re Gil's 7432 > >As I think Gary mentioned earlier, there is a potential equivocation >here with respect to the term "simultaneous." It's true that the >standard Sraffian framework involves a system of equations that >might be solved "simultaneously" to yield values for some subset of >prices of production, profit rate, and wage rate. It does not >follow, however, that the equations in this system must represent >economic processes that *occur* simultaneously. Quite to the >contrary, it is possible (and has been done) to introduce >time-specific variables in the Sraffian framework, which among other >things makes it possible to reflect the function of money as a store >of value--making it more than simply a numeraire good. But if you introduce time specific variables for inputs and outputs, then how can one solve for prices and profits simultaneously--won't there be too many unknowns to derive a solution? Hasn't this been Alan F's point all along? > >>(1) The equation for money appears alongside all the other >>commodities in such a formalization, and the contradiction between >>commdities on one side and money on the other is thereby elided. >>But this is the basic abstraction of a monetary production economy. >>It is an emasculation of of Marx's theory of money to treat it as >>any other commodity except that it alone is set to equal one in an >>algebraic solution. >> > > >No more than it is an "emasculation of Marx's theory" to posit that >commodities exchange at their respective values--a condition he >clearly rejects as empirically descriptive or analytically general >yet imposes as of the end of KI Ch. 5--or that workers are >necessarily paid a wage corresponding to the value of labor power--a >condition he assumes beginning in Ch. 6 but subsequently relaxes in >his analysis of capitalist accumulation in Ch. 25. The point is >that these additional aspects of money are simply *not at issue,* >and thus *nowhere invoked,* at the level of abstraction pursued by >Marx in KIII Ch. 9, to which the Sraffian analysis most directly >speaks. But the point is that once you use the Sraffian analysis to this level of abstraction you are boxed in and will not be able to move logically to functions of money other than as a numeraire. You say that the transition can be made--where? and by whom? and how? > > >>(2) Once one has put himself in the simultaneous straightjacket, it >>seems impossible to make a logical transition to a level of >>abstraction in which the features of money which are temporally >>based can be assimilated. Through the introduction of money even >>C-M-C separates sale and purchase by time. But there is no time in >>the Sraffian formalization and thus there is no capitalism. The >>formalization thus does not capture the essential features of its >>purported object. >> > >I believe this claim is built on the confusion between mathematical >and temporal simultaneity noted above. It *is* possible to >introduce time in the Sraffian formalization, and indeed has been >done. I should take this on your authority, I suppose. > Thus, if one were to read Marx in KIII, Ch. 9, as insisting that >output prices were determined "later" than input prices for the >corresponding goods, and were thus generally unequal to them, this >complication could readily be incorporated into the Sraffian >framework. But I don't think he insists on this. Well I think Shaikh's solution which only allows for price adjustments handles simple reproduction. > >Perhaps, but as I read it the discussion between Gary and Fred >involves a narrower question: is it logically coherent, in general, >to insist that the rate of profit is determined analytically *prior* >to prices of production? in Shaikh's solution the real income of the capitalist class is indeed determined temporally and logically prior to the formation of the vector of equilibrium prices. > And one can use a Sraffian formalization *with* money, that is no >more or less explicitly temporal than Marx's analysis in KIII, Ch. >9, to establish that this claim is *not* logically consistent in >general. Note in Shaikh's solution the inputs are assumed to be in the form of simple prices which means that the monetary expression of labor time is already given, and Shaikh holds it constant throughout the iteration so that total simple price will equal total price of production. He thus begins with a sum of money invested as capital which allows him to move logically to the expansion of capital in conditions other than simple reproduction. I just don't see how'll you introduce money as capital into the Sraffian formulation. > To put the point another way, since Marx nowhere *rules out* the >possibility of a steady state in which respective input and output >prices are equal, even if temporally separated, this Sraffian >demonstration is unavoidably relevant to Marx's--and >Fred's--categorical claims. > >Gil But simultaneous equations suffer a great disadvantage vis a vis the iterative method. The latter at least presents some plausible process by which equilibrium prices of production could be arrived at. Or at least it reveals the number of price adjusting iterations it would take to arrive at equilibrium and thus casts doubt on the very notion that any understanding of capital can be derived from searching for an equilibrium vector of prices. All the best, Rakesh
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