Empirically, prices are fairly close to proportional to labor values. But that is neither here nor there as far as the correctness of Marx's theory of value. To see that, you have to get to the last footnote in chapter 5 of Capital. (Most "refutations" of Marx are based on ignorance of the first few pages of chapter 1.)
From the foregoing investigation, the reader will see 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 oscillations 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.
-- Karl Marx. 1887. Capital, first english edition.
Only volume 1 was published in Marx's lifetime. But the question of the validity of Marx's theory, say, the value theory of labor, cannot be discussed without looking at volume 3, unpublished in Marx's lifetime.
Wicksteed had an early discussion of the validity of Marx's theory from a marginalist standpoint. Eugen von Böhm Bawerk's Karl Marx and the Close of his System is problably better known. His book is definitely important from a historical perspective. But its content is not all that insightful. Some anti-Marxists agree with me.
"The classic 'refutation' of Capital was made by a leading figure in the new economics, Eugen von Bohn-Bawerk. His refutation repeatedly misunderstood what it was refuting, and unknowingly repeated criticisms that Marx had made of Ricardo in manuscripts still unpublished at that time. Bohm-Bawerk also made the claim, often echoed since then, that in his discussion of value Marx had attempted 'a stringent syllogistic conclusion allowing of no exception,' that Marx attempted 'a logical proof, a dialectical deduction.' As already noted, Marx considered the idea of proving a concept to be ridiculous. Moreover, Engels had asserted, long before Bohm-Bawerk, that one only proves one's ignorance of dialectics by thinking of it as a means by which things can be proved. This was typical of a tragi-comedy of errors that has plagued the interpretation of Marx ever since.
Contrary to some interpretations, Marx did not change his mind about value and price between volumes of Capital. He explicitly worked out the analysis to be followed in Volume III in a letter to Engels written several years before publication of Volume I."
-- Thomas Sowell. 1985. Marxism: Philosophy and Economics, Routledge.
Sowell refers to Marx's letter of 2 August 1862. I have all sorts of disagreements with Sowell, which I forget. In some, I am probably critical of Marx than Sowell. One should probably ignore the final chapter of this book.
My next example is not from an economist:
"Marx of course knew that prices are determined in practice by various factors, including labour productivity, supply and demand, and the average rate of profit. If he disregarded these in the first volume of Capital, it was for methodological reasons and not because he thought value and price were the same thing; thus he cannot be reproached with inconsistency as between Volume I and Volume III, which deals inter alia with the average rate of profit."
-- Leszek Kolakowski. 1978. Main Currents of Marxism: The Founders (Book 1), Chapter XIII, Section 6.
I turn back to an economist:
"Writers on 'the transformation problem' since L. Bortkiewicz have focussed on an issue that is largely periperal; and others like E. Bohm-Bawerk have asserted that there is a contradiction between the analyses of Volumes I and III which is certainly not to be found there unless one reads into them an interpretation different from that which Marx repeatedly emphasized."
-- William J. Baumol. 1974. The transformation of values: what Marx 'really' Meant (An Interpretation). Journal of Economic Literature 12 (1): 51-62.
Even one of his students was not too impressed by Böhm Bawerk on Marx:
"As it was, most critics felt no hestitation in convicting him of having by the third volume flatly contradicted the doctrine of the first. On the face of it that verdict is not justified. If we place ourselves on Marx's standpoint, as it is our duty in a question of this kind, it is not absurd to look upon surplus value as a 'mass' produced by the social process of production considered as a unit and to make the rest a matter of distribution of that mass
Joseph A. Shumpeter, Chapter III. Marx the Economist, Capitalism, Socialism, and Democracy. Third Edition, New York: Harper and Brothers, 1942, 1947, 1950.
Valid, non-outdated criticisms of Marx exist. Böhm Bawerk does not have one.
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