For example,
“If v falls from 30 to 20 because ⅓ fewer labourers are employed with the growing constant capital, then we have before us the normal case of modern industry, namely, an increasing productivity of labour, and the operation of a larger quantity of means of production by fewer labourers.” (p 58)
But, of course, this too requires the condition of productivity remaining constant to be breached. In that case, with rising productivity, although the volume of material processed, and indeed the amount of equipment used to help process it rises, the value of that material, and those machines will have fallen. Indeed, as Marx points out, in Volume I, unless the machines are able to replace more paid labour than the labour-time required for their production, there is no reason for capital to introduce them. With the change in productivity implied here it would then be quite possible for the physical quantity of c to rise whilst the value fell.
Marx seems to have realised this was all a bit of a muddle, and, in dealing with a fall in wages, which to conform with a constant rate of surplus value requires a reduced working week, he concludes,
“It need hardly be said that this reduction of the working-time, in the case of a fall in wages, would not occur in practice. But that is immaterial. The rate of profit is a function of several variable magnitudes, and if we wish to know how these variables influence the rate of profit, we must analyse the individual effect of each in turn, regardless of whether such an isolated effect is economically practicable with one and the same capital.” (p 58)
The muddle could have been avoided simply by proceeding on the basis that these are two independent capitals operating at the same average level in different industries. Firm 1 could have been an agricultural producer, using more labour-power, and less constant capital, and firm 2 a flour mill using more constant capital and less labour-power.
Then, if the different scenarios facing a single firm were to be investigated, this could have been done separately. That would indeed have been interesting and fruitful, but would have required abandoning all the original constraints, and examining how varying rates of productivity, wages, length and intensity of day, etc. affected all of these proportions. That is, in fact, vital to an investigation of the rate of profit. Some of it is hinted at in the later chapter dealing with the falling rate of profit, but in far too little detail.
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