VALUE and DISTRIBUTION in the CLASSICAL ECONOMISTS and MARX' by P

OxfordEconomic Papers 36 (1984), 291-325

VALUE AND DISTRIBUTION IN THE CLASSICAL ECONOMISTS AND MARX' By P. GAREGNANI I. Introduction

1. THE theoryof value and distributionis at presentin a situationof unease and uncertainty:we no longer findthe same general agreementabout its basic elementswhich obtained untila few decades ago. Two main theoreti- cal developmentshave underminedthe dominanttheory which explained distributionand relative prices by means of the "equilibrium" of the two "opposing sets of forces",demand and supplyfor factorsof production. The firstdevelopment in orderof timehas been Keynes's refutationof the doctrineaccording to which a competitiveeconomic systemtends towards the full employmentof labour, i.e. towardsthat equilibriumbetween "demand and supply" of labour, which was to determinethe wage. Keynes' concentrationon the shortperiod, and the persistencein the General Theory of many traditionalpremises favoured the successive attemptsto reconcile his results with orthodox long-periodanalysis: but the weakening of the dominanttheory which nonetheless resulted from his workcan be seen both in the uneasiness which,in ever-changingforms, characterizes the renewed orthodoxy,and in the tendencyof Keynes' directfollowers towards a more radical departurefrom traditional theory. The second developmentconsists in the critiqueof the notionof capital as a "factor of production" measurable independentlyof distribution.2This critiquehas shownthe invalidityof some propositionsof the theory,like the inverserelation between the rate of interest(rate of profit)and the "quantityof capital" per worker,which are basic for the explanationof distribution in termsof demand and supplyfor "factorsof production". The uncertaintywhich has resulted from these developmentsfinds its expressionin authorswho thinkthat new theoreticalapproaches should be explored. It is also revealed by the natureof some of the work carriedout by those who adhere to the traditionalapproach.3 1 This paper whichdevelops under the impactof Sraffa's productionof commoditiesby means of commoditiessome propositionscontained in a Ph.D dissertationof 1955-1958, is based on notes delivered at a conferenceon "Marx's Transformationof Values into Prices of Produc- tion" held in Siena in 1972, and used thenfor lectures given in Cambridgeand elsewheresince 1973-4: in the meantime,references to the ideas contained in them have appeared in other works.I would like to acknowledgethe benefitI derivedfrom discussions with Piero Sraffa and fromcomments from many people and in particularby K. Bharadwaj, A. Campus, B. Cutilli, H. Kurz, and M. Pivetti.Financial assistance by the 'Consiglio Nazionale delle Ricerche' is gratefullyacknowledged. 2This line of criticism,hints of which may be found in Sraffa's 1951 p. XXII, was first broughtto lightin printby Robinson 1953. (See also Robinson, 1973, p. 195.) 3 Thus, the attemptto avoid the difficultiesbesetting the theoryappears to have led to an abandonment of the method based on "long-period positions" of the economic system, characterizedby a uniformrate of profit.This notion had been central to the theory of competitivedistribution and value since the very inceptionof systematiceconomic analysis. (See Garegnani, 1976, pp. 26-29.) 292 VALUE AND DISTRIBUTION

It is perhapsnatural that when thiskind of uncertaintyarises in a scientific field,there should also arise a tendencyto go back into the historyof the subject, and see when and how theorizingtook the turn leading to the presentdifficulties. When we do so and look back over the two centuriesof systematiceconomic analysis,we findthat, at the cost of severe simplifica- tion, we can distinguishtwo successive approaches to the theoryof value and distribution.The moderndemand-and-supply approach had in factbeen preceded by a differentapproach whichhad its centrein a notionof "social surplus". This earlier approach found its firstsystematic expression in Quesnay's Tableau Economique of 1758, became dominantwith the English Classical economistsfrom Smith to Ricardo, and was then taken over and developed by Marx at a time when the main streamof economic analysis was already movingin a differentdirection. 2. The purpose of this paper will be to consider this earlier "surplus approach" to value and distribution.Section II will examine the premises which distinguishit fromthe later demand-and-supplyapproach. Sections III and IV then set forththe problem of "measuring-value"which arose withinit and led to Ricardo's and Marx's explanationof value in termsof the labour necessaryto produce the commodities.At the end of Section IV, Marx's errorwith regard to prices of productionwill be seen as arisingfrom treatingas integralparts of a singlemethod for determining the rate of profit and relative prices, what can be developed as two equivalent but distinct methods for this determination:what we shall call the "Price-equations method" and the "Surplus-equationmethod". The solution based on the firstmethod will be considered in Section V, where it will be shown to consist of the price equations in Sraffa's Productionof Commoditiesby Means of Commodities,1960. The two solutionsobtainable on the basis of the "Surplus-equation method" will then be examined, respectively,in Section VI, dealing withthe "Integratedwage-goods sector", and in Section VII dealing with Sraffa's"Standard system".

II. The "core" of the surplustheories 3. The notion of social surpluscharacteristic of the classical theoriescan perhaps be seen in its simplestform in Quesnay's Tableau Economique, where we findits firstsystematic expression. Quesnay saw that if the social product-which he considered to consist entirely of agricultural commodities-4 was to repeat itself year after year withoutincrease or diminution,a part of it had to be put back into production.Besides the necessaryreplacement of the means of production,this part included the subsistence of the agriculturallabourers. What remained of the annual productafter deducting this part constituteda "surplus", or "produitnet",

4 As is well known,Quesnay excluded manufacturedcommodities from the social producton the groundthat theywere a mere transformationof agriculturalproducts. P. GAREGNANI 293 of which society could dispose without impairingthe conditions of its survival. The fact that the subsistenceof workerswas considered necessaryfor reproductionestablished a directlink between the analysisof reproduction and that of the distributionof the product among the classes into which societyis divided.Thus Quesnay linkedthe surplusto the landowners'share of the social product. And when Smith extended Quesnay's notion of surplusby showingthat surplusoriginated from production in general and not fromagricultural production alone, profitsemerged as a second component of the surplusalongside the rent of land, thus providingthe basis for the English classical economists'theory of distributionup to Ricardo. The determinationof the size of the social surplus was accordinglythe centre around which these theories revolved. In principle this way of determiningthe non-wageshares is simple.Two magnitudesare assumed to be known prior to the determinationof the surplus.They are: (i) the real wage, i.e. the quantitiesof the several commoditiesconstituting the wage rate,5(ii) the social product,i.e. the aggregateof the commoditiesproduced in the year. Since (iii) the technicalconditions of productionof the various commoditiesare also known prior to the determinationof the surplus,a knownsocial productimplies a knownnumber of labourersemployed.6 By multiplyingthe numberof labourersby the knownphysical wages, we obtain the part of the product that goes to the labourers, which we may call "Necessary consumption",using a phrase by Ricardo (1951-58, VI, p. 108). The surplus,i.e. the share of the product going to the classes of society otherthan the labourers,can thenbe determinedby subtractingthe "Neces- sary consumption"from the Social product, taken net of the means of production;7that is: Social product-Necessary consumption = Shares otherthan wages (surplus) (1) 'We are followingthe authorshere discussed in assuminga single "average" or "natural" wage and thus homogeneous labour. As is well known,the possibilityof reducinglabour to homogeneityrests on the suppositionof a constancyin the ratiosbetween the wages forlabour of differentqualities: see Ricardo, 1951-1958 I, pp. 20-23 on the constancyof relativewages (see also Smith, 1910, bk. i ch X vol. I, p. 130). These ratios were in fact leftto be studied outsidewhat will be indicatedbelow as "core" of these theories.(The difficultyraised by taking these ratios as knownin the face of differentphysical compositions of the wages for different kindsof labour, seems to have been implicitlydealt withby takingthe known real wage to be that of common unskilledlabour and then supposingthat the wages of other kinds of labour will tend to remain a constantproportion of it in termsof value.) 6 We are at presentassuming that each commoditycan be producedby means of one method only. The considerationof alternativemethods of productionof the same commodity,which providesone of the two bases forthe notionof a substitutabilitybetween factorsof production characteristicof moderntheory (cf. par. 7 below), can on the other hand only affectwhat has been said here by makingthe employmentof labour associated with a given physicalsocial product depend on the wage rate as well: under the hypothesisadopted in this paper the tendencyto adopt cheaper methodswill bringthe economyto a definitetechnique that giving the highestwage for the given rate of profit.(See Garegnani, 1972, p. 266-7 and 281). 7The assumption that the means of production are physicallyreproduced has the sole purpose of postponingthe complicationsarising out of errorsin Smithand Ricardo's notionof capital (par. 12 below). 294 VALUE AND DISTRIBUTION an equation where "shares otherthan wages" is the only unknown(see also the diagramFig. 1 below).

\ Techniques - Labor Einpl. Surplus =shares / t \ ~~~~~~~~~~~~otherthan S \ \ A< Ad~~~~~~~wages Real Wage - NecessaryCons. w / _

\st ~~~~~~~~~~~//

FIG. 1. A diagram of the "core" in the surplus theories.Underlining distinguishes circumstancesdetermined outside the core. Continuous arrows point to dependent magnitudes inside the "core"; discontinuous arrows indicate influencesstudied outsidethe "core".

The peculiarfeature of these theories-the determinationof the shares of the product other than wages as a residuum or "surplus"-thus has its logical basis in the considerationof the real wage and social productas being determinableprior to those shares. It is to the determinationof the real wage and to thatof the social productthat we musttherefore turn, however briefly,for an understandingof the view of the economic systemwhich underliesthe simple formalstructure of the surplustheories. 4. We have seen how Quesnay and the Physiocratsthought that the quantityof the productretained by the agriculturallabourers was fixedat the subsistencelevel (forexample Turgot 1786, ch. VI). The same was true for Ricardo who, however,while holdingthat an increase in wages above the subsistencelevel would tend to be reversedby the consequent increase in population, also freelyconsidered the possibilitythat the increase be absorbed into "subsistence" as a result of "improved habits" and thus rendered permanent (Ricardo, 1951-1958, II, p. 115). In assessing Ricardo's and Quesnay's view of the wage, it is in factimportant to note that the "subsistence"they referred to was always understoodas determinedby historical,rather than physiologicalconditions. Robert Torrens, to whom Ricardo referredas having "most ably illustrated"the subject (1951-1958, I. p. 97) argued that the "habits of the country"act in this respect as a "second nature" and, accordingly,the "natural price of labour" may vary not only from countryto country,but also in the same countryat the "differentstages of national improvement".And Ricardo' for his part, P. GAREGNANI 295 definedthe naturalwage as including"those comfortswhich custom renders absolute necessaries".' Adam Smith's position regardingthe "average" or "natural" wage was less clear-cutand, in some respects,more interestingthan that of Ricardo. He also saw the wages as tendingto an historicalsubsistence level, but he explained this by the "advantage" which the "masters" have in disputes over wages, ratherthan by any tendencyof the populationto growin excess of the possibilityof employmentoffered by accumulation.Thus, for example, Smithnoted how the "masters" could "hold out" much longerthan the workersin all wage disputes,since the master's"necessity" for the workman is not so "immediate"as the workman'sfor his master,and pointedout how "masters are always and everywherein a sort of tacit but constant and uniformcombination, not to raise wages": a "combination"against which, as Smithsaw it, the combinationsof workers,hindered by law, were of little avail.9 Marx, for his part, was also far fromadhering to a simple theoryof wages based on subsistence.He assertedthat the "regulatingaverage wage" is givenby an historicallydetermined level of subsistence,but the tendency to this "average wage" was the resultof a complex interactionbetween the actual wage and the size of the "industrialreserve army" of unemployed labour: a mechanismwhich gave considerableflexibility to his position on the probable, long-term,evolution of the "average" wage." Thus, at a closer inspection,what all these authorshad in common was not, as is oftenheld, the idea of a wage determinedby subsistence.It was the more general notion of a real wage governedby conditions(often of a conventionalor institutionalkind) that are distinctfrom those affectingthe social product and the other shares in it, and are thereforebest studied separately from them. This separation between the determinationof the

