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The Determination of Prices of Production Paolo Giussani The Determinationof Pricesof Production Sincethe turn of the century a multitude of criticisms have been directedagainst the so-calledtransformation of quantities of commodityvalue into quantities of price, on theassumption of a uniformprofit rate for all industries,as setforth in chapter9 of Marx'sCapital, volume 3. Commonto all thesecriticisms is the idea thatMarx's procedure lacks a transformationof the quanti- tiesof value of the means of production and of labor (the inputs). If thisdilemma is to be resolved- accordingto all thecritics - thetwo fundamentalequations of theMarxian transformation (totalprice = totalvalue; total profits = totalsurplus value) can obviouslyno longerbe simultaneouslyvalid. The resultof this is thatthe general profit rate can no longerbe calculatedfrom Marx'slaw ofvalue, and the value quantities themselves cease to playany role in thecalculation of prices of production. This resultstems directlyfrom the assumptionthat the pricesof the productsand thoseof the meansof production mustbe determinedsimultaneously, an assumptionthat has always been accepteduncritically by almosteveryone. This has been trueeven of Marxists,especially given the accep- tance by "left-wing"economists of Sraffa'stheory of prices and distributionof revenue.Yet thisresult is muchless obvi- ous than it may seem. Once the assumption(which is not foundin Marx) is provedto be irrationaland is thereforedis- carded,the criticisms directed against the Marxian determina- Paolo Giussaniis editorof the journal Plusvalore. 67 This content downloaded from 139.184.14.159 on Fri, 11 Dec 2015 13:23:49 UTC All use subject to JSTOR Terms and Conditions 68 INTERNATIONALJOURNAL OF POLITICALECONOMY tionof the prices of production and the rate of profit lose all their force. 1. The simultaneousdetermination of prices Noneof thediscussions of theprices of production that have ap- pearedso far,and certainly not Sraffa's 1960 treatment,1 hastaken thetrouble to provide a theoreticaljustification for the procedure of simultaneouscalculation of inputand outputprices. Nevertheless, thereis a kindof reasoning prevailing among the so-called experts, accordingto which "prices must necessarily be simultaneousprices, sincethe prices of all commoditiesare basednot on thecosts of production(or on thelabor) sustained in thepast, at thetime when thecommodities were produced, but on thecurrent costs (or the quantityof labor)." The astute observer will easily perceive that this is an entirelycircular argument. Ifprices are determined by current costs,it is necessaryto establishwhat these current costs are, but sincethe current costs are theprices themselves (of thevarious inputs),the whole thing comes down to saying that (current) prices aredetermined by(current) prices. Anotheridea, also expoundedby JoanRobinson, is much moreelementary - almost trivial. Since thecommodities of the sametype have the same price as outputand as input,this argu- mentgoes, the same price for those commodities is placed on the leftand on theright side of theequations used for price calcula- tion.Unfortunately, as we shallsee, this argument forgets that a givencommodity cannot operate as an inputand as an outputat thesame time. In reality,the procedure of simultaneous calcula- tionof pricescannot be givenany theoretical foundation; it is simplyan axiom,which works only so longas itis notshown to produceconsequences that are absurdand/or in plaincontradic- tionwith the facts. To findout whether this is indeedso, letus imaginea systemof production composed of three industries (A, B, C), each of whichuses onlyproductive inputs coming from theother two, and in whichsector C producesthe good serving as the real wages consumedby all the workers.The material This content downloaded from 139.184.14.159 on Fri, 11 Dec 2015 13:23:49 UTC All use subject to JSTOR Terms and Conditions WINTER1991-92 69 structureof this system is representedby means of the following schema: (1) Ba + La -> A Ab+ Lb - B Ac+ Bc + Lc -> C C = Ca + Ch+ Cc - La + Lb+ LC= L. If,for convenience, we nowsuppose that the system is repro- ducedon an unalteredscale (simplereproduction), it should turn outthat sector A exchangesits total product A againsta portion ofthe product of B andC, specifically,against the quantity Ba + Caywhile the commodity B should be exchangedagainst Ab + C¿>, andthe commodity C-Cc withAc + Bc.We thereforeshould have thefollowing series of equations (the last being a simpleidentity, sincethe quantity Cc is consumedwithin the same industryin whichit is produced): (2) A = Ba + Ca B = Ab+ Cb c-cc = ca + cb. As can be seen,the commodities that enter into the exchanges amongthe various productive sectors are only the outputs, that is, whatis foundon the rightside