Duncan, let's go back to your Understanding capital. The interested reader can skip the box and jump ahead _____________________________ So by my method I would make your equations on p. 100-1 the following: (1) Ps= [1+r]([1/2]Ps + W) (2) Pw= [1+r]([1/4]Ps + W) (3) W= [1/3]Pw (4) 35,000-15,000Ps-10,000Pw= r(15,000Ps + 10,000Pw) Since we are only changing the outward appearances of this system, the indirect and direct labor embodied in the ouput will remain invariant and thus so will the total value (35,000) which will determine the sum of the prices of production. _________________________ The left hand of equation (4) *is* surplus value (total value minus [modified]cost price); and it is set equal to the sum of branch profits. Duncan, I may not have written the equations correctly for what I propose now to solve by iteration. Of course you will immediately object to the results of my proposed iteration because while total value/price will remain unchanged from the initital equal exchange tableau, new value added, surplus value, and s/v will not. But.... 1. where is the evidence that Marx ever thought that if the cost prices are modified, the sum of surplus should remain the same? If he thought this, you would presumably be able to point to one quote in which Marx defines surplus value as total value minus value of inputs; that would prove for Marx the price of the inputs does not matter to the determination of surplus value. I have been unable to find one single such quote. Presumably Allin has not found one either. It is obvious that the sum of surplus value which is actually available for redistribution is total value minus cost price (as Marx repeatedly defines it), not minus value of inputs! So for matters of the transformation, I don't see how one could think the mass of surplus value, as defined by Marx, would remain invariant as cost prices are modified! 2. Why do you implicitly seem to be saying that if the value added, surplus value and s/v do not remain invariant that Marx's value theory would be compromised? It is clear that in a proper iteration, the labor theory of value provides us the steps by which to carry it out. IT IS AT THIS LEVEL--IN THE STEPS OF THE ITERATION--THAT THE MARX'S MACRO LABOR THEORY OF VALUE IS PRESERVED. Applying the output PV ratios on the inputs, we will get our first modified cost prices (I am not exempting v as you do). What are we to do? We could a. multiply the new respective cost prices by the old profit rate to determine branch profits (then total price will not equal total value); b. we could apply the old s/v ratio to the modified v to determine branch profits (then total price will not equal total value); or c. we could subtract from the invariant total value the total modified cost prices to redetermine s, which then divided by modified cost prices yields a modified r which then applied to each branch gives us finally micro-level branch profits the sum of which will indeed equal the (modified) sum of surplus value. The second equality is preserved while total value has been held invariant. The labor theory of value does not tell us to take (a)the old rate of profit or (b)the old s/v from the original so called value scheme and continue to use either out of a commitment to the labor theory of value even as it forces total price to break from total value. I argue that the only way forward consonant with Marx's own theory is c. So Marx's MACRO value theory tells us how to carry out the iteration. And I think it is possible indeed to to carry out this iteration in your example until you get a so called blissful equilibrium vector of prices (Gouverneur gives a very nice example of a completed iteration--maybe it's Shaikh's). In the final state, the invariant total value=total price; sum of surplus value (defined countless times by Marx as total value minus cost price or paid labor or capital advanced and as M' minus M)=sum of branch profits. The two equalities are preserved, though the latter is not an invariance condition. We are not changing the direct and indirect labor embodied in the output and thus that output's total value in terms of which total price remains determined. However, by modifying the cost prices we are changing the sum of surplus value which nonetheless must equal the sum of branch profits in the transformed scheme. We will get both equalities if we iteratively transform the scheme according to the assumptions in Marx's macro labor theory of value. We'll get different numbers if we go forward on course (a) or (b). You are doing it even a different (and very convoluted) way. To me Shaikh and Gouverneur seem to be doing it the right way. They only need to point out that it does not compromise the labor theory of value not to keep the sum of surplus value invariant and that in each one of the iterations, the sum of profits has been determined as equal to the (modified) mass of surplus value in that iteration. In short once surplus value is correctly understood to be total value minus cost price, it becomes clear that after no single iteration has the equality between the mass of surplus value and the sum of branch profits been broken. That is, as long as we carry out that iteration in the manner consonant with Marx's macro labor theory of value. All the best, Rakesh
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