8 Cfr. respectively,Torrens, 1815, quoted in Cannan, 1967, pp. 191-193; Ricardo, 1951- 1958, 1, p. 94. For the social element in subsistence,see also Adam Smith's definitionof "necessaries", 1910, bk. V, ch. II; vol. II, pp. 528-9. 9 In keeping with this view, pointingto the relative bargainingpower of the two classes, Smith saw that in an "advancing state of society", "masters voluntarilybreak trough[their] natural combination. not to raise wages", whereas the contrarywould be true in a "decliningstate of society" (Smith 1910, bk. I, ch. VIII; vol. I, pp. 56, 64). On the idea in Hicks-Hollander 1977, in Samuelson, 1978, and in Casarosa, 1978 accordingto which Smith and/orRicardo would have determinedthe "equilibrium" real wage as that balancing the growthof the supply of labour with that of its demand, resultingfrom accumulation,cfr Garegnani[1983], p. 311. 10Thus, for example, in Capital, vol. I, 1969a, ch. XXV p. 580. Marx admitsthat the real wage could rise in the long run to the extentin which the corresponding"diminution of the unpaid labour ... would [not] threatenthe [capitalist]system itself". This position has impor- tant implications.In particularthe fact that, under sufficientlygeneral hypotheses,technical change cannot lower the rate of profitcorresponding to a given real wage (cf. n. 6 above), entailsthe possibilityof a long-termrise in the real wage whichdoes not "threaten"the system: Marx's erroneous notion as to the possible effectsof technicalchange on profitsled him to discount this possibility.(Samuelson seems thus to move on questionable grounds when in 1971, p. 422 he reduces the question of the validityof Marx's approach to distributionto the question of "whetherreal wages rise or stagnateover a century".For furtherevidence against the idea that Marx held any simple subsistencetheory of wages, cf Baumol, 1983). 296 VALUE AND DISTRIBUTION wage and that of the social product is evident when, as in Quesnay or Ricardo, the wage is explainedin termsof a customarysubsistence, but the same separation between the two problems emerges in Marx and Smith, who admitteda greaterinfluence of currenteconomic conditionson the real wage. It is thisseparate determinationof the real wage that is expressedin its treatmentas a magnitudewhich is knownwhen the determinationof the othershares of the productis approached." As for the physicalsocial product the circumstancesthat were seen to determineit, thatis, basically,the accumulationof capital and the technical conditionsof production,12 were such that it was naturalto suppose it was knownprior to its divisionamong the classes. 5. It is importantto stresshere that this separate determinationof real wage and social product entails a structuringof the analysis which is radicallydifferent from that of the theorieswhich were to become dominant later. The surplustheories have, so to speak, a core whichis isolated from the rest of the analysis because the wage, the social product and the technicalconditions of productionappear there as alreadydetermined. It is in this"core" thatwe findthe determinationof the shares otherthan wages as a residual:a determinationwhich, as we shall see in the nextsection, will also entailthe determinationof the relativeprices of commodities.Further, as a naturalextension of this,we shall findin the "core" an analysisof the relationsbetween, on the one hand, the real wage, the social product and thetechnical conditions of production(the independentvariables) and, on the other hand, the shares other than wages constitutingthe surplus,and the relativeprices (the dependentvariables). An importantpoint to notice is that the treatmentof the real wage, the social product and the technical conditionsof productionas independent variables in the "core" in no way entailed denyingthe existence of influencesof any singleone of these threesets of variablesover the remaining two. The interactionbetween these circumstanceswas in fact freelyadmit- ted by the classical economistsand by Marx. An example is Marx's discus- sion of the "realization" of surplusvalue, in whichthe real wage played a key role in the determinationof the size of the social product(cf. e.g. Marx 1969a, III, pp. 492-49). Anotherexample is the reverseinfluence which the speed of growthof the social productwas generallyrecognized to have fora shorteror longerperiod on the real wage.

" As Marx observed "The foundationof modernpolitical economy .... is the conceptionof the value of labour power as somethingfixed, as a givenmagnitude" (Marx, 1969, vol. I, p. 45). 12 In factif we attemptto reduce analysesas differentas those of Quesnay, Smith,Malthus or Ricardo to theircommon basic elements,what we findis the view thatthe volume of the social product depends on: (i) the stage reached by accumulation,which governs the number of "productive"labourers employed; (ii) the technicalconditions of productionwhich regulate the physicalproduct per labourerand depend in turnon the stage reached by accumulation.(See Smith,1910, vol. I, pp. 1-2). The commoditycomposition of the social product,on the other hand, was studied fromthe angle of the needs of reproduction(cfr. for example Quesnay's Tableau Economique or Marx's reproductionschemes in chapters XX-XXI of vol. II in Capital), or else was leftto be studied case by case as the need arose. P. GAREGNANI 297

Moreover, the fact that those three sets of circumstancesappeared as independentvariables in the determinationof the surplus did not prevent the classical economistsfrom freely admitting influences of the surplusupon them: e.g. the classical economistsgenerally admitted the influenceswhich the level of profitcould have on the real wage, via the speed of accumulation, and Marx went furtherby consideringhow a fall of the rate of profit, consequent upon a rise of the wage rate, may reverse that very rise by checking accumulation and causing technical changes, thus re-creatinga sufficientlevel of labour unemployment(cf. par. 5 above). What the structureof classical analysisdid implywas that these interac- tions and reverse influences,like the influencesof the other factorsdeter- mining wages, social product and available techniques, were left to be studied outside the 'core'. The multiplicityof these influencesand their variabilityaccording to circumstanceswas in fact understood to make it impossibleto reconductthem to necessaryquantitative relations like those, studiedin the "core", betweendistributive variables and relativeprices and betweenoutputs or techniquesand the dependentdistributive variables and prices. 6. Now thisseparation of the analysisinto distinctlogical stages contrasts sharplywith what we findin the later marginalisttheories. In these, the determinationof the wage is in fact inseparable from,and symmetricalto, that of the other shares of the product.Moreover, the demand-and-supply mechanismused in thatdetermination implies that real wages and the other distributivevariables (and hence relative values) can only be determined simultaneously,and simultaneouslywith the volume and compositionof the product.Indeed, in later theory,distribution, outputs, and relativevalues of commoditiesare all determinedsimultaneously taking as data the tastes of consumers,the endowmentsof "factorsof production" and the technical conditionsof production.The determinationof these three sets of data is then seen as fallinglargely outside the domain of economics.As a result,in these theories the determinationof revenues other than wages and of relativeprices comes to includemost of economics.Instead of constitutinga limited"core" of economic analysis-dealing withthe necessaryquantitative relationshipsamong distributivevariables and among them and prices-it becomes almost co-extensivewith economics itself. The more limitedscope whichthe theoryof value has in the surplusapproach13 may howevergive it the greater flexibilitywhich is required by a subject as complex as economics. 1,15

13 The "core" mightin factbe describedas constitutingthe "theoryof value" such as we findin the surplustheories. 14 An importantexample of the greaterflexibility of the "surplustheories" seems provided by the attitude to possible deficienciesof aggregate demand: while Ricardo held that no "general gluts of commodities"were possible, a differentview of the problem was taken by Malthus or Marx, (who also worked within the same "surplus" approach to value and distribution,and were no less consistentwith it on the necessityof "shortchains of reasoning" in economicscf. Marshall, 1961, I, p. 773.) (footnote15 on p. 298) 298 VALUE AND DISTRIBUTION

The remainderof this paper will be exclusivelyconcerned with what has here been describedas the 'core' of the surplustheories. More particularly we shall be concernedwith the part of this "core" whichconsists of treating the real wages, as distinctfrom outputs or techniques,as the independent variable. 7. An effectof the above contrastin the structuringof the two theories may be seen in how modern authors,used to focusingattention on "consumers'choice" in the determinationof outputs,seem oftensurprised by the fact that in classical theories the changes in real wages are considered separatelyfrom changes in outputs,even in outputs of wage goods. The modern focus on consumers' choice and the correspondingsimultaneous determinationof prices and outputs is however an integralpart of the demand-and-supplymechanism for determining distribution just mentioned. Consumers' tastes for goods requiringdifferent proportions of factorsof productionare in fact supposed to determine,together with the choice between alternativemethods of production,the relative"scarcity" of these factors.When the explanationof distributionis different-aswe saw to be the case forthe classical economist-the need to studythe effectsof changes in wages on prices simultaneouslywith their effects on outputsis no longer evident (a similar need to study the effectsof a change in the technical conditionsof productionsimultaneously with its effectson the tastes of consumers-is for example denied in the marginalisttheories using those tastes as data.) It mighthowever be insisted that if non-constantreturns prevail,the output changes resultingfrom changes in real wages (and the consequent changes in prices and techniques adopted) will in turn affect pricesand the distributivevariables other than wages, and hence modifythe relationshipsstudied under the assumptionof givenoutputs. A simultaneous determinationof prices and quantitieswould thenseem requiredin orderto study those relationships.This line of argumentpresumes however the possibilityof expressingthe dependence of outputs upon changes in dis- tributionby means of functionalrelations of the same nature as those postulatedin modern theory,endowed, that is, with known propertiesof

15The classical surplus theories are characterizedby some authors as being concentrated on reproduciblecommodities, and hence "production", as opposed to the concentrationon commoditiesof the scarcitytype and hence on "exchange" whichwould be the hallmarkof the dominantmarginalist theories. Accordingly the two kindsof theorywould deal withtwo distinct series of problems,with an opposite practicalrelevance in relationto time,the classical theory becomingrelevant just when (in the long run) the marginalisttheory becomes irrelevant(cfr. e.g. Pasinetti,1977, pp. 6, 31-33). Whereas it aptlydescribes some differencesbetween the two approaches,this distinction seems not to go to the roots of the difference,which lies in the way in which both "production"and "exchange" are treatedin each approach. The determination of the wage on the basis of the forcesmentioned at par. 5 above-entailing the determination of profitsas a surplusand not by the "scarcityof capital" relativeto labour-also impliesthat the problemsof exchangethemselves cannot be viewed as problemsof "scarcity".This remains true whetherwe consider a short period, or a long period, in which plant in the several industriescan adapt to outputs. (For a criticalview of this criterionof distinctionsee also Roncaglia, 1979 pp. 145-6.) P. GAREGNANI 299 sufficientgenerality and with persistenceover time. If this were in fact possible it would be natural to consider the changes in the quantities produced simultaneouslywith the change in distributionfrom which they originate.But thisview was not thatwhich the Classical economiststook of the matterand, it seems, we today have even betterreasons than theyhad for not takingit. Thus forexample importantchanges in the real wage may have a multiplicityof effectson aggregatedemand, the intensityof which will depend on the particularcircumstances in whichthey occur and cannot, in our present state of knowledge, be reconducted to known functional relationsof sufficientgenerality and persistence.If this is admitted,it will appear that a general determinationof outputssimultaneously with relative prices is impossible,and thatthe basic procedurecan only be thatfollowed by the classical authors. They analysed changes in prices and outputs by what we may describeas two distinctlogical stages. In the first,the effectof the change in real wage was examinedwhile takingthe outputsas given. In the second stage, the possible effecton outputsof the initial change was analysed in accordancewith the circumstancesof the case under considera- tion,jointly with its possible secondaryeffects on prices and distribution,in the case of non constantreturns to scale (cf. Garegnani,1983 pp 311-312).

