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Here then is the old 3 equation equilibrium scheme (the fourth equation defines surplus value as total value minus cost price and then determines the sum of the individual branch profits as equal to surplus value) (1) c1 + v1 +s1 = c1 + c2 + c3 (C) (2) c2 + v2 +s2 = v1 + v2 + v3 (V) (3) c3 + v3 +s3 = s1 + s2 + s3 (SVA) (4) (C + V + SVA) - (C + V) = s1 + s2 + s3 the set of transformation equations should then be: (5) (1+r) c1x + v1y = Cx (6) (1+r) c2x + v2y = Vy (7) (1+r) c3x + v3y = r(Cx + Vy) (SVB) (8) (Cx + Vy + SVB) - (Cx + Vy) = r(c1x + v1y) + r(c2x + v2y) + r(c3x + v3y) The invariance condition of course is (9) (C + V + SVA) = (Cx + Vy + SVB), That is, the sum of original prices (call them simple prices) and the sum of the prices of production remain equal because they remain determined by the same total value of the output. At no point in carrying out the equalisation of the profit rates has the quantity of direct and indirect labor embodied in the output changed; since that total value was initially resolved into the simple prices C + V + SVA, it must also resolve without remainder into the prices of production Cx + Vy + SVB. We have an invariance condition, equation (9). However, the changes in unit prices brought about by an equalisation of the profit can lead of course to the modification of cost prices, but since this cannot change the total value of the product, this only means that surplus value must be modified by the exact same amount in the opposite direct. This of course is the meaning of the Ricardian and Marxian critique of the Smithean adding up theory of value: a change in cost (price) cannot change value, only surplus value (see II Rubin History of Economic Thought). So after the transformation and modification of cost prices, we will have (10) (Cx + Vy + SVB) =([(C + V) + a)] + [SVA - a]) {a can be negative or positive} The modification of the cost prices thus leaves the sum of the prices of production as equal to the sum of simple prices since the same total value determines both. At any rate, my set of transformation equations can be solved; my equations (invariance condition included) do not overdetermine the system. THE ONLY WAY TO DEFEAT MY ARGUMENT IS TO PROVE THAT EQUATION (7) SHOULD READ THIS WAY INSTEAD: (11) (1+r) c3x + v3y = s1 + s2 + s3 (SVA) That is, write that equation as Sweezy writes it on p. 118 of Theory of Capitalist Development, instead of the way I propose here based on the correct conception of surplus value. Sweezy argues that after the transformation, the output of Div III in the transformed scheme should equal the sum of surplus value in the *unmodified scheme* (SVA)! And this has gone without comment, much less criticism, for 60 years! I argue that the sum of surplus value, defined as total value minus cost price, should change as a result of the modification of cost prices and that the output of Div III should now be set equal to the modified sum of surplus value (SVB), which of course determines the sum of the respective Division profits [see equation (8)] At the root of the difference is the definition of surplus value. I argue that Marx resolves commodity value into its cost price + surplus value. Thus, as just argued, a modification of the former means a modification in the opposite direction in the latter. Since the completed transformation exercise aims not only to transform the outputs but to modify cost prices as well on the basis of a transformation of the inputs, it will also modify the sum of surplus value. Which is not to say that sum of surplus value should not continue to determine the sum of branch profits. This so called equality is of course preserved in my equation (8). The point of the completed transformation should then be to determine how modification of cost prices brought about by the transformation of the inputs from simple prices into prices of production changes the mass of surplus value (the whole point of the exercise is ruled out by Sweezy's equation system!) and thus changes both the average rate of profit and the prices of production. We can investigate interesting changes in relative prices as well. As we can show that substantive changes are brought about, we can then confirmMarx's intuition that it is possible to go wrong if the cost prices are left unmodified in an uncompleted transformation. I BELIEVE THAT I AM THE FIRST TO HAVE LOCATED THE ERROR IN SWEEZY'S TRANSFORMATION EQUATIONS WHICH DUE TO THE MISCONCEPTION OF SURPLUS VALUE BUILT THEREIN HAS LED TO THE SO CALLED TRANSFORMATION PROBLEM. I welcome any defense of the way Sweezy wrote the equation (which was the basis for the way Allin carried out his iteration; I have already laid out an alternative 9 step iteration which I argue preserves the labor theory of value). I would like to repeat that I do not think we should solve any problems in terms of an equilibrium vector of prices so that the inputs and outputs have the same unit prices of production. Despite Andrew B's one footnote, I believe that such a formalization is antithetical to Marx's project. But if we are going to put Marx into timeless, static equations and thereby study the properties of an imaginary self replicating system through algebra and iterations, then at least we should stick to Marx's own definitions. Yours, Rakesh

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