The mass of surplus value may rise because the rate of surplus value rises, and yet the rate of profit may fall, because the constant capital rises, so that the total of c + v rises relative to s. In economies based on manufacturing, this is inevitable, because the largest part of c consists of the consumed material. If productivity rises, it is tautologically true that a given amount of labour (v + s) processes a greater quantity of material (c), so that c rises relative to (v + s). The rate of profit would fall unless s rises sufficiently relative to v, as a result of the rise in social productivity, to offset the rise in c. In other words, if we first have 100 units of labour processing 100 units of material, with a rate of surplus value of 100%, we might have in money terms:
c 100 + v 50 + s 50, s` = 100%, r` = 33.3%.
If social productivity rises, by 50%, so that the 100 units of labour now processes 150 units of material, but the value of wage goods falls by 50%, so that the rate of surplus value rises to 300%, we would have:
c 150 + v 25 + s 75, s` = 300%, r` = 42.86%
If the value of wage goods falls by a smaller amount, so that the rate of surplus value, does not rise so significantly, we might have, say
c 150 + v 40 + s 60, s` = 150%, r` = 31.58%.
However, as Marx sets out, in the next few chapters, this is also not the end of the matter, because, in the same way that the rise in social productivity cheapens wage goods, and so raises the rate of surplus, so too, it cheapens constant capital, and thereby acts to counteract the rise in the mass of it consumed, which raises the rate of profit. For example, if the price of the material falls by 20%, equal to the fall in the price of wage goods, the price of the 150 units consumed falls to 120, so we then have
c 120 + v 40 + s 60, s` = 150%, r` = 37.50%.
“Since the rate of profit is the ratio of surplus-value to the total amount of capital advanced, it is naturally affected and determined by the fall or rise of surplus-value, and hence, by the rise or fall of wages, but in addition to this, the rate of profit includes factors which are independent of it and not directly reducible to it.” (p 191)
Mill is placed in a predicament that Ricardo himself did not face. Ricardo's antagonists drew out the contradiction, in his theory, in relation to the rate of profit. Conscious of those criticisms, Mill was led, as just seen, to define the rate of profit correctly, in terms of the ratio to both constant and variable capital, and not, as Ricardo had done, only to the variable capital. But, having done so, this makes it impossible for Mill to rationally explain why it is only variations in the rate of surplus value which determine movements in the rate of profit, i.e. a fall in wages results in a rise in the rate of profit, and vice versa.
This, of course, may be the case, as Marx describes in Capital III, Chapter 6, and 15, where there is a profits squeeze, when wages raise and the rate of surplus value falls, and vice versa, but it is by no means the only reason for the rate of profit rising or falling. Indeed, the rate of surplus value may rise, as wages fall, and yet the rate of profit fall, and vice versa. This is the essence of Marx's critique of those previous theories of the falling rate of profit, and the foundation of his own explanation of that tendency.
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