III. Ricardo's measurementof the value of aggregatesby means of embodied labour 8. We have seen the rationale behind takingthe Social product and the Necessary consumptionas given physicalaggregates when determiningthe shares otherthan wages in the surplustheories. But how are we to measure those two magnitudesin equation (1)? As we shall presentlysee, the theory cannot stop at conceivingthem as physicalaggregates and mustproceed to their measurementin value; will these values also be given when the physical aggregates are given? It is in connection with this problem of measurementthat the surplustheories of distributionmeet the question of value and with it, their chief analyticaldifficulty. The remainderof this paper will turnon thisquestion whichwill be taken up in the comparatively advanced formit assumedin the theoryof profitsof Ricardo's Principles.'6 Since we are concerned with aspects of the Classical problem of value whichare independentof the rentof land, we shall assume thatfertile land abounds and thatrent can accordinglybe ignored."7Thus, on the righthand 16 We are thusnot concernedhere withthe physicalmeasurement underlying the reasoningin both Ricardo's earlier Essay on theInfluence of a Low Price of Corn on the'Rate of Profit,and Quesnay's Tableau Economique (on these points cf. respectively,Sraff a, 1951, pp. xxxi-xxxii. n. 4, and Sraffa,1960, p. 93). 17See above par. 6. We may however notice how the characteristicseparation between determiningthe quantitiesproduced and determiningthe shares of the product other than wages (par. 6 above) allowed Ricardo to isolate the share of land rent.This separation(and the implicitassumption that each worker is assisted by the same capital, whatever the land cultivated,or the intensityof its cultivation)allowed Ricardo to take as given the productivity of labour on the no-rentland or, even, thatof the last labourerempoyed on land alreadyunder cultivation(on the latterpoint, cf. Ricardo 1951-1958, vol. I, p. 71). 300 VALUE AND DISTRIBUTION

side of equation (1) we shall findaggregate profits. Two observationsare however necessary in order to proceed to the rate of profit,on which Ricardo's interestwas in factfocused. The firstis that in Ricardo, as in the otherClassical economists,a yearlyproduction cycle is implicitlyassumed;18 the wages are supposed to be advanced at the beginningof the cycle and are thereforea part of capital. The second observationconcerns the factthat in determiningthe rate of profitRicardo operated as if capital consisted entirelyof the wages advanced for the year. In fact he saw the divisionof the product between wages and profitsas the only factor capable of influencingthe rate of profit,thus ignoring the independent influence exerted by the proportionbetween labour and means of production.19In order to give an account of his theoryof profitwhich is both consistentand sufficientlyfaithful, we shall assume thatproduction requires only very simple means of production,which can be ignored. Under the above assumptions,the annual rate of profitwill be expressed by the ratio between the social surplusand the annual wages or "Necessary consumption",i.e.

Social product- Necessaryconsumption (2) Necessary consumption 9. Suppose, now, thatthe "Necessaryconsumption" advanced to workers is reproducedin kind duringthe year and the yearlyaggregate profits can accordinglybe reckonedin physicalterms, that is, as a surplusproduct. Even under this most favourablehypothesis it would be impossibleto stop at a

18 "A year is assumed in politicaleconomy as the period whichincludes a revolvingcycle of productionand consumption"(James Mill, 1821, p. 185). 19 Cf. for example: "whetherthese increased productions,and the consequentdemand they occasion, shall or shall not lower profitsdepends solely on the rise of wages" (Ricardo, 1951-1958, I, pag. 298, our italics; for a similarstatement cf. also ibid pp. 289-292). More generally,Ricardo failed to show any awareness that the rate of profitcan change for causes otherthan changesin the proportionbetween wages and profitsin the (net) social product.The originof thiserror, which Ricardo sharedwith his contemporaries,can be tracedback to Adam Smith.In a well-knownpassage of Wealth of Nations he had argued that,although it may be thoughtthat besides wages, profitsand rents,the price of a commodityalso includesall that is necessaryfor replacingthe means of production,yet since the prices of the latterare in turn made of those parts,the entireprice "resolves itselfeither immediately or ultimatelyinto the same three parts of rent,labour and profit"(Smith, 1910, I, pp. 44-45). From this view of prices, in which we find in germ the correctidea of reducing capital to wages (and rents) advanced for variousperiods of time,Smith often slipped into the altogetherdifferent idea that capital can be reduced to the wages advanced for the currentyear. Marx indicated the above deficiencyof Ricardo's analysis as an erroneous identification between rate of profitand rate of surplus value (cf. for example, 1969, II, p. 463). Marx's criticismof Ricardo seems to have been misapprehendedas an accusationthat Ricardo "ignores non-wagecapital, at least when referringto the economyas a whole" (Steedman,1982, p. 126). However Marx did not deny thatSmith and Ricardo saw the existenceof means of production (cf. forexample the carefullyworded passage in 1969a, III, p. 841 and n. 51): what he said was that Ricardo ignoredthe effectof changes in the proportionof labour to means of production on the rate of profit(Marx, 1969, II, p. 373; on this point cf. also G. De Vivo 1982, pp. 91-92). P. GAREGNANI 301 physicalnotion of the two magnitudesinvolved, because the surplusproduct and the necessary consumptionwould generally consist of commodities whichare different,or are taken in differentproportions. The ratio between the two aggregateswould give the quantityof "surplusproduct" (a composite commodity)per unitof "necessaryconsumption" (a differentcomposite commodity),but not the rateof profit, i.e. the ratiobetween the values of the two magnitudes. In the PrinciplesRicardo is accordinglyfaced withthe need to measure the Social product and the Necessary consumptionin value terms and, hence, withthe problemmentioned above: will these given physicalaggregates also be given when expressed as value magnitudes? If the value expression of either aggregatewere to depend on the rate of profit,the determinationof profitsas a surplusin accordance withequation (1) or (2) above is threatenedby circularreasoning. Ricardo's startingpoint in dealing with value was Smith's theoryof the "naturalprice". Smithhad definedthe naturalprice as the sum of the wages and profits(we are ignoringrents) which must be paid in order to produce the commodity,reckoned at their "natural" or "average" rates (Smith, 1910, bk. I, ch. VII, pp. 48-51). As forthe unitin whichthese naturalprices should be expressed,Smith had suggesteda "real" or "invariable" measure of value consistingof the quantity of labour which a commoditycan "command", thatis, in modernterms, the wage unit (ibid,bk. I, ch. V, vol. I, p. 28). If, however,we use Smith'smeasure in equations (1) or (2) we are faced with exactly the difficultywe mentioned above: the value of the physicallygiven social productwill not be knownbefore the rate of profitis known.Take, for example, an economy employing3 millionworkers. The Necessary consumptionwill "command" 3 million labour-yearsand be a known magnitude.But the same will not be true for the Social product: with,for example, the capital consistingonly of the wages advanced yearly we assumed above, the Social product will command 3(1 + r), million labour-years,where r is the rate of profit,namely 3.3 m. if r= 10%, but 6.6 m. if r = 120%. We may accordinglyseem to be reasoning in a circle when we follow the surplus approach and attemptto determineprofits by differencein accordance with equation (2): in order to do that we need to know the size of the Social product,which is not knownuntil we know the veryrate of profitwhich is to be determined.20This dependence of the value of the product upon distributionmeans that, when we look at the Social product and the Necessary consumptionin value terms,the constraintby which one class cannot have more withoutthe other class having less-so evident if we could look at the product in physical terms-is no longer

20 The difficulty,however, is ultimatelythat of expressingthe capital requiredin production independentlyof distribution,(cf. Garegnani, 1960, pp. 18-19). Thus, we shall see in Section VI below how measurementsin termsof commanded labour are in fact compatiblewith the determinationof the rate of profitsin accordance withequation (2) above. 302 VALUE AND DISTRIBUTION

apparent:might not the real wage rise withoutaffecting the rate of profit,or vice-versa? Indeed Smith himselfoften lost sight of the constraintand envisaged the rate of profitand the wage as determinedindependently of each other.He wrote that "the naturalprice varies with the naturalrate of each of its componentparts" (Smith,1910, bk. I, ch. VI, vol. I, p. 56) giving rise to what has been described as Smith's "adding up theoryof prices" (Sraffa,1951, p. xxxv).21 And, afterSmith Malthus could argue that a tariff on corn would raise both the rent of land and the rate of profits,without apparentlyseeing the consequences these rises would be bound to have upon the real wage (e.g. Malthus 1951, p. 398, and passim).

10. Ricardo's greatmerit was in factthat he saw throughthese "appearances" (cf.par. 11 below) and broughtconsistency back intoeconomic theory. This achievementof Ricardo's Principleswas renderedpossible by relating the exchangevalue of the commoditiesto the quantityof labour necessary to produce them. Let us in fact suppose that the proportionbetween wages and profitsin Smith'snatural prices are the same for all commodities-as theywould be underour assumptionat par. 8 of a capital consistingonly of the advanced wages. All commoditieswould then exchange accordingto the quantityof labour required for theirproduction. The ratio between the values of any two aggregatesof commodities-or between sums or differencesof such values-would accordinglybe equal to the ratios between the respective quantitiesof labour embodied.22The value of Social product and of the Necessaryconsumption in equation (2) could then be "measured" in terms of the quantitiesof labour embodied, here indicatedby P and N, and we

21 Adam Smith's "adding-up theory of prices" seems often to have been construed as anticipatingthe demand-and-supplyexplanation of value and distributionof the latermarginal- ist theories,in contrastwith the explanationof the same phenomenalater provided by Ricardo. Thus, in 1954, p. 189, Schumpeterwrites of Smith'sconception of the "natural price" as "the rudimentaryequilibrium theory of chapter 7 [of the Wealth of Nations which]... points towardsSay and, throughthe latter'swork, to Walras", and originatesa "Smith,Mill, Marshall line" whichwas rivalto thatof Ricardo (ibid. 530, cf. also ibid pp. 557-558; 567-568, 599). A similarinterpretation is adopted by Maurice Dobb who, in 1973, refersto Smith's"determination of the generallevel [of wages and profits]by conditionsof supplyand demand forlabour and capital respectively"(p. 50, cf. also p. 112, and passim). This view of Smith'sapproach to value and distributionseems to overlook that,behind Smith'svague referencesto the rate of profitas determinedby the "competition"of capitalists,there lay, as we saw, the inconsistency of rates of wages, profitsand rent determinedindependently of one another.And it was just thisinconsistency that Ricardo and Marx criticisedSmith for. The demand and supplyforces of the modern theories, founded as they are, on the "substitutability"between "factors of production',(cf. above p. 76) are as absent in Smithas theyare in Ricardo. 22 As we saw in par. 9 the rate of profitcan be directlyenvisaged as a relativevalue, namely the value of the Surplusproduct (a compositecommodity) in termsof the Necessaryconsump- tion (a second compositecommodity): if all individualcommodities exchange accordingto the quantityof labour embodied, the same will be true of these two composite commodities: When the economyis not replacingits wage capital,equation (3), writtenas r = (PIN) - 1, shows how the rate of profitcan still be derived froma relative value: that of the Social product, relativeto the Necessaryconsumption. P. GAREGNANI 303 would obtain the rate of profitr as P-N N (3) where P and N are now known magnitudes.Thus, if we returnto our example of an economywith 3 m workers,a doublingof the real wage and, hence, of the labour requiredfor the productionof its constituentsfrom, for example, 1/3to 2/3 of a labour-year,would make the rate of profitfall from (3 - 1)/1= 200% to (3 - 2)/2= 50%. The constraintbinding changes in wages and changesin the rate of profitbecomes selfevident and no space is leftfor the illusion,generated by the appearance of price as a sum of wages and profits,that the rivalrybetween capital and labour "tends to increase the value of the productto such an extentthat each receivesa largerpiece" (Marx, 1969a, III, p. 503). In yetanother quotation from Marx, relatingpar- ticularlyto Ricardo: "It is thegreat merit of classical economy to havedestroyed this false appearance and illustion,this mutual independence ... of the varioussocial elementsof wealth"(Marx, 1969b, III, p. 830). 11. It may here be appropriateto notice how the nature of Ricardo's contributionin overcomingthe errorimplicit in Smith'sadding-up theory of pricesmay help us to comprehendMarx's oftenmisunderstood position with respectto what he called "vulgarpolitical economy". Ricardo had begun to overcomethe difficultieswhich had preventedhis predecessorsfrom seeing the constraintbinding wages to profitsand rents:however his verysuccess in bringingthis to lighthad the resultof exposingthe class antagonismswhich underlie the division of the product. In this situation, the attempt to preserve a harmoniousview of society took-Marx thought-the formof turninga blind eye upon the analyticaladvances of Ricardo and keeping closer to the "appearances" by whichthe price of the product,seen as the sum of profits,wages and rents,may seem capable of accommodatingthe rise in one of these elementswithout a decrease in the others. In Marx's ironicwords, already referred to above, these economistsheld that: "Even ifthis occasionally brings them to blows,nevertheless the outcome of this competitionbetween land, capital and labourfinally shows that, although they quarrelwith one anotherover the division, their rivalry tends to increasethe value of the productto suchan extentthat each receivesa largerpiece, so thattheir competition,which spurs them on, is merelythe expressionof theirharmony Marx,1969a, III, p. 503. The fact that these views were the result of adhering,as popular thought often does, to "appearances" explains the specificadjective "vulgar", i.e. popular,which Marx applied to these economists.Accordingly, Marx defines as ''vulgareconomy" that"economy" "whichdeals withappearances only", in contrastwith "classical politicaleconomy which has investigatedthe real relationsof productionin bourgeoissociety" (Marx, 1969b, p. 85, n. 1). In 304 VALUE AND DISTRIBUTION this"vulgar economy" he includes,if not the workof Say himself,that of his followersin France and Germany (Marx, 1969a, III, p. 500), and that of Seniorand hisfollowers (Marx, 1969b, pp. 596-7). Marx's frequentreference to the existenceof "vulgar representations"in Smith,an author forwhose scientificachievement he had the highestrespect, seems on the other hand apt to bringout the specific,and not merelyderogatory, meaning which he attributedto the expression"vulgar economy". The distinctionby Marx between 'vulgar' and 'classical' politicaleconomy turnedthus on a second, even more basic distinctionbetween two kinds of representationof the economic relationsof bourgeoissociety. There are, on the one hand, the "apparent relations" or "connections",which are those perceivedby the unsystematicobserver and whichare representedin Adam Smith's"adding up" theoryof prices,when "instead of resolvingexchange- value into wages, profitand rent[he] constructsthe exchange-value of the commodityfrom the value of wages, profitand rent,which are determined independentlyand separately"(Marx, 1969a, II, p. 217). In such an inconsis- tent representationof the economic system"[the] contradictorycharacter [of capital] is totallyconcealed and effaced... no contradictionto labour [is evident]"(Marx, 1969a, III, p. 467). There are, on the otherhand, the "real relations" constitutingthe "intrinsic", or "inner connections" of the bourgeois system.These are the relations broughtto light by systematic scientificanalysis. They centreon the constraintthat binds changesin wages to changesin profitsand rentsand reveal the economic antagonismbetween classes (forexample, Marx, 1969a, II, p. 166). Now, forMarx, these "inner connections"required, in orderto be revealed,that the productbe measured independentlyof its division between the three classes. Hence the role of Ricardo's measurementof values in termsof labour embodied in which,in Marx's own words, the value of the commodity"does not depend upon its divisioninto wages, profitsand rents"and constitutesinstead "the limit... forthe dividendswhich the labourers,capitalist and landlordwill be able to draw fromthis value in the form of revenue, wages, profitsand rents"; Marx, 1969b, III, p. 854; cf. also p. 274 and 1969a, II, p. 219.23

