Ian writes;
"I'm not missing the point at all. I'm denying your repeated assertions because they are backed up with mathematically inconsistent arguments and logically flawed inferences. The lov/ltv are the phlogiston of radical political economy."
Oh boy. It's late, and this is what I get.
First, I was not only defending the 'mathematically inconsistent' law of value. Say that it is that.
Still the physical quantities approach cannot itself render the law of value redundant as long as there is on going process and product innovation because the physical quantities approach requires that the system be settled in long term equilibrium.
Now freezing the technical conditions may be fine to show that distribution still has to be determined extra economically for the unknowns to be solved and that capital cannot be aggregated until that has happened and that the marginal productivity theory therefore makes no sense.
But the physical quantities approach can't serve as a theory of actual prices, so it can't have made value redundant.
There is obviously no real tendency towards a set of going prices in capitalism; under capitalism prices are going, moving; goods are also disappearing and new ones appearing. To be sure, some prices move much more slowly than others, but they're moving nonetheless as a result of on going process and product innovations which the Sraffian formalism can't allow without becoming indeterminate even after distribution has been settled.
But, lucky for us, the law of value does just fine--thank you--in accounting for the pattern of change in inter-temporal ratios over time, no matter how necessarily mediated and chaotic its mode of manifestation.
The 'physical quantities of things' system also provides no invariable measure of value once on going technical change is introduced (the standard commodity will change as well). So static is the system, it makes intertemporal comparisons in value impossible while Marx's whole essentially mathematical/quantitative system is meant (as Grossman argued) to measure the flow of value over cycles of production and realization--of course a big theoretical question for the capitalist system! Now to make such measurements Marx also invents a numeraire, a quantity of gold whose value is assumed never to change; that's as fanciful as the standard commodity but it serves its purpose of allowing Marx to make inter-periodic comparisons in the growth of capital and surplus value, which is simply impossible with the physical quantities approach.
Now you have also not spoken to my argument that Marx would not have found this physicalism of things materialist as it reifies entities and abstracts from the truly real temporal processes of social labor which by no means can be equated with an unobservable such as phlogiston, though it may appear as unobservable as that to some in a class divided society.
Now as for mathematical consistency. Let's say that the two equalities seem to over determine the value/price transformation equations.
First, I say that the equality between surplus value and profit does in fact hold in Shaikh's transformation in real terms, so that there is no inconsistency. But you gave no counter-argument.
Second, so what if the equations are overdetermined, as asked long ago by Michele Naples? Either that proves the law of value is invalid or that the law of value is incompatible with equilibrium. Why must the law of value be compatible with equilibrium to regulate prices? Where is your argument?
Third, I deny that we need equations for a complete transformation of the inputs from values to prices. The inputs are already in the form of prices. Marx takes as given the sum of money capital already invested, as argued by Fred Moseley. It can't be retroactively transformed; it makes no sense to do so. So there is no need for these full transformation equations which you say proves Marx mathematically inconsistent.
Rakesh