I'm striving to understand your view. Let's see if this argument works better. Start with what we agree on (I think). Marx's transformation, in itself, is an atemporal comparison of two possible states of a single economy, states which differ in respect of the pricing of commodities (according to values in the one case, in such a manner as to generate an equalized rate if profit in the other). Marx had a table which showed the inputs being purchased at prices equal to values and the output selling at prices that equalize profits. This is fine as a starting point, (a) because Marx wanted to root prices of production in values, so it makes sense to have the inputs at prices equal to values in the first instance, and (b) because -- as you say -- Marx hasn't yet developed the concept of price of production when he first draws up the table. Fine as a starting point, but it looks as if some more work is needed. The next question that suggests itself is: what would things look like if the inputs were purchased at prices of production too? (Marx only got as far as asserting that this would make no material difference.) So how are we going to examine the situation where the inputs are at prices of production too? To get at this we need a little model system that represents a complete economy (with its interdependencies), not just a few industries drawn from a larger economy. Agreed so far? Bortkiewicz offered one such little system, with 3 departments. He conceived of his system as a "time-slice" of an economy undergoing simple reproduction -- because this was the simplest assumption, and because it seemed adequate to test Marx's claim concerning the two equalities, total price = total value and total profit = total surplus value. Marx's claim being perfectly general, if it was shown to fail in the case of simple reproduction, it would be shown to be false. OK, I understand that you don't want to have anything to do with the assumption of simple reproduction, constant technology, and an equilibrium where input prices equal output prices. So let's reinterpret Bortkiewicz's table as representing a time-slice from an economy where labour productivity is increasing at 5 percent per period. Let's say the slice is at period t, with certain means of production coming forward from t-1 as inputs, and certain means of production being produced during t, for carrying forward to t+1. The initial value table: c v s value I 225.00 90.00 60.00 375.00 II 100.00 120.00 80.00 300.00 III 50.00 90.00 60.00 200.00 Tot. 375.00 300.00 200.00 875.00 Where B. would assume that the physical quantities and unit values of the means of production coming forward from t-1 are same as those of the means of production going forward to t+1, we'll assume that the physical quantity going forward to t+1 is 5% greater than the quantity coming from t-1, while the per-unit value is 5% smaller on the output side than on the input side. Now we do the iteration, as I suggested before. Start with Marx's stage 1 transformation: c v profit price I 225.00 90.00 93.33 408.33 II 100.00 120.00 65.19 285.19 III 50.00 90.00 41.48 181.48 Tot. 375.00 300.00 200.00 875.00 I observed that the aggregate price of output of Department I stood here in a ratio of 1.0889:1 (408.33/375) to the value of that output, and proposed to revalue the means of production as inputs by the same factor (i.e. I was supposing that their price as inputs at the beginning of t "ought to be" the same as their prices as outputs at the end of t). Let's correct that. My next-round figure for the aggregate price of the means of production as inputs (408.33) has to be adjusted in two ways: 1) By assuming that the quantities are the same on the input and output sides, I have overstated the quantity of inputs by 5 percent, and hence overstated the aggregate price accordingly. Thus we need to divide my figure by 1.05. 2) We assume the value of money is constant (as you said). Therefore, aside from any adjustment due to equalization of profit, the unit price will be 5 percent lower on the output side than the input side, due to the 5 percent drop in per-unit value. My initial calculation ignored this, "carrying back" the output price unaltered. To correct for the drop in unit prices from inputs to outputs, we have to multiply my figure for the aggregate input price by 1.05. Thus the combined correction factor is 1.05/1.05 = 1. In other words, no correction to my figures is needed after all. The next table looks like this, if we take a total profit equal to the total surplus value from the original value table (200) and distribute it in proportion to capital advanced: c v profit price I 245.00 85.56 95.33 425.88 II 108.89 114.07 64.30 287.26 III 54.44 85.56 40.37 180.37 Tot. 408.33 285.19 200.00 893.52 As I said before, total price (893.52) has come unstuck from total value (850). Hold to one of Marx's equalities and you break the other one. What happened? Well, it shouldn't really be a surprise. A difference in physical quantities between outputs and inputs makes no difference to the value or price of production tables, in aggregate terms, since it is completely offset by the change in unit values (and prices, given a constant value of money). There _is_ a difference, but it's invisible in the aggregate tables: the _unit_ prices of production are no longer the same for inputs and outputs. As you wished, unit output prices are lower. What do I conclude from this? "Aha, so Marx was completely wrong. We can forget about exploitation of labour as the source of profit. Capitalism is fine and just after all"? Of course not. With this loophole opened, it's possible to cook up examples a la Steedman where profit and suplus value do not just diverge by a few percentage points, but have nothing to do with each other. But as Paul C has repeatedly said, we have to subject this sort of thing to sensitivity analysis -- to get a feel for what are plausible numbers for real capitalist economies. Steedman's examples are theoretical freaks, of no practical significance. Allin Cottrell.
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