23 When faced with passages like the ones above, it seems surprisingthat various authors followingwhat looks like an establishedtradition, should attributeto Marx's theoryof value some "qualitative" role differentfrom that which the theoryhad in Ricardo, i.e. that of measuringthe productindependently of its division(cfr. P. Sweezy, 1946, p. 33; the idea finds an earlyexpression in Hilferding1949, e.g. pp. 130-132. A recentclear-cut expression of this positionmay be foundwhen it is claimed that "the idea that the theoryof value developed in vol. I of CAPITAL is a (bad) theoryof relativeprices is ... untenable" (Medio, 1977, p. 382). Medio (a participantin the Siena conferencementioned above) appears howeverto contradict thisclaim of his, when in the verynext line, he admitsthat "the cost of productiontheory of price seems to be unsatisfactory[because] it contained an apparentelement of circularity... the calculation of the rate of profitrequires valuing [product,wage goods and means of production]at their equilibriumprices. The latter,however, can not be calculated without knowingthe rate of profit".Here indeed we have a verygood reason forMarx's "bad" theory of relative prices: for what means were available to Marx for breaking that "apparent circularity"if not the labour theoryof value developed by Ricardo for that verypurpose? P. GAREGNANI 305

IV. Marx's "prices of production" 12. And for this analysisof the innerorganic connection" binding wages and profits,Marx took the road whichRicardo's theoryof value had opened up for him. As we saw (par. 8 and n. 20) when determiningthe rate of profitRicardo had operated as if capital could be resolved entirelyinto the wages advanced for the year. Marx started by clearing up this confusion which Ricardo had inheritedfrom Smith. He showed thatthe proportionwhich the means of productionbear to the labour (and hence, to the wages advanced) constitutesa factorwhich can influencethe rate of profitindependently of the proportionin which the productis divided between wages and profits. Accordingly,he distinguishedcapital into two parts: the wages advanced or "variable capital" and the means of productionor "constant capital". To simplifyour exposition,we shall assume that constant capital is entirely consumed during the yearly productioncycle (i.e. consists of circulating capital) and shall retain the assumptionof free land. If, then,commodities exchangedaccording to the quantitiesof labour embodied,the rate of profit would be determinedas r= s (4) c + v where c and v are respectivelythe "constant" and "variable" capitals, measured in termsof the labour necessaryto produce them,whereas s, the social "surplusvalue", is Ricardo's (P-N) and is measuredby the quantity of "surplus labour", the labour exerted in the year over and above that necessaryfor reproducingthe wages.24 Commodities however do not exchange according to the quantities of labour embodied. If we look at "natural" prices as resolvingthemselves into wages and profits,as Ricardo did, we findthat these wages and profitsare presentin differentproportions in the prices of differentcommodities and the latterdo not, therefore,exchange in proportionto the labour necessary fortheir production. Ricardo had admittedthis in termsof "modifications" to the rule that commoditiesexchange accordingto the labour embodied: his argumentconcerning profits continued however to restultimately on that rule.25 24 Equation (3), by which we expressed Ricardo's determinationbecomes, in the new symbols,r = s/vand its differencefrom equation (4), due to Marx's considerationof the organic compositionof capital,may become clearerif we rewriteequation (4) as s/v r=(c/v) + 1 25 Ricardo struggledwith that problem untilthe end of his life. Cfr. the paper On Absolute and Exchangeable Value, Ricardo 195 1-58 V, whichwas in factwritten in the summerof 1823, just beforehis death. A misunderstandingof the positionof Ricardo and of Marx's criticismof it seems to occur when in Steedman 1982, it is assertedthat Marx was "quite wrong... to say that Ricardo's approach was inherentlyincapable of providinga theoryof the rate of profit", (continuedoverleaf ) 306 VALUE AND DISTRIBUTION

Marx faces the question in the manuscriptsposthumously published by Engels as vol. III of Capital and, in the sketch of a solution he provides there, he comes withinone step of a correct general solution. He even indicatesthe step whichis yetto be taken-though, as we shall see, he failed to realize its consequences.26 13. There, Marx startsby askinghimself why commodities do not generally exchange accordingto the quantitiesof labour necessaryto produce them.The answerhe givesis simple: if commoditiesexchanged according to that principle,those produced with capital of a higher "organic composition" (i.e. a higherproportion of "constant" to "variable" capital) would give a lower rate of profit.Thus, suppose that only corn and steel are where,as the contextshows, "Ricardo's approach", as distinctfrom Marx's, would be founded on the idea that "the general rate of profitand the prices of productionmust be determined simultaneouslywithin the theory"(ibid. p. 124). In factthe basis of Ricardo's argumentin the Principles,is the assumptionof the constancyin the value of commodities"in the productionof whichno additionalquantity of labour is required" (e.g. Ricardo, 1951-58 I, pp. 110-11.1). Ricardo's actual procedure seems thereforeno differentfrom Marx's in admittingthat com- moditiesdo not exchangeaccording to the quantityof labour embodied,but in determiningthe rate of profitas if they did so exchange-by looking, that is, for a commoditywhich would constitutea "medium",such that"Those on the side of thismedium would rise in comparative value witha rise in the price of labour. . . and those on the otherside mightfall fromthe same cause" (Ricardo, 1951-58, for Marx cf. p. 34 below). Moreover Ricardo, like Marx, uses the rate of profitso determinedto ascertain how far the relativeprices of commoditiesdeviate from,or change independentlyof, the relativequantities of labour embodied. The main differencebetween Ricardo and Marx lies thereforein whetherthis logical orderis explicitlyfollowed and justified,as it is by Marx, or has instead to be extractedfrom an argumentwhich, if taken literally,far from being a "simultaneous"determination of prices and the rate of profit,would be contradictory,since it would rest on ignoringthat very dependence of relative prices on distributionwhich is admitted elsewhere in the argument.Now, this criticismof Ricardo is preciselythe one expressed by Marx when for example he charges Ricardo with a "erroneous confusionof cost prices and values" (Marx, 1969, II, p. 199). It would on the other hand contradict the facts to view Ricardo's procedure as a better preparationthan Marx's for the later simultaneousdetermination of prices and profits:when the lattercame, with Bortkiewicz,Seton and Sraffa(cfr. n 32 below) it grew out of Marx's equationsfor prices of production,rather than directly out of Ricardo's less definiteprocedure. 26 We mayhere noticethe curiousmisunderstanding according to whichthe labour theoryof value is held to be incompatiblewith the existenceof alternativetechniques (cf. Morishima, 1973, p. 189, Steedman, 1982, p. 65). The dependence of labour values on the technique adopted would not in factprevent their use in determiningthe rate of profit,any more than the similar dependence of physical inputs prevents them from playing the same role in price equations (8) below: labour values would allow determiningthe rate of profitcorresponding to each technique,and hence that which could be shown to rule under free competitionat the givenwage (cf. p. 3 n. 6, above). Here we may also noticethe misconceptionby whichSamuelson in 1974, p. 292, writesthat "in a regimeof values ... the techniquethat minimizes values at r = 0 willminimize them for all r's, a shortcomingof the values model". A confusionoccurs here between the labour theoryof value, by which the several commoditiesexchange according to embodied labour-and the differentconditions under which costs for the same commodity,produced with alternative techniques,should equal the ratio between the respectivequantities of labour embodied,when the techniquemaximizing the net productper workerwould in factdominate at all levels of the real wage. Equal organic composition as betweencommodities does not conceptuallyentail equal organiccomposition as betweenalternative techniques, as shown forexample by Samuel- son's "surrogateproduction function", 1962, whichrests entirely on labour value conditions,but clearlydoes not entail dominationof one techniqueover all others. P. GAREGNANI 307 produced in the economy and, the "rate of surplus value" s/v being for example 1, the organic compositionc/v is 1 for corn and 3 for steel: steel productionwould give a rate of profitof 25% as against the 500/oof corn prodution.The competitivetendency to a uniformrate of profitwill then make steel exchangefor more thanthe quantityof corn embodyingthe same amount of labour, so as to raise the surplusvalue (the differencebetween value of outputand value of capital) in steel productionand lower it in corn productionuntil the two ratesof profitbecome the same. It may thenappear thatthe divergenceof the priceof steel in termsof cornfrom the ratioof the respectivequantities of labour embodied, has the meaningof redistributing surplus value away fromthe surplus industriesto the "deficit" industries (fromthe corn industryto the steel industryin our example). Marx in fact arrivedat thisconclusion and argued thatwhen the redistributionhas been completed,we shall findin each branchof productionthe same rate of profit we obtain in equation (4), by distributingtotal surplus value over total capital:27 just as when 5 sacks of corn are re-distributedproportionally among 10 people, each will end up with 5 of a sack, irrespectiveof the initial distribution.The prices of productionthat ensure this resultwill be those obtainedby applyingthe rate of profitcalculated in equation (4) to the capital used in each branch.In our steel and corn economy:

