**From:** Paul Cockshott (*wpc@DCS.GLA.AC.UK*)

**Date:** Mon Oct 01 2007 - 07:27:47 EDT

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Well Steedman has gone part of the way, the final stage would be to use the calculus of Newton to express things as instantaneous rates of change. The annual rate would then be given as an integral. -----Original Message----- From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of Fred Moseley Sent: 01 October 2007 03:26 To: OPE-L@SUS.CSUCHICO.EDU Subject: [OPE-L] Fwd: Re: [OPE-L] models with unequal turnover periods Hi Paul C, this is a follow-up to my message of Saturday. Is Steedman's treatment of unequal turnover periods in Sraffian theory described below the kind of thing you had in mind, or something different? Do you think that this is an acceptable solution to the problem of unequal turnover periods in Sraffian theory? Thanks. Comradely, Fred ----- Forwarded message from fmoseley@mtholyoke.edu ----- Date: Sat, 29 Sep 2007 09:33:28 -0400 From: fmoseley@mtholyoke.edu Reply-To: fmoseley@mtholyoke.edu Subject: Re: [OPE-L] models with unequal turnover periods To: OPE-L <OPE-L@SUS.CSUCHICO.EDU> Quoting Ian Hunt <ian.hunt@FLINDERS.EDU.AU>: > Dear Fred, > One initial lead on semi-finished products is Steedman "Marx After > Sraffa": 182-3. Steedman refers us for further detail to Morishima > "Marx's Economics", CUP, 1973, Hi Ian, Sorry for my delay in responding. I have had no time for opel this week. Thanks very much for these references. I took a quick look at Steedman, and he does exactly as you say: 1. The Sraffian system of equations is redefined to be in terms of a unit "short period" (a "week" he calls it), and all real-world turnover periods are expressed as "integer multiples" of this "week". In Steedman's words: "It was assumed, arbitrarily, at the beginning of the this chapter [and indeed in the whole book up to this point] that each productive process takes one 'YEAR' to complete, but such a STRONG ASSUMPTION is NOT REALLY NECESSARY. Suppose instead - and FAR MORE PLAUSIBLY [!]- that each process takes an INTERGER MULTIPLE of some SHORT PERIOD, called a 'WEEK'... All inputs to and outputs from a 'productive activity' are now defined to be those involved *IN ONE WEEK'S OPERATION* ..." (p. 182; brackets and capitalized emphasis added) 2. Under this assumption, not only are "partially used machines" (and other forms of fixed capital) assumed to be "joint products" (i.e. fully consumed each "week"), but also "partially finished products" are also assumed to be "joint products" (i.e. as distinct commodities with prices of production each "week"). "Correspondingly, the number of products involved will be increased, PERHAPS GREATLY [!], since any 'SEMI-FINISHED' PRODUCT, in the normal sense, will now appear as one of the specific products of a particular WEEK-LONG PROCESS and must be regarded as a DISTINCT COMMODITY. Each product, whether a finished product, a semi-finished product, or a partially used piece of fixed capital equipment, is thus treated as a distinct 'COMMODITY' and has ITS OWN PRICE OF PRODUCTION." (ibid.) 3. Next, the Sraffian system of equations is rewritten, and the rate of profit that is determined by these equations is the "RATE OF PROFIT PER 'WEEK'": "Once the above CONVENTIONS have been adopted, one may simply write pB = ma = (1+r)pA where is it now understood that r is the RATE OF PROFIT PER 'WEEK', that B, a, and A refer to *all* the WEEK-LONG PRODUCTION ACTIVITIES, and that p, B and A contain entries for *every* 'COMMODITY' as now defined. (ibid; a superscript m on p in the above has been omitted). 4. Thus we can see that the rate of profit that is determined by this redefined system of equations is a "week rate of profit", not the annual rate of profit. The "week rate of profit" is determined simultaneously with hypothetical "week prices of production" at the end of each "week" (hypothetical because "partially finished products" and "partially used machines" are not actually exchanged at the end of each week). This theory implies that the rate of profit that is equalized by capitalist competition is this "week rate of profit". It seems to me that Steedman's "far more plausible" assumption is not very plausible at all. By contrast, the rate of profit that is determined in Marx's theory is the annual rate of profit, which is determined by the ratio of the total surplus-value produced in the economy as a whole in a year to the total capital invested in that year. Marx's theory assumes that the rate of profit that is equalized by capitalist competition is this annual rate of profit. It seems to me that this is a "far more plausible" assumption. Comradely, Fred ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program. ----- End forwarded message ----- ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program.

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