may be required, but the wear and tear must rise, so c rises as a result. The fall in prices of materials requires a change in productivity, which breaches another of the original constraints.
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