2009 article, originally published in Re-reading Marx: new perspectives after the critical edition, edited by Riccardo Bellofiore and Roberto Fineschi, London/New York: Palgrave Macmillan, pp. 211â30.
(For its abstract see the Abstracts of all chapters, p. 7.)
Contents
Introduction
§1 The published drafts for Part Two of Das Kapital III
§2 A note on Marxâs method in Capital
§3 A formal presentation of alternative interpretations of the Das Kapital I categories from the perspective of those of the Das Kapital III manuscript
§3.1 Rate of surplus-value and rate of profit
§3.2 [CC-1] Method of Concretion at Volume I level: abstract explanandum
§3.3 [CC-2] Method of Concretion at Volume III level: concretion
§3.4 [CP-1] Method of Completion at Volume I level: partial explanation of âconcretumâ
§3.5 [CP-2] Method of Completion at Volume III level: completion
§3.6 Some conclusions and a preview
§4 The 1864â65 manuscript and the text of Capital III Part Two
§4.1 General outline
§4.2 Chapter 8: the problematic
§4.3 Chapter 9: a cheerful accommodation for the inconsistency
§4.4 Chapter 10: gloomy reflection
§5 Notes on a small 1878 manuscript: diverging rates of surplus-value
Conclusions
References
Introduction1
In Part Two of the third volume of Capital Marx addresses the famous transformation of the rate of surplus-value into the general rate of profit. This article discusses Marxâs 1864â65 manuscript on this issue â the text that Engels (selectively) used for his edition of Das Kapital III. We shall see that this text is a research manuscript rather than a near to final presentation of the matter, and that Engels polished away this preliminary status of the manuscript â in this I merely confirm the view of the MEGA editors.
The assessment of Marxâs transformation procedure very much hinges on our view of the method that he adopted. Two main alternative interpretations of the method are set out in §3 below. Even if only one of those would make Marxâs transformation procedure methodologically legitimate, we shall see in §4 of this essay that, paradoxically, it is not obvious that Marx intended to adopt this method. Thus the main object of this essay is to lift the discussion on the âtransformation problemâ to a more fundamental level.
References without mention of author (e.g. M:272 or E:208) are to works of Marx as follows (full references are in the bibliography).
| M |
Marx (1992M/1864â65): main manuscript for âDas Kapital IIIâ (MEGA); |
| E |
Marx (1894E/~1864â65): Das Kapital III as edited by Engels (MEW); |
| F |
Marx (1894F/~1864â65): Capital III in the Fernbach translation. |
The first date is the date of first publication; the second one indicates the year(s) of composition of the manuscript. A tilde ~ before the second date means that the text, as edited by Engels, is roughly based on that manuscript.
Within citations italics are always in the original. Any underlining is my emphasis. Unproblematic insertions in quotations are in square brackets. Comments are in curly brackets. The indication âmtâ after a page number (for example 370-mt) means âmy translationâ. Within my translations the original German term also appears, in case, in curly brackets.
§1 The published drafts for Part Two of Das Kapital III
Engels edited the text of Part Two of Das Kapital III from a 1864â65 manuscript of Marx. For the main argument of this essay it is important that this manuscript thus dates from before the final manuscript of 1866â67 for the first edition of Das Kapital I (1867).2
The transcript of the German 1864â65 manuscript was first published in 1992 (MEGA II/4.2). There is no (published) English translation.3 A 1857â58 manuscript, the Grundrisse, contains notes concerning the problematic of this part.4 A more mature â though relatively short â draft dates from 1861â63, first published in 1980 (MEGA II/3.5), first English translation 1991.5
Other relevant texts, published for the first time in 2003, can be found in MEGA II/14. This includes a substantial manuscript dating from 1875 as well as four shorter texts from (probably) 1871?, 1873â75?, 1877â82 and 1878? (see §5 for a note on especially this last manuscript).6
A final number of eleven draft texts for Das Kapital III (dating from 1867â68) is to be published in MEGAâs II/4.3. Herewith the publication of Marxâs manuscripts for the work will be complete (Vollgraf and Roth 2003, p. 382).
From reading the 1864â65 manuscript it is obvious that it reports preliminary investigations; it includes âtry outsâ together with mistakes of which the author at some point becomes aware. In Engelsâs manner of carrying out his editorial work, this investigative character of the text has been polished away; hence it has seemed for over a century that much of Das Kapital III (and II) was in a rather finalised state â as including its Part Two. I am, of course, not the first to observe this (see e.g. Vollgraf and Jungnickel 1994 and Heinrich 1996; cf. Roth 2009 and Heinrich 2009). In fact, there was no simple solution to the problem that faced Engels: most of the drafts were not in a readable state for non-specialists. The problem is that, given the solution he adopted, he gave very ill warning as to his interventions.7
§2 A note on Marxâs method in Capital
Although in my view, the project of Marxâs Capital is based methodologically on a development from Hegelâs Systematic Dialectics (cf. Arthur 2009), the main argument of this essay can do without this stringent position. Instead, I just emphasise one, less controversial, aspect of Marxâs method in Capital, namely that it proceeds by way of conceptual development. Between the three volumes of Capital, as well as within each one, we have a movement of âlevels of abstractionâ, running from abstract, relatively indeterminate, general and simple concepts to increasingly concrete, determinate, particular and so complex concepts. At the earlier levels, certain complexities are suppressed, or âbracketedâ. Each time it is the âinsufficiencyâ of the earlier presentation that drives on to the introduction of further complexities. (For the purposes of this essay, these levels of abstraction may even be interpreted in terms of a movement from âsimple modelsâ to âcomplex modelsâ in the course of which initial ceteris paribus assumptions are increasingly dropped.)
