[OPE-L:7399] Commodity money in a Sraffian system

[Gil Skillman <gskillman@xxxxxxxxxxxxxxxxx>]

Hi Fred, I wonder if you would see the thought experiment developed below
as speaking cogently to the issues you've raised in your recent discussion
with Gary.

> Imagine a standard n-commodity Sraffian system of prices of production
> with one
> key variation, that one of the n commodities, "gold," acts as the universal
> means of exchange in the hypothetical capitalist economy under study.
>
> This additional stipulation has two immediate implications:  first, the
> prices
> of the non-money commodities are all measured in gold units per commodity (so
> that all costs and revenues are expressed as quantities of gold).  Second,
> per
> Fred and Marx (KI: p. 189, Penguin edition), the money commodity itself
> "has no
> price," so the "price of production" equation for the money commodity must
> rather be thought of as essentially an accounting condition, to the effect
> that
> each unit of gold produced must equal the sum of the constant and variable
> capital costs associated with producing that unit, multiplied by (1+r),
> where r
> denotes the rate of profit common to all n lines of commodity production. To
> focus the argument, suppose further that the composition of capital varies
> across production techniques in the specific sense that the n commodity-
> specific vectors of unit input requirements are linearly independent.
>
> The corresponding Sraffian price-of-production equations thus constitute, by
> construction, a system of n non-redundant equations in n+1 unknowns:  the
> rate of profit r, the money wage rate w, and the (n-1) non-money commodity
> prices.  But now let us assume, following Fred, that the money wage rate w is
> given and the rate of profit r is determined "prior" to the prices of
> production.  The values of w and r are thus fixed, rendering a system of n
> equations in the (n-1) production prices.  This system is overdetermined,
> and there is
> thus in general *no* set of production prices that will satisfy these
> equations simultaneously.
>
> There is no reason to think that the values of w and r will
> serendipitously be
> determined in such a way to allow a mutually consistent set of commodity
> prices to exist, since it is exactly the point of Fred's key assumption
> that w and r are
> determined logically "prior" to these prices, and thus their respective
> values
> cannot depend on a given realization of them.  Thus the predetermined
> values of
> w and r would make the system "work" only by accident--nothing in the
> logic of
> their determination guarantees it.
>
> I understand this thought experiment to have two key implications for Gary
> and
> Fred's discussion, one substantive and one methodological:
>
> 1)  Substance:  The conclusion of this exercise supports the sense of Gary's
> earlier point [in OPE-L 7334]:  *either* the rate of profit that Fred
> understands to be determined "logically prior" to prices of production is not
> the same profit rate actually faced by competing capitalists, contrary to
> Marx's representation in KIII, Ch. 9,*or* the hypothesis that the
> capitalist profit rate is determined prior to production prices is logically
> inconsistent in the case of a competitive capitalist economy (i.e., one in
> which the "law of one price" obtains for all non-money commodities and the
> rate
> of profit) with commodity money.
>
> 2)  Method:  This exercise suggests a possible answer to Fred's questions
> concerning the relevance of Sraffian "matrix algebra" analysis to Marx's
> analytical concerns. Without this sort of analysis, there is no evident
> way of
> verifying that the claims made by Marx concerning quantitative relations
> among
> prices and/or values, or the analytical priority of the profit rate
> relative to commodity prices,
> are in fact logically coherent. This assessment seems to
> hold especially for an *aggregative* or "macro" representation of Marx's
> value
> categories.
>
> Gil