"If the deployment of matrix algebra to demonstrate some of the inconsistencies of some of Marx' hypotheses isn't enough to convince you that Occam's razor is applicable to the ltv, what makes you think you'd be convinced by the use of nonlinear diff eqs.?"
But you're missing the point, not speaking to it: you can't bypass value--a temporal measure of real labor processes--and compute prices and profits (once distribution is settled) from Sraffian quantities of physical things as long as there is qualitative change in outputs and inputs and changes in techniques of production from period to period.
To aggregate inputs and outputs you'll need value, the temporal measure of real labor processes of which physical things are only evanascent reifications. It's the technical conditions that are the extra entity insofar as they are only the materializations of social labor time anyway. Those physical quantities did not drop from the sky.
And it's not like one is invoking what was the equivalent of atoms or genes in Boltzmann's or Mendel's times; real laboring time is already palpable enough. There is no similar appeal to the unobservable here. So the discredited positivist strictures against unobservables have no traction here. If that is what you mean by Occam's Razor.
Value is not an extra entity in a changing economy; it is necessary. Don't see how you are speaking to what I wrote.
I also don't think there are inconsistencies in Marx's hypotheses, namely I don't think there is a transformation problem. First, I have argued here that Marx did not admit to leaving the means of production and wage goods in values. He argued that they were paid for at market prices; hence, they don't need to be transformed; moreover, it makes no sense to transform something retroactively. He did admit to equating wrongly the value transferred from the means of production from the flow price of the means of production. This introduces a small error of no consequence to his tables, and the economists' focus on the failure to transform the inputs has been a waste of time.
I understand that I'm bucking one hundred years of consensus about what was Marx's mistake, but there you have it, and I am confident I am right.
Second, even if one admits that inputs have to be transformed from values to prices of production and one further demands the provision of a vector of equilibrium prices (and again I think the search for such a vector is misguided), I think Shaikh's fixed point iteration shows that one can be derived from values. The difference between the mass of surplus value and the mass of profit is only apparent.
Now there are criticisms of his interpretation. Hodgson and others say that Shaikh has shown no relation between values and prices because one need not begin with values to arrive at the equilibrium prices at the end of the iteration. I agree that Shaikh's iteration does not prove that prices are derived from or are functions of value; they only show that they could be.
But I don't think he intended to do more than that--that is, deflate the charge of logical impossibiity/inconsistency. That's why he has tried to show empirically the power of value in accounting for intertemporal changes in exchange ratios.
"Sraffa's argument was deployed against the then mainstream of the profession on their own terms. That his work has non fatal, yet serious, ramifications for Marx' work should no more bother Marxists than quantum theory should have bothered Einstein. There's plenty left to analyze and explain with what's left."
I believe that it is best understood as an immanent critique of neo classical economics (see for example EK Hunt's brilliant summary in his history of economic thought), not a correction of Marx's logical contradictions in his value price transformation tables. There are many reasons why the Sraffian model can't be taken as model of even the simplest features of capitalist reality--it effaces intra branch competition, it requires that the profit rate be exactly equal for solutions to be computable; it rules out product and process innovation; its numeraire as standard commodity changes period to period. How something so sterile could be said to be improvement over Marx's theory boggles the (ok my) mind.
As I said I don't there is a logical problem with Marx's realistic theory. There is rather a real contradiction: capitalism both requires and makes it impossible for prices to be a function of values. Price of production is ony the reconciliation of this real contradiction.
It's not a waste of time to insist that abstract labor time--such a pedestrian reality, so uninteresting to the bourgeois mind--remain the foundation of economic analysis.
Rakesh