of expressions(1), whilethe inputs(the left side) have been exchanged in the previous period. It is quiteobvious that no outputcan be exchangedagainst an input,since therecannot be use values thatfunction simulta- neouslyas inputsand as commodities.If a particularproductive use value(e.g., oil) is playingthe role of input, this means that it is in theform of productive capital and thereforecannot at that timebe foundin the (capital) commodity form. Equations(2) representdirect exchanges of commoditiesfor This content downloaded from 139.184.14.159 on Fri, 11 Dec 2015 13:23:49 UTC All use subject to JSTOR Terms and Conditions 70 INTERNATIONAL JOURNAL OF POLITICAL ECONOMY commodities;if we transformthese barterexchanges into ex- changes for commodity-money,the situationis worsened.The outputsBa + Ca, Ab+ Cb,Ca + Cb mustnow all be computedfirst and thenrealized in money,that is, say,di fourth commodity, before theycan be used as productivecapital. The assumptionof the si- multaneouscalculation of input and outputprices in factimplies the eliminationof thisnecessity, something justified at timesby the pretextthat "purchases, sales, and production always occur simulta- neouslyfor all sectorsand individualcapitals, without interruptions makingpossible the passage fromone phase to the next." The objectionis clearlyirrelevant, since if we are movingfrom di partic- ular groupof inputsto a particulargroup of outputs,as in the so-calledlinear models of production,the phases of sale/purchase and of productionfor these groups obviously cannot occur at the same time.The variousproduction processes must take place at the same time withrespect to each otherin the varioussectors, and afterthis the products can all be exchanged.2To do away withthis "minor"detail is basicallyequivalent to assumingthat circulation is nota constituentelement of the market economy, or (analogouslyto Ricardo'squantitative theory of money)that inputs enter the pro- ductionprocess without prices and leave it withprices, that is, the productsdo nothave the form of commodities. 2. The simultaneouslinear equations The moderntheory of pricesand distributionis clearlyforced by its own premisesto assume the simultaneousdetermination of theprices of inputsand outputs.If one wishesto obtainthe prices of productionfrom the known data concerningthe production technology,together with knowledge of one of theso-called dis- tributivevariables (e.g., the wage rate),without the aid of other unwelcomequantities (among which the "value" of thecommod- ities is obviouslyparamount), it is necessaryto adopt the same temporalindex for the prices of theinputs and theoutputs, or else it will no longerbe possibleto determinethe rate of profit. To illustratethis elementaryfact, let us imaginea systemof This content downloaded from 139.184.14.159 on Fri, 11 Dec 2015 13:23:49 UTC All use subject to JSTOR Terms and Conditions WINTER1991-92 71 two industries,A and B, each of whichproduces a productive input,with the commodity B also beingused as thewage good. Witha timespread between the price of the inputs and the price ofthe outputs (a spreadindicated by the indices t and t + 1), the systemof production prices would assume the following form: (3) + = [Ba Bta]pbt(l+r) Apat + i [^"«í+V»i](1+r)=l>p»í+r The expressionsin equation(3) forma systemof two linear first-orderdifference equations, whose solution requires prelimi- naryknowledge of thequantity r (the rate of profit), which will enterinto the coefficient 1+r. Alternatively,ifwe treatr as an unknownfunction of t (i.e.,r/+i), a furtherequation for the deter- minationof T/+1is required,an equationthat cannot be con- structedin theframework of theSraffian theory, that is, without theaddition of other quantities. 3. The physicalsurplus Economistsof theSraffian school rarely miss an opportunityto assertthat the category of surplusvalue is unnecessaryfor the determinationofthe rate and the volume of monetary profits, the simplesurplus in physicalterms being sufficient for this. Not withoutreason, they like to designate their own theoretical orien- tationas "one based on thesurplus approach'' It is therefore appropriateto investigatewhether this concept of materialsur- plus is indeeddefined sufficiently to play the role that its sup- portersassign to it. Evenchildren know that the strict conception of a surplusin purelyphysical terms is an absurdity,since the quantity of matter (and/orenergy) in theuniverse is constant,or at least can be changedby there is no knownforce. One musttherefore employ a differentconcept of surplus,a surplusthat is a quantityof use This content downloaded from 139.184.14.159 on Fri, 11 Dec 2015 13:23:49 UTC All use subject to JSTOR Terms and Conditions 72 INTERNATIONAL JOURNAL OF POLITICAL ECONOMY valuesthat can be utilizedby
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