Steve, Duncan and others, Please turn to pg. 98-99 of Duncan's book. Duncan takes the unit prices of production for the outputs and transforms the inputs in terms of them. This is exactly what Allin did. It's what Marxists have been doing for 100 years. I want to challenge the logic of this by simply introducing the reality of productivity change.. Duncan's transformation of the steel inputs now has the sum of their prices exceed the sum of their values. 15,750>15,000 I want to step back and do something exceedingly simple, but it's a path that is blocked if one needs to amortize the investment made in learning all the properties of equilibrium prices. Let us assume that productivity is increasing 5% a period. So since the value of a steel unit is monetarily represented by $2 at the end of this period, the value of a unit of steel input would be $2.11 Now that means where Duncan had assumed that the steel inputs for both branches represented 7500 physical units of steel, there is really only 7109 units which had a value of $15000. Similarly, Duncan assumes that the wheat input of $10,000 represents 6,667 units of wheat. But again if we assume that productivity has increased 5%, then wheat inputs with a value of 10,000 only represent 6,329 units of wheat. The unit value of wheat as input would $1.58, instead of $1.50 as for the output. Again these discrepancies would of course be much less of course if we assumed less productivity growth. Now the question becomes what should the unit prices of production be for the inputs? It should be obvious now that the inputs cannot be transformed into the same unit prices of production as the outputs. This is the main point. No lecture about my ignorance of identity matrices is a response to this. That is, if we use Duncan's output p's on the inputs ($2.10 for steel, $1.40 for wheat), then both wheat and steel would have prices of production less than their values. For ease of calculation, I asked Allin to do one simple thing. Let's transform the inputs such that sum of the cost prices don't change. In Duncan's example, it's 25,000. What makes this quite easy is that if we use the same P/V ratios (2.1/2 and 1.5/1.4) for the outputs and apply them to the inputs, it turns out almost just right. (1.05x$2.11x7109 +.93x$1.58x6329=a little bit more than 25,000, +45). There would have to be only the smallest change in the PV ratios over time if one wanted to keep the total cost prices the same after the transforming of the inputs. But even this is not necessary; it only preserves the original calculation of the r. And it becomes unbelievable to me that one could dismiss as implausible that after the transforming of the inputs, Marx's determination of the average rate of profit will no longer make sufficient sense to even allow the right to be tested as a hypothesis. It may not hold in cases of simple reproduction or equilibrium prices, but who cares? Why won't it hold in cases where unit values and unit prices of production are changing, even gradually, over time? Again, my point is that I don't know what unit prices of production in terms of which to transform the inputs. I just know that they couldn't have been the same as for the outputs. And all this talk about long term *unit* prices of production has not yet been backed up by a single quote in Marx. I am just saying that as long as we are keeping the value of money constant (to which Duncan agrees) and the least bit concerned with the utterly realistic condition of rising labor productivity, one cannot use the same unit prices of production on the inputs as derived for the outputs, thereby eliminating time and characteristic productivity growth from the system. And one doesn't have to allow anything to go to see how such a system could easily work. All the best, Rakesh
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