Dear Paul,
I still don't see why the empirical fact that relative sectoral prices
are closely correlated with estimated embodied labor coefficients (which
isn't exactly what you've shown, as I understood your earlier account)
should make the transformation problem irrelevant. I think Marx wrote ch
IX of Vol III to come to grips with a genuine theoretical problem, which
was how to reconcile the labor theory of value with competition broadly
understood to include all the factors that influence the formation of
relative prices. I think (as I have explained in detail in Understanding
Capital and elsewhere) that he had the view that the labor theory of
value operated as a conservation law at the level of the aggregate of
capitalist production. I know this is controversial and unacceptable to
many people, but it's still where I come out. I still have yet to see
where the hypothesis that embodied labor coefficients govern market
relative prices leads in terms of a fruitful research program.
This is, to repeat, not to downplay the importance of empirical findings
on the structure of prices and profit rates in real capitalist economies,
which, if they are replicable and reflect widespread structural
regularities, are of obvious scientific importance.
Duncan