(SSAS+ scAc) (5) (csAs + ccAc) + (vsAs + VcAc) Ps = (Cs+ Vs)(I + r)l (6) pc = (CC+ vc)(l + r)J in whichthe prices of productionps of steel and pc of corn are referredto physicalunits of the two commoditiesrequiring a unit of labour for their production (so that cs + vs + s = cc + vc + sC= 1), and As, Ac indicate the quantitiesproduced of the two commodities.The way in which r is calculated implies on the other hand that the prices ps and pc are expressed in termsof the compositecommodity constituting the social product,taken in the quantityrequiring a unit of labour for its production.28 This reasoning(according to whichthe rate of profit-the key variable of the system-is determinedby equation (5) as if commoditiesexchanged in proportionto the quantitiesof labour necessaryfor their production, may go a long way towardsexplaining why Marx thoughtit possible to conducthis argumentin vol. I and II of Capital on the basis of just that assumption, postponingto vol. III the determinationof the prices of production.) 14. If this is what we findin the posthumouslypublished Chapter IX of Book III of Capital, Marx did not fail to notice a shortcomingin this

27 Cfr. for example the illustrationof the cotton mill in Marx 1969a, III, p. 155. 28 Marx's conditionthat total prices should equal totalvalues is in factequivalent to takingas numerairethis particular composite commodity, which is also thatproduced with the "average" organiccomposition. 308 VALUE AND DISTRIBUTION intended solution. Competitionwill distributeprofits in proportionto the "prices" of the constantand variable capitals,and not in proportionto their "values" (i.e. the quantities of labour embodied). He wrote accordingly "thereis alwaysthe possibilityof an errorif the cost price of a commodityin any particularsphere is identifiedwith the value of the means of production [and variable capital] consumed by it".29 Marx seems to have leftthe question there. Had he attemptedto correct that"error", he would soon have foundthat the price equations modifiedby estimatingthe capitals at theirprices mustdetermine not only the prices of productionbut also the rate of profit:equation (5) would thereforehave stood out as incorrect.Let us in factmodify equations (6) by expressingboth the constant capital, assumed here to consist of steel, and the variable capital, consistingof "corn", in termsof prices. We obtain

pc = (ccp,+ vcpc)(1+ r)} PS= (csPs+ vspc)(l+ r) ( It is sufficientto divide both equations by one of the two prices,say pc to realize thatMarx's two independentprice equations containin factonly one unknown,the relativeprice ps/p,and are thereforecontradictory if r is to be determinedby equation (5): in the price equations the uniformrate of profit can only be determinedsimultaneously with the relative price of the two commodities. It is not difficultto see wherelay the faultin the notionof a redistribution of surplusvalue which,as we saw, led Marx to equation (5). Unlike the 5 sacks of corn which do not change in size relativeto the 10 people in the course of the redistribution,the size of the social surplus value does so change relativeto capital. This surplusvalue is in fact the price of production of the surplusproduct, and cannot but change relativeto thatof social capital when, with the redistributionof surplus value, relative "prices" in general come to divergefrom relative "values".30 As we saw in par. 9 the profitrate is but the relativevalue of those two compositecommodities and it will not be equal to the ratio betweenthe quantitiesof labour embodied in them any more than the relativeprice of any two commodities. 15. There is, however,a sense in whichMarx's errorwas suggestive.The errorcan be envisaged by us as the resultof treatingas integralparts of a single method (for the determinationof the rate of profit)what are in fact when consistentlydeveloped, two equivalent methods, each of which is

29 Marx, 1969a, III, p. 165. As is well knownMarx indicatesby 'cost-price'the value (price) of the capital (constantand variable) used up in the productionof the commodityin question. Marx continues the passage quoted above with the words "our present analysis does not necessitatea closer analysisof this point". 30 It is curious to note how Hilferding,in his answer to Bohm Bawerk's critiqueof Marx, neatlymisses thispoint when he writes:"It is obvious thatthe change in distributionmakes no differencein the total amount. . . of surplusvalue undergoingdistribution". Hilferding 1949, p. 160. P. GAREGNANI 309 sufficientto determinethat rate. The first,which we may call the price- equationsmethod, is exemplifiedby equations (7) and determinesthe rate of profits-or, more generally,the relation between the wage and the profit rate-simultaneouslywith relative prices. However, the basic idea of profits (the non-wage share) as a surplusproduct, which they can be seen to be wheneverthe economyis in a self-replacingstate, inevitably leads one on to attemptsome simplermethod. The lattermethod, which we may here call the Surplus-equationmethod, is exemplifiedby equation (4) or (3) for the case in which commoditiesexchange according to the labour embodied. Essentially,it depends on the possibilityof expressingboth the surplus and the capital that appear in the equation in termswhich are proportionateto theirvalues but do not containthe unknownprices, so thatthe profitrate is the only unknown. As sections VI and VII below indicate, this second method is also available for sufficientlygeneral hypothesesand it appears to exhibitsome advantagesof simplicityand transparencyover the Price-equationsmethod.

V. The "Price-Equations Method" of determiningprofits 16. The "Price-equationsmethod" consistsof the generalizationof equations (6). In these equations we assumed thatconstant capital consistsof one commodityonly. When that assumptionis abandoned, the constantcapital of each industryhas to be distinguishedinto as manyquantities of embodied labour as there are kinds of means of production.To each of those kinds a differentprice of production applies: the additional unknownprice thus introduced will entail an additional price equation.3' Matters are even simplerfor the variable capital: the assumptionof a uniformreal wage ensures that in all industriesvariable capital consistsof the same composite "wage commodity":we may thereforeapply to it the single price obtainable from the prices of its constituentcommodities. We may now writethe price equations obtained by generalizingequations (6) for the case of any number k of commoditiesa, b,... k.

31 A determinationof the rate of profitbased on Marx's price equations was proposed as early as 1907 in L. von Bortkiewicz,1949. In thatarticle Bortkiewicz acknowledged a debt to Tugan Baranowsky,who had used a similarmethod to show that Marx was mistakenin his determinationof the rate of profit.It is fromthe latter author that Bortkiewiczapparently derived the groupinginto three sectors (means of production,subsistence goods and luxury goods) of the variousindustries to whichMarx had separatelyreferred when dealingwith prices of production.The aggregationof the means of productioninto a single sector is however in contrastwith the need to disaggregateconstant capital, and Bortkiewiczhad to referto a single price of production,thus treatingthe price systemas if only one capital good existed in the economy.Bortkiewicz's aggregation of constantcapital also helped to hide the factthat, as we shall see below, the measurementin termsof labour embodied of the elementsof capital can be replaced by a physicalmeasurement. However, a second solution to Marx's problem of the determinationof the rate of profitwhich did not sufferfrom the deficiencyof the aggregationof capital goods and was based on work by Dmitriev was advanced in Bortkiewicz,1954 (cf, below p. 23, n. 39). 310 VALUE AND DISTRIBUTION

Let: a be produced duringthe year by La labourers assisted by the constant capitals Aa, Ba, ... Ka, (some of which may be zero) consisting of commodities a, b... k; thus requiring a total quantity A La + Aa + Ba + ...+ Ka of direct and indirect labour;

Lb, Ab, Bb, Kb, B; ...; Lk, Ak, Bk, - Kk, K, be the analogous quantities in the production of commodities b... k; w be the quantity of labour necessaryto produce the given real wage; Aa,Ab, ..Ag (such that a. +Xb + Ag=1) be the quantitiesof labour embodied in the wage goods, g in number,constituting a unit of the "wage commodity"A, whichwe then choose as the numeraire. We shall have:

[(AaPa + BaPb + KaPk) + Law](1 + r) = Apa [(AbPa + BbPb+... Kbpk)+ Lbw](l + r) = Bp, ...... (8) i...... 8 [(AkPa + Bkpb + K-IkPk) + LkW](l + r) = Kpk AaPa + AbPb+ ... Agpg= 1 Equations (8) are (k + 1) in number and contain the same number of unknowns:the rate of profitr and the k prices of productionPa, Pb Pk It can now easily be seen thatthe need to distinguishthe constantcapital of an industry,say a, into the quantities Aa, Ba,... Ka also makes it inessentialto measure them in terms of labour embodied: the prices of productionPa, Pb, P--Pk can be directlyapplied to the physical inputs of a, b, ... k, and the same applies to the variable capitals (Law), (Lbw), etc., consistingof the composite"wage commodity"(which, being our numeraire, has a unit price).32 These physical measurementsare clearly preferable, because they only depend on the method of productionof the commodity concerned and not, in addition,on the methods of its direct and indirect means of production,like the correspondingquantities of labour embodied. Equation (8) can thereforealso be read withthe quantitiesw, Aa, Ba, etc., taken as physical quantities.33Henceforth we shall adopt this alternative readingof equations (8). Equations (8) are however those we findin Sraffa's Productionof Com- modities by Means of Commodities,Chapter 11.34 Sraffa's own symbolswere

32 The possibilityof physicalmeasurements in Marx's equations of the prices of production, when modifiedby applyingprices to the capitals, appears to have been firstnoted in printin Seton, 1957, p. 151, n. 3. 33 Even the numericalvalues of the coefficientswould remainunchanged if we choose forthe unit of each commoditya, b, ... k, the quantityof it requiringa unitof labour forits directand indirectproduction. 31 Cf. the equations in Sraffa1960 p. 6, which differfrom equations (8) above, because in Sraffathe wages are included, commodityby commodity,in the quantitiesof the means of production. P. GAREGNANI 311 chosen forequations (8) so as to bringout the factthat his equations are the same as Marx's equations (5) and (6) once these are modifiedby applying theprices of productionto variable and constantcapital. The factthat such a modificationhad been suggestedby Marx himselfhas not preventedit from changinghis equations (5) and (6) beyond easy recognition.The essential point howeveris that equations (8) provide a general solutionfor precisely the same problem which Ricardo and Marx had faced by means of the labour theoryof value. The characteristicpremises of the surplusapproach, forwhich the real wage and the social productare given when determining the rate of profitand relativeprices (par. 4 above) have remainedunaffected and, therefore,the notionof profitsas a residual and the associated view of the forcesdetermining distribution have also remainedunaffected. 17. Equations (8) are howeverless transparentthan Ricardo's and Marx's equations (3) and (4) were about the forcesgoverning the rate of profit.The basic asymmetrybetween a wage independentlydetermined and profits resultingas a residual is obscured: in equations (8), to envisage profitsas a differencebetween the value of the product and that of the wages and means of productionmakes no more sense than the reverse procedure of obtainingthe value of the productby adding the profits,the wages and the value of the means of productiontogether. More fundamentallythe question is that these "appearances"-the very ones which had misled Smith and later authors into thinkingthat profitsand wages could be determined independentlyof one another-make it more difficultto graspthe properties of the system. These "appearances", which Ricardo had overcome by measuringvalue in termsof embodied labour, are in factengendered by the difficultyof viewingthe effectsof the interdependenceof prices,and are here dispelled by the mathematicalconsideration of the systemof price equations.35Thus, fromequations (8) it resultsthat once the real wage is given, the rate of profitis determined,so thatthe two cannotchange independently of one another.Moreover, system (8) reveals that,under sufficientlygeneral conditions,there exists an inverserelation between the real wage and the rate of profit(below par. 20). But a reasoningthat relies on theoremswhich abstractfrom the contentof the problems analysed cannot fullyovercome the difficultyof graspingthe effectsof the interdependenceof k + 1 unknowns,and cannot thereforehave the transparencyof surplus equations like (3) or (5).36 That transparencywas in fact ultimatelydue to the

3 The individualprice equation may indeed misleadinglysuggest, with its seemingsymmetry betweenprofits and wages, and, above all, its seemingrepresentation of price as a sum,the idea that the two rates can be determined"independently and separately" fromone another (cf. par. 9 above). Not surprisinglyit is only later in the developmentof theorythat the price equations reveal theirimplications as to the constraintlinking the real wage and the rate of profit. 36Thus, the nature of profitsas a residual can be clarifiedby Sraffain the firstchapter of 1960 only by showinghow prices just sufficientto repay the wages and replace the means of productionbecome contradictorywhen a surplusproduct comes into existence.The fact that thisindirect route had to be followedto exhibitwhat would have been so evidentin equations (continuedoverleaf) 312 VALUE AND DISTRIBUTION

"picture" whichcorresponded to those equations: that of a knownproduct to be divided between wages and profits;with the rate of profitoriginating fromthe distributionin proportionto the amount of capital of the surplus whichthis product shows above the knownamount of wages. This "picture" allowed a concretemental representation of a highlyabstract analysis: in the 'picture'the dependenceof the rate of profiton real wages was seen,and the propertiesof the economic systemassociated with this key relation were under a correspondinglyeasier grip.37 Naturally,reality need not be simple,and need not allow forthe existence of a surplus equation like (3) or (5), beyond the hypothesesnecessary to validate the labour theoryof value. But the point we wish to make is that the recovery,if at all possible, of that "picture" under the present more general assumptions,would constitutean importantscientific advance. It would do so because it would entail a bettergrip over the economicsystem's known properties: and it would make it correspondinglyeasier to gain greaterknowledge by askingfurther questions.38 In the next sectionwe shall indicatehow, under our presentassumptions, a determinationof the rate of profitalong the lines of the "Surplus equation method" becomes possible,provided we focusour attentionon the sectorof the economywhere the generalrate of profitis in factdetermined. We shall then see, in Section VII, that a similar,even simpler"picture" of distribution becomes available in the shape of Sraffa's"standard system" when we envisage the rate of profit,and not the wage, as the variable whichcan be determinedoutside the "core" of the theory.

