Marx summarises Mill's argument.
““Though […] tools, materials, and buildings […] are themselves the produce of labour […] yet the whole of their value is not resolvable into the wages of the labourers by whom they were produced.” [He says above that the replacement of capital is the replacement of wages.] The profits which the capitalists make on these wages, need to be added. The last capitalist has to replace from his product “not only the wages paid both by himself and by the tool-maker, but also the profit of the tool-maker, advanced by him himself out of his own capital” (op. cit., p. 98). Hence “… profits do not compose merely the surplus after replacing the outlay; they also enter into the outlay itself. Capital is expended partly in paying or reimbursing wages, and partly in paying the profits of other capitalists, whose concurrence was necessary in order to bring together the means of production” (loc. cit., pp. 98-99). “An article, therefore, may be the produce of the same quantity of labour as before, and yet, if any portion of the profits which the last producer has to make good to previous producers can be economised, the cost of production of the article is diminished… It is, therefore, strictly true, that the rate of profit varies inversely as the cost of production of wages” (op. cit., pp. 102-03).” (p 192)
The fallacy in Mill's argument comes down to this; in arriving at the value of the commodity, he fails to take into account, when determining the value of all of the commodities that form components of it, the value of c contained in them. So, although he correctly argues that the rate of profit must be calculated as s/(c+v), in determining the value of c, he fails to take into account the value of c in its own value. So, for example, let us say that Mill is calculating the rate of profit on woven cloth; he recognises that this profit must be calculated on the value of the yarn used in its production, as well as the value of the labour-power used to weave the yarn. However, he fails to take into account the value of the cotton used in the production of the yarn, when determining its value. But the value of profit, in the value of the yarn, bought by the weaver, also forms part of the value of his constant capital. Its value can rise and fall, as well as wages.
“Mr. Mill needed only to put on one side that part of the whole product which is resolvable into profit (irrespective of whether it is paid to the last or to the previous capitalists, the co-functionaries in the production of the commodity) and then put that part which resolves into wages on the other, and the amount of profit would still be equal to the surplus over the total amount of wages, and it could be asserted that the Ricardian “inverse ratio” applied directly to the rate of profit.” (p 193-4)
But, of course, the value of the yarn, as with the value of the total social product, does not resolve solely into wages and profits (or the division of profit into interest, rent and taxes), i.e. into v + s, but also into c, i.e. the value of cotton in the value of the yarn, and so on. This is the same error made today by those who think that by including the value of intermediate production in GDP, they are including the value of constant capital. They are not, for the reasons Marx sets out. GDP is only a measure of value added, i.e. it is only a measure of he new value created by labour, (v + s), including in the value of all those commodities that comprise intermediate production. It only represents the equivalent of Department I (v +s), whilst all of the value of Department I (c), of the capital reproduced out of current production, in kind, is thereby omitted.
Setting aside the value of the constant capital, Mill's argument is that the rate of profit, calculated on final output, is the profit not only over the total of wages, but also over the total of profit, which, for Mill, is equal to the capital advanced.
“Hence this rate can obviously be altered not only as a result of a rise or fall in wages, but also as a result of a rise or fall in profit. And if we disregarded the changes in the rate of profit arising from the rise or fall in wages, that is, if we assumed—as is done innumerable times in practice—that the value of the wages, in other words, the costs of their production, the labour-time embodied in them, remained the same, remained unchanged, then, following the path outlined by Mr. Mill, we would arrive at the pretty law that the rise or fall in the rate of profit depends on the rise or fall of profit.” (p 194)
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