Duncan,
I agree with what you say below and take note of
what J. Levy wrote concerning this. The problem
is how we deal with technical change and valuation
as we move from one period of production to another.
To be sure, we could start with a model that resembles
Marx's reproduction schemes. Yet, when we introduce
technical change and assume some initial drops in
price as Marx does, we are confronted with problems.
a. How do we deal with the loss of capital value
as prices decrease?
b. Are these loses, to some extent, anticipated by
capitalists as they figure "moral depreciation"
into their pricing strategies?
c. Given we answer "a" and "b" in a way that takes
into account decreases in prices and values, how
do we move to model that applies to a modern
economy where there is a conscious effort to
prevent nominal price decreases?
Thus, I see the overall project as two-fold. First,
the effort has to be to understand Marx in the
context of the time he lived -- a world with price
decreases as productivity increased. Second, once
we have a better idea of Marx's outlook, we can,
hopefully, develop a view of the economy of today
in which prices generally do not fall and, indeed,
more often, increase.
Thus, my problem with simultaneous valuation is that
it loses much of whatever Marx was trying to say and
leaves us in a different world without the tools he
developed.
Duncan says:
If you write down an explicitly disequilibrium model with time subscripts
differentiating commodities at different times, thus allowing for prices
of inputs and outputs to differ, one solution will be the equilibrium
prices where the inputs and outputs have the same (relative) prices. This
is also the easiest solution to analyze, and its existence is a good
indication that the equations make sense. As an historical aside, this
seems to be the approach Marx took, for example, in his work on
reproduction schemes.
John