The first comes in a footnote at the end of Chapter 5 in which Marx discusses the nature of capital. I give the relevant part of the main text with the footnote below:
“The conversion of money into capital has to be explained on the basis of the laws that regulate the exchange of commodities, in such a way that the starting point is the exchange of equivalents.1”So here Marx is referring to the idea, taken from the Classical economists, that real world prices fluctuate around prices of production (or Classical equilibrium prices based on cost of production plus a uniform rate of profit), and that he admits that these prices of production do not equal labour values. This appears to be the first point where Marx raises this issue, and it is astonishing something so important is relegated to a footnote, when it contradicts the theory of value in the first chapters of Capital.
(1) “From the foregoing investigation, the reader will sec that this statement only means that the formation of capital must be possible even though the price and value of a commodity be the same; for its formation cannot be attributed to any deviation of the one from the other. If prices actually differ from values, we must, first of all, reduce the former to the latter, in other words treat the difference as accidental in order that the phenomena may be observed in their purity, and our observations not interfered with by disturbing circumstances that have nothing to do with the process in question. We know, moreover, that this reduction is no mere scientific process. The continual oscillation in prices, their rising and falling, compensate each other, and reduce themselves to an average price, which is their hidden regulator. It forms the guiding star of the merchant or the manufacturer in every undertaking that requires time. He knows that when a long period of time is taken, commodities are sold neither over nor under, but at their average price. If therefore he thought about the matter at all, he would formulate the problem of the formation of capital as follows: How can we account for the origin of capital on the supposition that prices are regulated by the average price, i.e., ultimately by the value of the commodities? I say ‘ultimately,’ because average prices do not directly coincide with the values of commodities, as Adam Smith, Ricardo, and others believe.” (Marx 1906: 184–185, n. 1).
Now the second footnote comes in Chapter 9 and relates to Marx’s examples in this chapter:
“The calculations given in the text are intended merely as illustrations. We have in fact assumed that prices = values. We shall, however, see in Volume III., that even in the case of average prices the assumption cannot be made in this very simple manner.” (Marx 1906: 244, n. 1).However, the context shows that the “calculations” where Marx assumes that value equals price are merely those in Chapter 9, and this can hardly be taken to be a statement where Marx is saying that all examples throughout volume 1 assume value equals price. Nevertheless, as in the first footnote, Marx notes that “average prices” (or prices of production) cannot be taken to be equal to labour values.
As is often pointed out by critics, the theory of value in volume 3 of Capital contradicts that in volume 1, and these two footnotes intrude into the theory in volume 1 and hint at the different theory in volume 3. Once we accept the value theory of Marx in volume 3, so much of volume 1 becomes nonsense and worthless, as, for example, the following:
(1) Marx thinks that the labour value of units of gold or silver have a tendency to determine prices (as discussed here).All these are rendered false and absurd if prices only ever equal labour values rarely and by accident.
(2) The idea that it is possible to accurately measure the value of skilled labour by looking at the exchange values of products of skilled labour as against products of unskilled labour (Marx 1906: 51–52) makes no sense unless Marx really believes that commodities tend to exchange at pure labour values.
(3) Marx states explicitly that:“It is true, commodities may be sold at prices deviating from their values, but these deviations are to be considered as infractions of the laws of the exchange of commodities, which, in its normal state is an exchange of equivalents, consequently, no method for increasing value.” (Marx 1906: 176–177).
Now it might seem strange that Marx contradicts himself in the footnotes, but it is not that surprising because Marx wrote drafts of volumes 2 and 3 of Capital before volume 1 (see here), and it is likely that, under pressure from Engels to produce a work in defence of communism, Marx’s ideological commitments skewed volume 1 so that it presented capitalism in the worst light possible and with an extreme and dogmatic defence of the labour theory of value, which, in view of his work on the draft of volume 3 of Capital, Marx knew to have severe problems, such as the transformation problem.
That is very probably why Marx never bothered to publish volumes 2 and 3 of Capital in his lifetime. The suspicion is that he never did so because he was unsatisfied with his attempts to defend the labour theory in volume 3, and only ever hinted at these problems in volume 1, and if he had gone into extensive details the whole theory of value in volume 1 would have been shattered.
Marx, Karl. 1906. Capital. A Critique of Political Economy (vol. 1; rev. trans. by Ernest Untermann from 4th German edn.). The Modern Library, New York.