Allin, In your examples, if one assume that there is one natural unit of the outputs of mp and wg for each unit of value, then PV ratios become unit prices. This simplifies matters. I argue that Marx sets a constraint to the transforming of the inputs--that the sum of their (transformed) prices of production should equal their total value just as the total value of the outputs equals the sum of their prices of production (this is the point Marx makes on p. 266). For some reason, you cut me off in mid paragraph before the constraint is fully articulated. But this is exactly why Marx never bothered with the transforming of the inputs: it simply would not change the total cost price of the inputs and thus the value theoretic calculation of r in the second tableau, though of course there would be different cost prices in the individual branches and different kr's for the outputs. But Marx had shifted the theory of value from the microeconomic domain of relative prices to the macroeconomic domain of the average rate of profit, as Mattick jr has been saying for two decades. Your iterative process breaks the constraint. You are led to break it by modifying the cost prices on the basis of PV ratios derived in this period. My claim throughout this discussion has been that the PV ratios in the previous period cannot be determined on the basis of this one period of data. It is better to leave them and the individual branch cost prices unknown than to have them determined through backward causation. You will respond that you are doing no such thing. Rather you are trying to show me what the unit prices would be, were the system in a state called equilibrium. It is only because economists feel naked without the ability to determine equilibrium prices that they think they have to get modified cost prices, no matter the absurdity of the method used, on the basis of unit prices that will be the same as for the outputs. If you can't do this, you can't compete with your fellow economists on their own pseudo terrain of a general equilibrium 'solution' to price determination. But do note how statistically insignificant what you are doing is. After your first iteration: on the basis of the PV ratios or unit prices derived for the outputs, the total prices of production for the input now are about 2% greater the total value of the inputs in the first tableau. How little different would have the PVs in the previous period had to have been for the sum of prices of production of the inputs to equal the total value of the inputs as laid out in the first tableau? Let me give you an indication. But we are going to have talk about real world things now, so please be prepared for the transition. Assume productivity had increased 5% at the end of this period compared to the end of the previous period (so the inputs are made up of 357 and 286 physical units of the mp and wg, respectively, though their value is 375 and 300, respectively). Your own example shows that unit prices would have to have been about 3 cents more for the input means of production (1.12) than for the unit prices of the output means of production (1.09) and the unit prices for the input wage goods would have been about 1 cent more than than the unit prices for the output wage goods (.95) . (These of course are not uniquely determined unit prices; there is a small allowable range for the couplet of the unit prices which would allow for the sum of the prices of production of the inputs still to be determined by their value after the equalisation of the profit rates. ). That is we can stipulate that prices do not change significantly, e.g, more than 5% interperiodically and it is still easy to show that there is a range in which the unit input prices sold that would have allowed the meeting of the constraint that the total value of the inputs determined the total sum of their prices of production. Moreover, if if we use the same rate of profit for the previous period as this one, it turns out the ratio of the cost price for dept 1 relative to dept 2 remains roughly the same as in this period. Again nothing but a small range for interperiodic change. To anybody but an economist that Marx's transformation assumes (and actually constrains within realistic parameters) change in the PV's or unit prices over time would not be a mark against him but an indication of the much greater realism of his theory than your iterative or simultaneous method by which somehow by miracle the inputs are revalued (and how exactly does this happen?) by PV's which can only be derived *after* this period is completed. You are willing to ditch Marx's value theory simply because you will not allow the saving assumption of time subscripts. Would any theory other than a revolutionary critique of bourgeois society not be allowed such a simple and completely realistic saving assumption? Let us be clear about the nature of the intransigience we are confronting. Again, I have given you no method to determine what the unique set of unit input prices were; I do not believe that solving for a vector of equilibrium prices is any more important in understanding capitalism than solving for the effects of the re-introduction of dinosaurs "computed" from ancient DNA would be on capitalist dynamics. Equilbrium has nothing to do with capitalism. It is not a real force which only heroic entrepreneurs can break; it is not telos towards which the system is headed despite the bankruptcies, unemployment and overcapacity around us. It is a no-thing, it is a concept imported from physics to make economics an apology for the chaos of capitalism. At any rate, i don't think the determination of the unit input prices or the modified cost prices for each branch is important. For I have shown that it was perfectly reasonable for Marx to have assumed that the transforming of the inputs would not change the total cost price as already laid out in the tableaux. That Marx assumed this is no good grounds to dismiss his labor theory of value as so illogical (all we need is time subscripts and completely reasonable interperiodic changes) that the Marxian law of value cannot be used and tested in accounting for empirical realities of capitalism. And if it is reasonable to assume that there can be no change in the total cost price from the transforming of the inputs, then the value theoretic determination of the general rate of profit, the resolution of the contradiction between the average rate of profit and the law of value, and the two equalities all go through as sufficiently logical that the theory based on them can now be tested against rivals in terms of how well it accounts for real world dynamics. See you on the other side of comparative statics, the oxymoron of dynamic equilibrium and static prices, ok? All the best, Rakesh
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