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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