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A Logical Interpretation) Chapter Eighteen Value and Production Prices (A Logical Interpretation) The transformation of values into production prices, a subject to which Marx devoted fewer than twenty pages, is generally considered to be the Achilles’ heel of the Marxist theory of value. Economists – Marxists and non-Marxists alike – have especially focused on the mathematical aspect of the problem. Marx himself could only have used the mathematical apparatus of his time, and this led him to introduce certain simplifying hypotheses into his analysis. Is Marx’s analysis valid without these hypotheses? The coherence and rigour of Marx’s analysis have been criticised using more or less relevant arguments. At the end of the 1970s and in the early 1980s, some economists showed that, even without Marx’s simplifications, the transformation of values into prices of production is, mathematically, perfectly ‘defensible’. We are referring especially to Duménil and Lipietz.1 It is about time we change the way we think about the transformation problem, and move on from its mathematical and technical aspects to its logical meaning. To avoid any misunderstanding let us high- light that we do not think that the mathematical dis- cussion is secondary. Marx himself was not satisfied with his mathematical formulations. Undoubtedly, he left unfinished algebraic work that needed to be com- pleted, if only for the sake of the beauty of the presen- tation and the love of rigour (mathematical rigour, in 1. See Duménil 1980 and Lipetz 1985. 234 • Chapter Eighteen this case). This algebraic work, however, has taken on an importance that is patently greater than the nature of the problem in need of resolution. As Lipietz has remarked, the transformation problem has not only been used by some theo- reticians who analyse ‘economies without production, with two goods and a con- tinuum of agents’, in order to attack the validity of the law of value and Marxist rigour in general. It has also been ‘the Achilles’s heel of the attacks directed at, including from within the labour movement, and as early as in the last century, the whole of Marxism’.2 Our interpretation of the transformation problem is not an alternative to the mathematical solutions, but is rather complementary to them. We will first pres- ent the problem as Marx outlines it, and indicate the key ideas that form the basis of the interesting mathematical solutions. Then, we will attempt to formu- late a new interpretation. 18.1 Marx and the transformation of values into prices of production We know the formula for the valorisation of capital Prof = s/Tturn (c + v) or: s/v Prof = Tturn (c/v + 1) This formula shows that the greater the rate of exploitation (s/v), the shorter the average turnover time (Tturn), while the lower the c/v relation, the greater the rate of valorisation, which here becomes the rate of profit. Marx notes that in a system characterised by the freedom of capital and labour to move from one branch to another, it is perfectly logical and neces- sary to assume that the rates of exploitation and the rates of profit of different branches will tend to equalise. It can be assumed from the above, as a speculative assumption, that the profit and the rate of exploitation of each individual capital can be considered as equal. This equalisation is obviously never complete. For in this case, the capitalist system would be in perfect equilibrium and capital would not move from one productive branch to another. In other words, an economy in the ideal state of equilibrium would imply a single rate of profit and a single rate of exploita- tion for all capitals. Consequently, commodities cannot be sold at (or around) their value because of the organic composition of capital, which is different: ‘If a capital whose percentage composition is 90c + 10v were to produce just as much surplus-value or profit, at the same level of exploitation of labour, as a capital of 2. Lipietz 1983, p. 54..
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