From: Fred Moseley (fmoseley@MTHOLYOKE.EDU)
Date: Mon Feb 20 2006 - 09:07:25 EST
On Mon, 13 Feb 2006, Paul Cockshott wrote: > I am not sure that I want to devote the two weeks to a month > that it would take to work out the maths of this, but there > are obvious mathematical modelling strategies that one can use. > > 1. For each industry and each input one must distinguish > a) a working stock of each means of production required to sustain > production of the final output at a unit level > b) a consumption rate of the means of production that is implied by > production at the unit level. > Combined these two give us a stock which can be valued as capital > and a flow required for the labour value and reproduction cost > calculations. > > 2, To handle turnover time one introduces the concept of a stock of > work in progress that is required to produce the final output. One > then divides each industry into a pair of industries, the first element > of the pair produces the final output but requires a working stock > of work in progress to do this. This working stock is then analysed > using rules 1.a and 1.b above. The second element of the industry > is engaged in the production of the work in progress, This has the > inputs the one would normally have for the industry but its output > is the work in progress commodity, > > It can be seen tha this device doubles the number of commodities > in the system - it now has the original n sold commodities plus > n other commodities which represent work in progress. > > Of course depending on the level of detail to which one wants to > pursue the analysis you could split an industry up into several > sub phases. To take the cannonical ricardian example of wine > production one might split it into grape production, juice > production, fermentation and maturation, the output of each of > which represents work in progress. > > An agriculturally based industry like that may actually be better > analysed using Sraffas fixed period analysis, but if one looks > at plastics production, there are stocks of various intermediates- > ethylene, styrene etc > which themselves represent work in progress. In the latter case one > is dealing with continuous flow production. Hi Paul, thanks for sketching this out. I certainly do not want you to spend weeks trying to work this out (especially since I don't think it can be done!). I don't see how your "work in progress" method adequately deals with the problem of unequal turnover times, but I will think about it some more. In the meantime, I have a few questions for clarification: 1. Are you suggesting that there separate equations for those sub-industries that produce "works in progress"? 2. Are the "works in progress" assumed to be sold at prices that are determined simultaneously with the prices of the regular output (similar to Sraffa's method of treating fixed capital as "joint products")? 3. Or, alternatively, are the "works in progress" not sold and thus do not have prices that are determined; i.e. the prices of the "works in progress" are not unknowns in these additional equations? But, in this case, wouldn't there be more equations than unknowns? 4. It seems to me that your method still assumes that the overall turnover period - the time elapsed from the purchase of inputs to the sale of outputs produced with these inputs - is still the same for all industries (as in Sraffa's formulation), and also seems to assume that the subperiods into which the identical turnover period is divided are also all the same, so that the exchange of all commodities for each other still takes place at the same time. This all-round exchange happens more frequently, but it is still a simultaneous all-round exchange of all commodities for each other. Do I understand your correctly? 5. It also seems to me that the all-round exchange of all commodities at the same time is necessary for the simultaneous determination of the prices at which commodities exchange. Is this not correct? Thanks in advance for your clarification. Comradely, Fred
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