§3 A formal presentation of alternative interpretations of the Das Kapital I categories from the perspective of those of the Das Kapital III manuscript
§3.1 Rate of surplus-value and rate of profit
In this section I use the following four main concepts and definitions. Circulating capital (k):
ki = ci + vi [definition] (1)
where c and v are the parts invested in means of production and in labour-power (the wages sum of wl). For simplicity, we abstract throughout, like Marx, from fixed capital and from differences in turnover time.8 The subscript i refers to a specific sector of production (later, the subscript j will refer to any other sector).
The rate of surplus-value (s´):
s´i = f(e*i) [explanation â pro memory] (2a)
si = s´ivi [explanation; here reduced to definition] (2b)
(where e* is the ratio of âsurplus labourâ and ânecessary labourâ).
Capital I posits surplus-value (s) and its increase as the driving force of capital. The focus of the middle part of Capital I is the explanation of surplus-value in terms of labour-time and of the productive forces of labour operating on the means of production.9 The rate of surplus-value (s´) is the concentration of these explanatory determinants. Here, as for Marx in the Kapital III manuscript, all this explanation is assumed. Thus we have s´ as a determinant for s. It remains to be seen (cf. the subsections below) how it is also a determinant for profit (r) and the rate of profit (r´):
r´i = ri/ki [definition] (3)
The spectrum of wages is posited synchronically equal for all sectors (wi = w), hence:
wli = vi [approximation] (4)
For the sake of brevity, I posit throughout this section a number of assumptions without further argument. For our purposes there are three types: âsimplificationsâ serve to make a problem tractable; the same applies to âstage simplificationsâ (these, however, are dropped in a later stage); âapproximationsâ {Annäherungen} set out the uninhibited result of forces (tendency laws).
The assessment of Marxâs general rate of profit transformation in the 1864â65 draft for Part Two of Das Kapital III depends very much on the view of how the categories presented in this part are connected to those of Capital I. We shall see (§4) that Marx is aware of the importance of the connection, and how he hesitates about the Part Two consequences (his self-interpretation!) for the, then, draft of Das Kapital I. Both in order to shortcut the discussion in the next section (§4), and because the categorical connections are not obvious, the current section sets out a brief formal presentation of the two main alternatives (§3.2â§3.5). Note that a formal presentation necessarily loses conceptual richness; on the other hand, once quantitative matters are involved â as is the case â it is a means of precision.
For the purposes of this section I reduce Marxâs complex method of many stages (levels of abstraction) to simply two stages: that of Capital I and of Part Two of Capital III. The movement to the later stage is one of increasing determination (concretion or completion).
In considering surplus-value and production, we can, of course, not get around exchange and prices. We assume that âmarket pricesâ converge to what I provisionally call âsupply pricesâ (and what Marx will call âproduction pricesâ in Capital III). We want to explain production (x = pq) in terms of these convergence prices (p). In principle we can adopt two methods, and we can take these as possible interpretations of the two stages referred to. I call them âthe method of concretionâ (§3.2â§3.3). and âthe method of completionâ (§3.4â§3.5). For both methods, we shall be concerned throughout with synchronic matters only (some synchronic uniformity of sectors of production may go along with diachronic change).
§3.2 [CC-1] Method of Concretion at Volume I level: Abstract explanandum
Before we get to the explanation of the prices p, we first explain an abstract approximation of them, labelled âpiâ (
Ï iqi = ki + s´ivi [explanation of a construct/abstractum] (5)
Via the moment of s´ivi this incorporates the explanation represented by equations (2a and 2b). We proceed by adding two simplifying assumptions. First, that of synchronically uniform rates of surplus-value:
s´i = s´ (for all i) [simplification or approximation] (6)
A key question is whether this is indeed a simplifying assumption or rather an approximation of a systemic force (see §3.3, §4.1 and §5). Second, that of synchronically uniform compositions of capital:
(k/v)i = k/v (for all i)Â [stage simplification] (7)
Dividing (5) through vi, and making use of (6) and (7), we have:
Ï iqi/vi = k/v + s/v (for all i)Â [implication] (8)
Because wli = v (eqn. 4), then substituting wli for vi, and multiplying by w, we also have:
Ï iqi/li = k/l + s/l (for all i)Â [implication] (9)
In the way I have presented it here, it is the implication of the construct that its prices (
Even if Marx introduces the (general) rate of profit only in Capital III, another implication is that we have uniform rates of profit since (cf. eqn. 3):
r´i = s´vi/ki = s´/(ki/vi) = s´(k/v) [implication] (10)
(This is roughly how I interpreted Capital I until my study of the 1864â65 manuscript discussed in this essay.10 In §4 we will see that this interpretation makes Marxâs Das Kapital III manuscript transformation procedure methodologically mistaken.)