(3) or (5) provides an example of the loss of transparencyreferred to. A furtherand perhaps more strikingexample of thislack of transparencyis the sense of noveltywhich, as late as 1961, under the name of "non-substitutiontheorem", greeted the propositionthat, in an economy like that of equations (8), the real wage is given irrespectiveof the "demand of consumers", when the rate of profit(rate of interest)is given (cf. Samuelson, (1966) p. 528)-a proposition whichwould have been obvious fromequations (3) and (5), or from(9) and (10) below. 3 Of course Social product,Necessary consumptionand Social capital, are, in themselves, highlyabstract notions. The mindcan howeverfit them into a "picture"and proceed to operate with them (just as the mind of a child can work with an abacus), as if they were concrete objects connectedby the simplerelations of part and whole. This mentalprocedure drastically differsfrom that which we have when entirelyabstract mathematical notions must be resorted to in order to deal withvariables like the prices and quantitiesof commodities,which, though more concrete(i.e. more directlyexperienced) are both numerousand interdependent. 38 The loss of the "picture"which was associated withequations (3) or (5) should in factnot be confusedwith the loss of a mere didacticdevice, whichcould alwaysbe made good by using appropriate,simplifying assumptions. The natureof thisloss may perhapsbe best illustratedby referringto the uneasinesswhich some physicistsfeel at the loss of the "pictures"of physical realitywhich were providedby the notionsof "waves" and "particles".This uneasinessinduces one physicistto hold that "as a systemof calculationwhich gives the rightanswers [quantum theory]is overwhelminglysuccessful. But whetherit tells us anythingabout what matteris actuallylike is anotherquestion". And the commentof a science historianto this was "if we were forbiddento talk in termsof models at all, we should have no expectationsat all, and we should then be imprisoned... inside the range of our existingexperiments", where "model" appears here to mean somethingcloser to what we have called "picture", than to what economistsare at presentin the habit of calling "model" (Pippard, 1962, pp. 33 and Hesse, 1962, pp. 56-7, our italics). P. GAREGNANI 313

VI. The surplus-equationmethod and the wage-goods sector 18. Let us single out the price equations of the commoditiesa, b, ... h consistingof the wage goods a, b, ... g, constitutingthe "wage commodity" (par. 16 above) and of theirdirect and indirectmeans of productiong + 1, ... h. The definitionof these commodities,h in number(with h - k), implies thatin theirh price-equationswe findas unknownsonly theirh pricesplus the rate of profitr. It followsthat these h equations, togetherwith the last equation in system(8), definingthe wage commodityas thenumeraire, will be sufficientto determinethe rate of profitand the h prices independentlyof the remaining(k - h) price equations. This means that,once the real wage is given,the generalrate of profitwill depend exclusivelyupon the technicalconditions of productionof the wage goods and their direct and indirectmeans of production.The technical conditionsof productionof the others commodities-i.e. the luxurygoods and the means of produtionspecific to them-will only be relevantin order to determine,by means of the remaining(k - h) equations of system(8), such prices for these commoditiesas will yield the rate of profitdetermined by the firsth equations.39 19. Let us now look more closely at the part of the productivesystem whichdirectly or indirectlyreproduces the aggregatewages advanced to the workersfor the year.40This part of the economy constituteswhat we may call the "verticallyintegrated sector of the wage-goods", or integrated wage-goodssector for short. Let us then expressboth the net yearlyproduct of this sector and the wages paid in it, in terms of Smith's "labour- commanded"standard of value, i.e. in termsof the quantityof labour which those aggregatesof commoditiescan buy. Both these two quantitieswill be knownbefore the rate of profitand pricesare known.The net product,being the yearlywages of L labourers,will evidently"command" L labour years,

"9The principleaccording to which the rate of profitis determinedby the conditionsof productionof wage goods, and of their direct and indirectmeans of productionalone, is a generalizationof thatwhich Ricardo appears to have used in his Essay on Profit(1815), when he concluded that "it is the profitsof the farmerthat regulate the profitsof all other trades" (1951-1958, IV, p. 23; VI, p. 104). If we in factassume thatwages consistentirely of "corn", and that this is produced by itselfand labour, as is required in order to validate Ricardo's argument,then the h commoditiesentering directly or indirectlythe wage narrowdown to the single commodity'corn'. The role of wage goods in determiningthe rate of profitwas first pointedout, it appears, by Dmitrieff,1974, p. 59 ff.It then emerged again in the solutionsof the so-called problemof "transforming"Marx's "values" into "prices of production",advanced in Bortkiewicz,1952, where the author recognisedhis debt to Dmitrieff,and also in Bort- kiewicz,1949. 40For the unique determinationof such a sector cf. Garegnani, 1972, p. 264, and, more generally the notion of a "sub-system" in Sraffa, 1960, p. 69. We may note that the determiningrole of this "sector" of the economyin no way depends on actuallybeing able to isolate it withinthe real economy: the rate of profitwould be determinedin the same way, if the wage-goods advanced to the workerswere not being reproduced.The "sector" is therefore best consideredas a purelylogical construction,which, like Sraffa's"standard product" to be consideredin the next section,has the purpose of givingtransparency to the forcesregulating the rate of profit. 314 VALUE AND DISTRIBUTION whereL is the knownnumber of labourersemployed in the economy.4"The wages paid in the sector,on the otherhand, will be those of the L, labourers requiredfor the directand indirectproduction of the "necessaryconsumption", a knownmagnitude, since the real, wage and the technicalconditions of the direct and indirectproduction of its constituentsare known. These wages will therefore"command" L,, labour-years. It followsthat in the integratedwage-goods sector,the amountof profits in terms of "commanded labour" constitutesa "surplus value" (L - L,) which is known before the rate of profit and the relative prices are determined.This surplusvalue coincidesnumerically with Marx's own social surplusvalue s (since L = v + s and L,, = v), thoughit differsfrom the latter in conceptionbecause: (i) it is the surplusvalue of the wage-goods sector, and not that of the entireeconomy; (ii) it is expressed in termsof labour commanded and not in termsof labour embodied.42 When we proceed, as we must,from the amountof profits(surplus value) to the rate of profit,the obstacle we meet is that, unlike the value of the productand of the wages, the value in "commandedlabour" of the means of productionof the integratedwage-goods sectoris not knownindependently of the prices. We seem to be unable to proceed with a "surplus equation" where the rate of profitis the only unknown(above par. 15), and to be forced to returnto the price equations. This obstacle is not insuperable however.Under our presenthypotheses43 it can be overcomeby the device of "reducingto labour" the means of production:as will be presentlyseen thisdevice allows us to expressthe value in commandedlabour of the means of production as a functionwhere the rate of profitis indeed the only unknown. The capital requiredfor the integratedproduction of any commoditycan in factbe regardedin eitherof two alternativebut equivalentways. The first is that,confined to a singleyearly production cycle-between, say, moments

41 The factthat the value of thisnet product,expressed in labour commanded,is independent of the rate of profitdoes not contradictthe fact,stated in par. 9 above, thatthe value in labour commandedof any commodityis not independentof that rate. The constancyof the value of net outputof the wage goods sectoris in factdue to the changes in physicalsize whichthis net productundergoes as the real wage changeswith the rate of profit.It mayhelp the readerto note that the use made here of the labour commanded standard has no connection with that suggestedby Sraffa,in op. cit. par. 41-42, that is of using as numerairea quantityof labour commandedwhich would varywith the rate of profitin such a way as to remainequivalent to the "Standard product". 42 It should be noted that the net output of the integratedwage-goods sector is physically homogeneouswith the wages paid there, since both consist of the same composite wage- commodity.The amount of profitsin the sector could then be determinedas the difference betweentwo physicalquantities of the wage commodity,and the rate of profitcould be seen to arise fromthe distributionof this surplusproduct over the capital of the wage-good sector, reduced to wages in the manner we shall consider in the next paragraph. The commanded labour standardused in the texthas howeverthe advantagethat in termsof this,the productof the integratedwage-goods sector is constant as the real wage changes either in level or in composition. " Fixed capital of constant efficiencycan however be easily shown to leave the present argumentunaffected, (cf. p. 53 n. 46 below). P. GAREGNANI 315

(-1) and (O)-which we adopted for prices equations (8): capital there includes the means of production,besides the wages, both kinds of capital being advanced at moment (- 1): the value of the capital so conceived involvesthe unknownprices of the means of production.The second way of looking at capital, however,proceeds to consider the productionof these means of productionand considersit as the resultof previous stages in the productionof the finalcommodity: the stage between moments(-2) and (-1), in which the means of production of the commodityhave been produced; the stage between (-3) and (-2) in whichthe means of production of those means of productionhave been produced, and so forth.The resultof thisprocedure is thatcapital is reduced to wages with,generally (in the case of circularproduction, when the commodity,or one of its means of production,requires itselfdirectly or indirectlyin order to be produced) a residual of means of productionwhich may be rendered small at will by carryingthe process on througha sufficientnumber of stages. These wages are howeverconceived as havingbeen advanced forvarying periods of time; not only at moment(-1) but also at (-2), (-3), etc. The advantage of this device is that, when measured in "labour commanded", these advanced wages will be given by the quantitiesof "dated labour" theyare the wages of. Unlike the prices of the means of production44in the other view of capital, they will thereforebe known quantities since the methods of productionof both the commodityand its means of productionare known. A simple example will show how this second view of capital can be applied to the means of productionof the integratedwage-goods sector to obtain a "Surplus equation" determiningthe rate of profit.Consider an economywhere (besides the general assumptionsalready made in par. 12) we suppose thatwages consistonly of "corn". "Corn" is produced withone "plough" per worker:the "plough", entirelyconsumed during the year,is in turnproduced by one unassistedworker. The L, labourersemployed in the integratedwage-goods sector will thereforebe distributedhalf in (directly) producingthe "corn", and half in reproducingthe "ploughs": the capital advanced for,the year (reckoned,therefore, according to the firstof the two views above) will consistof the wages and the plough. If we take now the

44We are in fact expressingthe prices of the means of production by means of these "advanced wages" and the profitson themfor the relevantperiods of time. This is made clear by the procedurefor this "reduction of the commodityto dated labour", whichconsists of taking the price equation of the commodityand replacingthe prices of means of productionwith the expressionsgiven by the respectiveprice equations. The opeation is then repeated with the pricesof the second layer of means of produtionappearing in the equation thus modified,and so forthfor the furtherlayers, which appear in successionafter each round of substitutions(see forexample Sraffa,1960 pp. 34-35). When looked at fromthis "dated labour" angle the other view of capital appears to be the resultof "collapsing" all the successivestages of production into a singleyear-a "collapsing" whichis made possible by the availabilityat the beginningof the year of the productsof all the intermediatestages, that is the means of production.It should howeverbe rememberedthat the reductionto dated labour constitutesa more logical device, as is shown by the fact that, when the productionof a commodityis "circular", it cannot be conceived as startingwith unassisted labour. 316 VALUE ANTD DISTRIBUTION

