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

From: Gil Skillman (gskillman@mail.wesleyan.edu)
Date: Mon Jul 01 2002 - 13:33:46 EDT

```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
```

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