The theory of value and prices
From the beginning the discussion of Marx’s work centred on the theory of value and prices. When Friedrich Engels, in his Foreword to the second volume of Capital, rejected the idea that Marx had plagiarized the theory of value and surplus value from Johann Karl Rodbertus, he invited the economists to show “how an average rate of profit can and must come about, not only without violating the law of value, but precisely on the basis of this law” (Engels 1885 [1978]: 102), and announced that the third volume would contain Marx’s definitive solution of the problem.
Of the contributions to Engels’s “prize essay competition”, which came inter alia from Wilhelm Lexis, Julius Wolff, Achille Loria, Conrad Schmidt and P. Fireman, none was convincing. When the third volume of Capital was published in 1894, the interest centred mainly on Marx’s solution to the so-called “transformation problem”. (For a detailed history of the controversies, see Dostaler 1978 and Faccarello 1983a, 2000b.)From the standpoint of the neoclassical theory Marx’s theory of value and prices was criticized by, among others, Philip H. Wicksteed (1884, 1885) and Vilfredo Pareto (1902). One of the most influential critiques of Marx’s procedure for the transformation of values to prices (and of the rate of surplus value to the rate of profits) was Eugen von Bohm- Bawerk’s “Zum Abschluβ des Marxschen Systems” (“Karl Marx and the close of his system”) (1896 [1949]). Bohm-Bawerk accused Marx of having given up the value theory expounded in vol. I of Capital with his theory of prices of production expounded in vol. III. Between the first and the third volume of Capital, he contended, there is “an irreconcilable contradiction”. He declared that a determination of the general rate of profits and of relative prices in the way Marx intended was impossible and that Marx’s theoretical work has “a past and a present, but no permanent future”.
But although Bohm-Bawerk failed to notice the real shortcomings of Marx’s theoretical construction, Rudolf Hilferding ([1904] 1949), who was to play the leading role in defending Marx in the ensuing debates, could not counter Bohm-Bawerk’s attack convincingly. Note however that, in his 1904 answer to Bohm-Bawerk and in his book Das Finanzkapital (1910 [1981]), Hilferding started a sociological interpretation (see above) of Marx’s theory of value, which was to be taken up later by a few authors such as Nikolai’ Boukharin in Economic Theory of the Leisure Class (written in 1914, published in 1927) and Rosa Luxemburg in her posthumously published Einfuhrung in die Nationalokonomie (1925) - a line of thought above all developed in Isaak Illich Rubin’s writings in the 1920s (Rubin 1927 [1978], 1928 [1972]), especially his 1928 Essays on Marx’s Theory of Value (Faccarello 1983b, 2000b; for a historical setting of Rubin, see Boldyrev and Kragh 2015).Ladislaus von Bortkiewicz (1906-07 [1952], 1907) deserves the credit for having first demonstrated the errors of Marx’s transformation algorithm, and for presenting a correct solution procedure. Bortkiewicz demonstrated, first for the case of unidirectional production processes (where he harked back to a contribution by Vladimir K. Dmitriev (1898 [1974]) and then also for a circular, three-sectoral production system, that the rate of profits and relative prices can be determined on the basis of Marx’s set of data by solving a system of simultaneous equations. Similar findings were presented in two neglected contributions by Georg von Charasoff (1909, 1910), who not only anticipated some of the arguments that were proposed later in the discussion of Marx’s “transformation problem”, but also noted the duality properties of the price and quantity system. Moreover, in the course of his investigation he defined and made use of the concepts of a “production series” (Produktionsreihe), of “original capital” (Urkapital), and of “basic products” (Grundprodukte), thus anticipating Piero Sraffa (1960) with regard to the related concepts of a reduction series to dated quantities of labour, the Standard commodity, and the basics/non-basics distinction.
Bortkiewicz’s approach to a solution of the transformation problem, which was first made available in an English translation by Paul M. Sweezy in 1942, was subsequently generalized by Josef Winternitz (1948), Francis Seton (1957), and Paul A. Samuelson (1957).A milestone in the understanding and further development of the surplus approach of the classical economists and Marx was Piero Sraffa’s Production of Commodities by Means of Commodities (1960). Without entering into an explicit critique of Marx’s economic theory, Sraffa demonstrated that the general rate of profits can be ascertained on the basis of the classical set of data (given quantities, given real wage rate, and given methods of production) only simultaneously with the prices. The implications of Sraffa’s modern reformulation of the surplus approach to the theory of value and distribution for Marx’s theoretical construction were concisely stated by Ian Steedman (1977): on the basis of the classical set of data a consistent determination of the general rate of profits and of relative prices is possible; the recourse to labour values is dispensable. Moreover, Steedman also stressed that labour values and prices more generally depend on income distribution if there is a choice of technique and that Michio Morishima’s “Fundamental Marxian theorem”, according to which “the equilibrium rate of profit is positive if and only if the rate of exploitation is positive” (1973: 6) need not hold in systems with (pure) joint production.
While Sraffa (1960) and Steedman (1977) have implicitly or explicitly shown that Marx’s (labour) value-based reasoning is difficult to sustain, there have been various attempts to defend or reinterpret it. Here it suffices to mention only the reconstruction of Marx’s labour theory of value suggested independently from each other by Duncan Foley (1982) and Gerard Dumenil (1983). The reconstruction emphasizes the relation between money and labour time that preserves the rigorous quantitative relation between paid and unpaid labour, on the one hand, and the aggregate wages bill and aggregate gross profits, on the other. It became known as “the new solution” to the transformation problem, which is a misnomer, because the punchline of the argument is that there is no transformation problem. The “new view” has been criticized for, among other things, not being a faithful interpretation of Marx and that it wrongly conveys the impression that the classical surplus-based approach to the theory of value and distribution stands or falls with the labour theory of value.