LabOLur (b) LabOur

2 1 2

Time -2 -1 0 -2 -1 0

FIG. 2. The "dated labour" curve for the aggregateof wage goods paid as yearly wages (curve a) and the proportional distributionof labour over time in the productionof the wage commodity(curve b). second, "dated-labour" view of capital, the latter emerges instead as the wages of the two quantitiesof "dated labour" shownin Fig. 2a: L,/2 labour years applied at moment(-2) forproducing the "ploughs", which are then used in the successive "stage" of corn production-togetherwith a further L,/2 labour years applied at (-1). Expressed in "commanded labour" the wages, to which the entirecapital of the integratedwage-goods sector has thus been reduced, will equal the correspondingquantities of dated labour i.e. L,/2 advanced at (-2) and L,/2 advanced at (-1). The rate of profitcan thenbe seen to emergefrom the distributionof the surplusvalue L -L,, in proportionboth to the wages advanced, and to the time by whichthey have been so advanced, account being taken of compound profits,that is LV L 2L L-LU=r- 2+2r2u + r 2 (9) where the term rL,/2 indicates the share of surplus value allotted to the capitalistsadvancing the wages paid at time (-1); and the term 2rL,/2, togetherwith the compound profitterm r2L,/2, indicates the share allotted to those paying the wages at time (-2). The rate of profitis the only unknownin (9). 20. It is now convenient to divide both sides of equation (9) by L, obtaining L -L 1 = rI+2r 2+ r2 (9a) LU 2 2 2 and proceed to some propertiesof our "surplusequation" (9a) whichcan be easily shown to hold beyond our presentsimple example. On the leftof the equalitysign we find,expressed in commandedlabour, the amountof surplusvalue per workerin the integratedwage-goods sector. This amount is identical to Marx's rate of surplusvalue s/v and depends purelyon the level of the real wage and on the labour requiredfor the direct P. GAREGNANI 317 and indirectproduction of its constituents.On the rightof the equalitysign we findinstead a functionexpressing the amountof profitsper worker,also expressedin commandedlabour, whichwould be necessaryin the sectorin order to pay a rate of profitr. This function,which we may call "profit function"for short,depends purelyon the proportionaltime distributionof the labour necessaryto produce the wage commodity(see Fig. 2b): it does not thereforedepend on the level of the real wage, but only on its compositionand on the methodsfor the directand indirectproduction of the wage-goods. The "profitfunction" has an importantproperty which can easily be seen to hold with any kind of circulatingcapital, and with fixed capital of constantefficiency: it is zero when r = 0 and thenit risesmonoton- ically with r.45 The solutionof the "surplusequation" (9a) can now be representedin the diagramof Fig. 3a where r is measured horizontallyand the rate of surplus value is measured vertically.We have there the curve Os representingthe "profitfunction", which rises monotonicallyfrom the origin(In the case of our example it will rise indefinitelyas r rises indefinitelyas in Fig. 3a; in the case of "circular production" it rises indefinitelyas the rate of profit approachesa "maximumrate of profit"R as in Fig. 3c). The rate of surplus value, (L - L,)IL0, can on theother hand be representedby a horizontalline. The level of the rate of profitwhich solves the equation will be that for whichthe "profitscurve" Os cuts the surplus-valueline. The fact that the "profitscurve" is monotonicallyrising ensures that the solution will be unique and positivefor any positiverate of surplusvalue-i.e. forany level of the real wage less than the productper head in the integratedwage goods sector). Figure 3a or 3c make it clear that thissingle positive rate of profit, depends exclusivelyon two circumstances:(i) the rate of surplusvalue; (ii) the proportionaltime-distribution of the labour necessaryto produce the wage commodity,which determinesthe shape of the "profitfunction". The fact that the "profitfunction" is an increasingfuncton also makes clear a second set of propertiesof the system,pertaining to the relation between the wage and the rate of profit.A rise in the wage, leaving its

" When we admit fixed capital of constant efficiencythe validityof the propertyof the "profitfunction" mentioned in the text can easily be seen if we startfrom the functiong(r) givingthe profitsobtaining on a "pool" of n machinesof kind K, one of age 0, one of age 1 and so on up to the last, of age (n - 1), where n yearsis the lifeof machinesK. For r = 0 these profitswill be zero, and for r >0 theywill be given by

g(r) [: r(i r;" - g)=[(I7(1Pk r)" -I] where Pk is the price in labour commandedof a new machine K. Now, the functionin square bracketsis a monotonicallyincreasing function of r. It followsthat the "profitsfunction", in which functionsof the above form will be multiplied by, or added to, those of form [(1 + r)0- 11,will also be zero for r = 0 and will thenmonotonically rise withr. It should also be noticed that the integratedwage-goods sector will now have to be definedso as to include amongits fixedmeans of productiononly sets of machinesof uniformage distribution,with the correspondingconstant yearly replacement appearing in the gross output of the sector. 318 VALUE AND DISTRIBUTION

L-L (a) L-L (b) L

O A~'C* O\L C*

0 0 '*

L-Lv

I -,

0 R r (c)

FIG. 3. Determinationof the rate of profitwith reference to (a) the rate of "surplus value" (b) the "surplus value" expressed in labour commanded of the integrated wage-goods sector. (c) indicates the shape of the "profitsfunction" when produc- tionis "circular". commoditycomposition unchanged will decrease the rate of profit.This will be so because the rate of surplusvalue (LILr) - 1 will decrease withthe rise of Lt, and will thereforeintersect the unchanged "profitsfunction" for a lower rate of profit:cf. the shiftfrom B to B' in Fig. 3a. The same conclusion can be seen to apply if the real wage changes in composition,but in such a way thatit increasesin one or more components with no decrease in any of the others. In order to see this, it is however convenientto shiftour attentionfrom Fig. 3a which relates to rates of surplus value (L-L ,)/L, to Fig. 3b which refersinstead to the aggregate surplusvalue (L - L,) in the integratedwage-goods sector as a whole. With the assumed incrementin some componentsof the real wage, the amountof surplus value will decrease by the amount AXL,of the labour required in order to produce that incrementfor the aggregate wages. On the other hand, for r>0, the curve OS of total profitsin the wage-goods sector will "rotate" upwards from OS to OS' because of the profitsaccruing on the P. GAREGNANI 319 wages paid forthe additionallabour AL, Both changes will have the effect of decreasingthe rate of profit.46 However, when the compositionof the real wage changes in such a way thatwhile the quantityof some componentsrises, that of othersfalls, and it becomes accordinglyimpossible to referunambiguously to a rise or fall in the real wage-the profitcurves, whether that of profitsper worker (Fig. 3a), or that of total profits(Fig. 3b), can change in any way whatever.The rate of profitmay then change in a directionopposite to that in whichthe rate of surplusvalue has changed-in line withwhat Marx saw as possible when the organic compositionof social capital changed togetherwith the real wage (cf. e.g. Marx, 1969b, III, p. 869). 21. These properties,made easily visible by surplus-equations(9) and (9a) are thus closer than we might perhaps have expected to Marx's conclusionson the matter.In particular,it is confirmedthat the rate of profit depends on two factorsonly, the rate of surplusvalue slv, and the proportions between means of produtionand labour. However, the correctionof the errorimplicit in equation (5) modifiesMarx's specificationof the second circumstance,in termsof the "organic composition"clv of social capital, in two importantrespect. In the firstplace the proportionof labour to means of productionon whichthe rate of profitdepends is thatof the integratedwage-goods sector, and not that of the economy as a whole as Marx thought.This in turn impliesthat he was mistakenin believingthat changes in the relativeoutputs of commoditiescould affectthe rate of profit,through variations in the proportionof labour to the means of productionin the community.47It also implies that Marx was equally wrong when he thoughtthat, throughthe same variations,changes in the technicalconditions of productionof "lux- uries", or of their specificmeans of production,could affectthe rate of profit. In the second place, the proportionof labour to means of production cannot be expressedby the ratio clv, and mustinstead be expressedby the proportionatedistribution over time of the labour necessaryto produce the wage commodity,or by the quantitiesof the several means of production,in the price equations. This is a consequence of the factthat it is impossibleto measurecapital by a singlemagnitude independent of distribution.This fact, whichdeeply affectsthe validityof the marginalisttheories (above par. 1),

46 The monotonicallyincreasing character of the profitsfunction also impliesthat in equation (9a) a single value of Lo will correspondto any positive level of r or, in the case of circular production,to any value of r where 0 = r

has some importantconsequences also here: thus if Marx had been correct the relative price of the productsof two distinctprocesses of production would always change monotonicallywith r, whereas in fact such relative pricesmay inverttheir direction of change as r rises (falls)monotonically.48

VII. The "surplus-equationmethod" and Sraffa'sstandard system 22. The basis of our discussionof the surplustheories has so farbeen the Classical economists' premise according to which, when approachingthe determinationof profitsand prices, the real wage should be treated as an independentvariable. A differentview of the wage is howeversuggested in Sraffa,1960. Sraffabegins by observing (p. 9) that the wage, besides a minimumconsisting of the necessarysubsistence, may include a share of the surplus.He proceeds to argue (ibid.,p. 33) that under these conditionsthe wage would have to be taken as given "in termsof a more of less abstract standard" and, accordingly, "it would not acquirea definitemeaning until the pricesof commoditiesare determined". Then, he continues, "the positionis reversed[and] the rate of profits,as a ratio,has a significance whichis independentof anyprices, and can wellbe "given"before the prices are fixed". A discussionof the view of the operationof the economic systemwhich seems to underlieSraffa's suggestion would bringus beyond that "core" of the theorywith which we are here exclusivelyconcerned (cf. above par. 7). Our present interest-confinedto examiningSraffa's use of the "Surplus equation method"-requires us only to consider how far the suggested change in the independent distributivevariable is compatible with the surplusapproach to value and distributionwhich is the subject of thisarticle. 23. When withinthis approach to distributionwe envisage changesin the rate of real wages over time,we may attributethese changesto eitherof two circumstances:a long-termevolution of the social conditionsdetermining the level of subsistence, or the kind of economic circumstanceswhich authorslike Smithor Marx thoughtmight keep the wage above the level of subsistenceeven forlong periods of time (par. 4 above).49 In the firstcase, 48 There is a furtheraspect of Marx's views which, when appropriatelymodified finds confirmationin the surplusequation of the wage-goods sector. It regardsthe role of prices in "re-distributing"total surplus value in proportionto the capital employed in the individual industries.This role can be detectedwhen we look at the integratedwage-goods sector and at the pricesappearing there. The same cannothowever be said whenwe look at the economyas a whole, since in thatcase the amountof surplusvalue is not givenbefore the prices and rate of profitare given. 4 The view thatthe wage can exceed the level of subsistencefor long periods of time seems indeed impliedalso in the veryidea of a risingsubsistence level. This rise can resultonly from wages remainingabove the previoussubsistence level fora period of timewhich is long enough to engenderthose 'habits' whichmay then become a 'second nature' in Torrens's phrase later adopted by Ricardo (par. 4 above) and by Marx in 1969b, III, p. 859). P. GAREGNANI 321 the real wage will evidentlyhave to be taken as a given magnitudein the "core" of the theory(par. 5). The same will be true in the second case only if the share of the surplustaken up by the wage depends on circumstances actingthrough the wages. The real wage will then appear in the "core" as the magnitudewhich has been determinedin both level and compositionby the circumstancesin question: profitswill continue to be determinedas a pure residual,though now theywill not constitutethe entiresurplus. The share of wages in the surplusmight however be alternativelydeter- mined by circumstancesacting throughprofits, like those which Sraffa envisageswhen, afterthe passage already quoted, he writesof the rate of profitas a magnitude "susceptibleof being determined.... by the level of the moneyrates of interest" (Sraffa1960, p. 33.) Then, the rate of profitwill become the independentvariable withinthe "core" and the wage, an unknown,can be treated as an "abstract" value magnitudewhich can be measured in termsof any standard.50'51 Thus, Sraffa's replacement of the wage by the rate of profit as the independentdistributive variable can be seen to result fromhis choice of one of the two views thatcan be taken of the circumstancesdetermining the divisionof the surplusbetween wages and profits.As such it appears to be no less compatiblewith the surplusapproach to distributionthan the other view, adopted by Smith and Marx, when they saw those circumstancesas actingthrough the wage. In eithercase we findthe basic distinctionbetwen subsistenceand surplus,and we also findthe determinationof the divisionof the surplusby means of social and economic circumstanceswhich, whether they act throughwages or throughprofits, are best studied outside the "core" where the unknowndistributive variable is determinedtogether with relative prices. In formal terms,what we have if we follow Sraffa is a modificationof the analysis conducted in that "core": the modification consistsof the addition,so to speak, of a second layer to the determination of the surplus by the differencebetween social product and "necessary consumption"(par. 6 above). In thissecond layerwe have the sharingof the surplusbetween wages and profits,and the rate of profitappears there as a "datum" or independentvariable, with the surpluswage as the unknown. The diagram(Fig. 1) may accordinglybe modifiedas in Fig. 4 below.

