[OPE-L:7400] RE: Commodity money in a Sraffian system

From: mongiovg (mongiovg@stjohns.edu)
Date: Tue Jul 02 2002 - 14:44:30 EDT

Since Gil's posts basically reinforce my points to Fred I can be brief.

Fred, by the way, tells me he's on the road and is internetting 
intermittently.  Gil came into the discussion just when OPE-L entered a lull.

Regarding Gil's thought experiment: setting the money wage would in effect  
normalize the relative prices if the profit rate is given as per Fred's 
hypothesis. If you fix another price, i.e. the price of gold, the system can't 
help but give rise to an inconsistency in general conditions.

Gil reminds us of Marx's remark that "gold has no price." It is interesting to 
me that Gil interprets that to be equivalent to what a modern economist means 
by "gold is the numeraire and therefore its price is 1."  I interpreted it the 
same way in my earlier exchange with Fred.  But Fred obviously doesn't see 
Marx's phraseology as equivalent to "the price of gold is one."  Let's pause 
over this for a moment.  The statement "gold has no price" is clearly a 
different statement from "the price of gold is unity." Here's the question: 
was Marx just saying badly what the modern economist means by making gold the 
numeraire, or was he trying to say something different, as (I take it) Fred 

If Marx was trying to say something different, is what he's saying sensible?  
Fred's reading seems to attribute some sort of "metaphysiscal" (for want of a 
better word) significance to Marx's argument that I find unhelpful for making 
sense of the world. But I'll be interested in Fred's response when he has a 
chance to post again.


>===== Original Message From Gil Skillman <gskillman@mail.wesleyan.edu> =====
>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
>>of the non-money commodities are all measured in gold units per commodity 
>>that all costs and revenues are expressed as quantities of gold).  Second,
>>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
>>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 
>>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
>>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
>>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 
>>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
>>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
>>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

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