1) s' variable, v/C constant.
Because v/C is constant, it can be used interchangeably with v1/C1, i.e. they are the same. So, if we have p' = s' v/C and p1' = s1' v/C we can get rid of the v/C in both equations, so that p' is related to p1' in the same proportion as s' is to s1'. In other words, if the organic composition of the capital remains constant, the rate of profit changes in the same proportion as the rate of surplus value.
Once again, Marx draws a number of conclusions from this that I don think follow either logically or in practice. For example, he argues that it is only the relative not absolute values of v and C that count. Mathematically, that is absolutely true, if v is 100 and C 200, that comes down to 1/2, just the same as if v is 100,000 and C is 200,000. But, in practice, of course, we know from Volume I that these absolute differences do reflect very different conditions. So above, the 100 v could represent a simple cotton spinner, and the 200 C, that labour plus an equivalent amount of constant capital in the form of a single spindle, and a small amount of cotton. But, the 100,000 v could represent 10,000 spinners whose complex labour operates advanced machinery with thousands of spindles each spinning large amounts of cotton. The latter represents a far more developed stage of development in which the rate of surplus value would necessarily rise.
Marx says,
“... this applies to all capitals of equal composition whatever their absolute magnitude.
80c + 20v + 20s; C = 100, s' = 100%, p' = 20%
160c + 40v + 20s; C = 200, s' = 50%, p' = 10%
100% : 50% = 20% : 10%.” (p 64)
But, if we take capitals in different industries, with this same organic composition, but greatly different values of C, it is even more likely that this larger C will reflect a much more developed industry (or economy if we consider different countries) such that it may represent very productive advanced machinery and large quantities of materials with the labour-power employed also producing large amounts of relative surplus value.
If the actual values of v and C are the same then by definition the amount of surplus value itself will vary in proportion to the rate of surplus value. In that case, the rate of profit will also vary in the same proportion as the quantity of surplus value.
The formula showing that is.
P':p1' = s'v:s1'v = s:s1
Marx then says,
“It is now clear that with capitals of equal absolute or percentage composition the rate of surplus-value can differ only if either the wages, or the length of the working-day, or the intensity of labour, differ.” (p 64)
But, that is not true as indicated above. Even with capitals of the same absolute composition, one might have a few very productive machines, processing a lot of material, with a few highly paid, highly skilled workers, producing large amounts of relative surplus value, whilst another has a lot of less productive machines, processing a smaller amount of material, and employing a larger number of lower paid, unskilled workers, producing less relative surplus value. The nominal wages in the former will be higher than in the latter, and yet the rate of surplus value could still be higher. That is all the more the case if their additional productivity means that this labour appears as complex in the way Marx describes in Volume I. Where it is only the relative composition of the capital that is the same this is even more possible to occur.
That is not to say that the examples Marx then proceeds to give are wrong, only that they are not exhaustive or necessarily an accurate representation of how such different capital compositions affect the rate of profit in practice.
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