50 The treatmentof the wage as a residualneed not howeverentail the treatmentof the wage as an abstractvalue quantity.Commodities which play a primaryrole in workers'consumption may provide a more significantmeasure of the wage than is provided by other commodities. The concept of the wage as an abstractvalue magnitudedoes not, on the otherhand, prevent the use of the "integratedwage-goods sector",with respect to any of the commoditiesin terms of whichwe may wish to measure the wage. With r as the independentvariable in equation (9a), the rate of surplusvalue would be the unknown,giving the unique wage correspondingto the given level of r (cf. above n. 46). 51 E. Burmeisterfails to realize this implicationof Sraffa's suggestionabout an exogenous determinationof the rate of profitwhen in 1977, p. 68 n., he writes"Sraffa's measure of the real wage is flawed ... [the] weightsare not related in any way to human needs". 322 VALUE AND DISTRIBUTION

~~~Social Produict | ateof D/ Jr \ I ~~~~~~~~profits cnqe - / Laboipl. \\ I . 0 |~~~~~Ei~l S~lrp1LloSu--11p1lus tramOfWat ge

Substance-+ Necessan' | partof wage Colns.

FIG. 4. A diagramof the "core" of the surplustheories when we admitthat the wage may share in the surplusbecause of causes actingthrough the rate of profit(compare withFig. 1 above).

24. The treatmentof the wage as an abstractvalue quantitymakes a very simple Surplus equation possible for the studyof the relationbetween the wage rate-or preferablyits surplus component-and the rate of profit (Sraffa,1960, pp. 9-10). As is well-known,under the hypothesisof single- product industriesa unique set of positive proportionsalways exists such thatthe net productconsists of a compositecommodity which requires itself as its only means of production.The unique composite commoditythus defined,which depends exclusivelyon the technicalconditions of production, is what Sraffa calls "Standard commodity". A replica of the real economy,employing the same numberof workers,but producingexclusively the Standard commodityconstitutes them what Sraffa calls the "Standard system".The considerationof the wage as an abstractvalue quantitycan then be used in order to measure the wage in terms of the Standard commodity.In the "Standard system"we shall accordinglyhave a physical homogeneitybetween all threemagnitudes on which the relation between the wage and the rate of profitdepends, namelythe net product,the wages and the means of production. Let us then take the standard net product as our unit of the standard commodity.Let us also choose as a unit of labour, the labour employedin the real economy,and hence in the Standard system,so that the wage rate w, paid postfactum, coincides with the total wages in either.Looking at the standardsystem we may write w = 1- rM (10) where M is the amount of the standard commodityused as means of productionin the standard system.If we then referto Sraffa's"Standard ratio" R, between the standard net product and M we have R = 1/M or M = 1hR whichwhen substitutedin equation (10) gives

w = I1- r (10a) R P. GAREGNANI 323

The linear relation (10) or (lOa) between r and w also applies to the real economyas soon as wages are measured in termsof the standardcommodity. The price equations of the standard systemare then identical to the equations of the real economy, except for the multipliersapplied to the latter in order to take the industriesin the proportionsof the standard system. What the standard systemdoes, is only to provide a 'surplus equation method' of arrivingat that relation,with the corresponding'picture' of the relationsof distribution(par. 17 above); in Sraffa'sown words,the purpose is "to give transparencyto a systemand render visible what was hidden" (1960, p. 23).52

Instituteof PoliticalEconomy, Universityof Rome.

REFERENCES

BAUMOL, W. J. (1983), Marx and the Iron Law of Wages, AmericanEconomic Review,Papers and Proceedings,May. BORTKIEWICZ, L. (1949), Zur Berichtigungder GrundlegendenTheoretischen Konstruktion von Marx im DrittenBande des 'Kapitals', Jahrbucherfur Nationalokonomie und Statistik, July1907, English Translationin the Appendix to P. Sweezy's edition of E. von Bbhm Bawerk, Karl Marx and theClose of his System,New York. BORTKIEWICZ, L. (1952), Wertrechrungand Preisrechrungim MarxischenSystem, in three parts, Archiv fur Sozialwissenschaftund Sozialpolitik,July 1906-Sept. 1907. English translationof the second and thirdparts, in "InternationalEconomic Papers", n. 2. BRADLEY, I. and HOWARD, M. C., eds, (1982), Classical and Marxian Political Economy, Macmillan,London. BROWN, M. SATO, K. and ZAREmiBKA, P. (1976), Essays in Modem Capital Theory,North Holland, Amsterdam. BURMEISTER, E. (1977), The Irrelevance of Sraffa's Analysis withoutConstant Returns to Scale, Journalof Economic Literature,XV, March. CASAROSA, C. (1978), A New Foundation of the Ricardian System,Oxford Economic Papers XXX. CANNAN, E. (1967), A Historyof the Theoriesof Productionand Distribution1776 to 1848, Kelley, New York. DE Vwvo,G. (1982), Notes on Ricado and Marx, Contributionsto PoliticalEconomy, n. 1. DOBB, M. (1973), Theoriesof Value and Distributionsince Adam Smith,Cambridge University Press.

52 Sraffa'sreference here is to the transparencyaquired by propertiesof the systemlike those pertainingto the inverserelations between w and r, or to switchesin methodsof production, etc., To referto a 'directlink' between the use of the standardcommodity and the use of the labour theoryof value by Marx, "to expose the natureof (the) exploitation[of labour]" (cf. for example,Eatwell, 1975, pp. 543-4) would thereforeseem misleading.The basic analyticalrole of the labour theoryof value whichwe saw in Sections III and IV leaves no room forits use in expressingexploitation, (which, it seems, would only consistof showingwhat is already clear, that is that workersdo not get the entireproduct: cf. p. 13, n. 23 above). Moreover, Sraffa's use of the standardproduct, though strictly analytical, is "auxiliary"(Sraff a, 1960, p. 31) and is thereforeunlike that of Ricardo and Marx, who depended on the labour theoryof value for theirconclusions regarding the rate of profitand relativeprices. 324 VALUE AND DISTRIBUTION

DIMrFRIEFF,V. K. (1974), Economic Essays (1904), English tr., Cambridge UniversityPress, Cambridge. EATWELL,J. (1975), Mr. Sraffa'sStandard Commodity and the Rate of Exploitation,Quarterly Journalof Economics,LXXXIX, November. GAREGNANI,P. (1960), Il Capitale nelle teoriedella distribuzione,Giuffr&, Milano. GAREGNANI,P. (1972), Heterogeneous Capital, the ProductionFunction and the Theory of Distribution,Review of Economic Studies,XXXVII, June 1970, reprintedin Hunt and Schwartz(1972). GAREGNANI,P. (1976), A Change in theNotion of Equilibriumin Recent Workon Value and Distribution,in Brown, Sato, Zarembka, (1976). GAREGNAN[,P. (1983), The Classical Theory of Wages and the Role of Demand Schedules in the Determinationof Relative Prices,American Economic Review, Papers and Proceedings, May, LXXIII. HESSE, M. D. (1962), Models and Matter,in Toulmin (1962). HILFERDING,R. (1949), Bohm Bawerk's Criticismof Marx, Sweezy ed, MerlinPress, London. HICKS,J. and HOLLANDER,S. (1977), Mr. Ricardo and the Moderns, The QuarterlyJournal of Economics,August 1977. HUNT,E. K. and SCHWARTZ,J. G., eds (1972), A Critiqueof Economic Theory,Penguin Books, London. MALTHUS, (1951), Principlesof Economics 2nd ed., repr.Blackwell, Kelley, London-New York, 1951. MANDEL, E. (1975), Late Capitalism,New Left Books, London. MARSHALL,A. (1961), Principlesof Economics,Guillebaud's Variorumed., 2 vol. Macmillan, London. MARX, K. (1969a), Theoriesof SurplusValue, 3 vol., Lawrence and Wishart,London 1969-72. MARX,K. (1969b), Capital, 3 voll., Lawrence and Wishart,London 1969-74. MEDIO, A. (1977) Neoclassicals, Neo-Ricardians and Marx, in Schwartz(1977). MILL, J. (1821), Elementsof Political Economy,Longmans, London. MoNTANia, G. (1977) Scarce Natural Resources and Income Distribution,Metroeconomica. MORISHIMA,M. (1973), Marx's Economics,Cambridge University Pess, Cambridge. PrPPARD, A. B. (1962), Particlesand Waves, in Toulmin (1962). QuADRIo CuRzio, A. (1967), Rendita e Distribuzionein un Modello Plurisettoriale,Giuffr6, Milano. PASINETTI, L. L. (1977), Lectureson the Theoryof Production,Cambridge UniversityPress, Cambridge. RICARDO, D. (1951-1958), Works,Sraffa ed., 9 vol., CambridgeUniversity Press, Cambridge. ROBINSON, J. (1953), The ProductionFunction and the Theoryof Capital, Review of Economic Studies,XXI. ROBINSON,J. (1973), Capital Theory up to Date, Canadian Journalof Economics,May 1970, III, rep. in CollectedEconomic Papers, vol IV, Blackwell, Oxford. RONCAGLIA,A. (1979), Sraffaand the Theoryof Prices,Wiley, Chichester. RowTHoRN, B. (1976), Late Capitalism,New LeftReview, n. 98, August. SAMUELSON, P. A. (1961) A New Theorem on Non Substitutionin Samuelson (1966). SAMUELSON,P. A. (1962), Parable and Realism in Capital Theory: the SurrogateProduction Function,Review of Economic Studies,XXIX. SAMUELSON,P. A. (1966), The CollectedScientific Papers of Paul A. Samuelson,M.I.T., Press, CambridgeMass. SAMUELSON,P. A. (1971), Understandingthe Marxian Notion of Exploitation:a Summaryof the So-Called TransformationProblem between Marxian Values and CompetitivePrices, Journalof Economic Literature,IX. SAMUELSON, P. A. (1978), The Canonical Classical Model of Political Economy, Journalof Economic Literature,December, XVI. SAMUELSON, P. A. (1974), Marx as Mathematical Economist, in Trade, Stabilityand Mac- roeconomicsEssays in Honour of Lloyd Metzler,Academic Press, New York, London. P. GAREGNANI 325

SCHEFOLD,B. (1976), DifferentForms of Technical Progress,Economic Journal,LXXXVI. SCHUMPETER, J. A. (1954), Historyof EconomicAnalysis, Oxford Univesity Press, New York. SCHWARTZ,J. (1977), The SubtleAnatomy of Capitalism,New York. SETON,F. (1957), The TransformationProblem, Review of Economic Studies,June, XXIV. SMITH,A. (1910), The Wealth of Nations,2 vol. Dent and Sons, London. SRAFrA,P. (1951), Introductionto Principles,in Ricardo (1951-1958), vol I. SRAFrA,P. (1960), Productionof Commoditiesby Means of Commodities,Cambridge University Press, Cambridge. STEEDMAN, I. (1982), Marx on Ricardo, in Bradley and Howard, (1982). SWEEZY, P. (1946), The Theoryof CapitalistDevelopment, Dennis Dobson, London. TORRENS, R. (1815), An Essay on theExternal Corn Trade etc.,London. TOULMIN, S., ed., (1962), Quanta and Reality,A Symposium,Hutchinson, London. TURGOT, A. R. J. (1786), Reflexionssur la productionet la distributiondes richesses,Paris.