§3.3 [CC-2] Method of Concretion at Volume III level: concretion
We drop the construct
Variant (a)
Marx (at some point, see §4.2-§4.3) defines this constellation as follows.
⢠Analogous to the
piqi = ki + s´ivi [explanation] (11)
Via the moment of s´ivi this again incorporates the explanation represented by equations (2a and 2b).
⢠Rates of profit converge to uniform rates:
r´i = r´ (for all i) [approximation] (12)
⢠Non-uniform compositions of capital (thus 7 is dropped). Hence in general:
(k/v)i â (k/v)j [empirical observation] (13)
⢠Uniform rates of surplus-value (thus 6 is maintained):
s´i = s´ (for all i) [simplification or approximation] (6)=(14)
Because of the diverging k/v there is no labour-commanded or labour-embodied proportionality for the production prices p (we merely have piqi/vi = (k/v)i + s´). Marx is aware and explicit about this. Rather more problematical is that the combination of the three restrictions (12), (13) and (14) is impossible.
r´i = s´vi/ki = s´/(k/v)i [implication] (15)
Thus r´i â r´j. We can have uniform profit rates only with either (1) both of s´ and (k/v) uniform (the
Variant (b): reconstruction of variant (a)
The obvious way to mend the incompatibility is to reconstructively drop the (simplifying) assumption of uniform rates of surplus-value (14).11 So we have:
s´i â s´j [empirical observation] (14*)
Whence we derive:
r´i = r´ = (s´ivi)/ki (for all i) [implication] (15*)
In this reconstruction the micro equality of profits and surplus-value (r = s) is maintained;12 by implication we also have the macro R = S. Each at this level.
Variants (a) and (b)
Instead, Marx endeavours to get around the incompatibility via a macro-micro détour in which he transposes quantities between the two levels, and that in effect results in:
r´i = r´ = [(s´vi)+
δ i]/ki [âmethodologically illegitimate détourâ] (15**)
(with the aggregate sum of the
However, within the constellation of the Concretion Method this is methodologically illegitimate (though not for the reasons usually stated). Since the two explananda
§3.4 [CP-1] Method of Completion at Volume I level: partial explanation of âconcretumâ
There is also a very different interpretation of what happens at Capital I level. In this alternative we have no
piqi = ki + s´ivi + ui [partial explanation] (16)
As in CC-1 the moment of s´ivi incorporates the explanation represented by equations (2a and 2b). Again, we proceed by adding on the two simplifying assumptions of synchronically uniform rates of surplus-value and of synchronically uniform compositions of capital:
s´i = s´ (for all i) [simplification/approximation] (6 =) (17)
(k/v)i = k/v (for all i)Â [stage simplification] (7 =) (18)
Here, however, we have from the beginning no labour-commanded or labour-embodied proportionality because of the factor u:
(piqi)/vi = k/v + s/v + ui/vi [implication] (19)
(cf. 8 and 9 above). It has been argued (e.g. by Moseley) that Capital I, merely provides a partial explanation of prices (in a different way, of course, nor does CC-1 provide a full explanation).13
§3.5 [CP-2] Method of Completion at Volume III level: completion
Rates of profit converge to uniform rates:
r´i = r´ (for all i) [approximation] (12) = (20)
Hence we have for (what is now explicitly thus called) prices of production:
piqi = ki + ri [accounting identity / empirical observation] (21)
piqi = ki + r´ki [putative explanation] (22)
This is a putative explanation pending the determination of r´. Again, we have non-uniform compositions of capital (thus the simplifying assumption of equation 18 is dropped):
(k/v)i â (k/v)j [empirical observation] (13) = (23)
The uniform rates of surplus-value thesis of equation (17) is maintained; however, given equation (22) it is considered to play no (new) role at the current level.
s´i = s´ (for all i) [simplification/approximation] (17)
Reordering equations (20)â(22) we have:
r´i = r´ = ri/ki (for all i) [implication] (24)
Because the pq in the two price equations (16) and (22) are on the same plane, it is now methodologically legitimate to transpose quantities from the one level to the other (CP-1 and CP-2). (Cf. the Marx/Engels (in)famous aggregation tables of Capital III, chapter 9.)
Substituting (16) and (2b) into (21) we have:
ri = si + ui [implication] (25)
ri = s´ivi + ui [implication] (26)
In fact, this is a shortcut for Marxâs aggregation tables. However, it deserves a serious warning (and here the usual critiques come in), namely that it is assumed that the unexplained factor of ui concerns, and so is to be allotted to, profits rather than (in part) any other factor in equation (16).
We now aggregate surplus-value (S) and profits (R):
S =
Σ si [aggregation] (27)R =
Σ ri [aggregation] (28)
Next it is posited that S explains, and fully determines, R:
R = SÂ Â Â (right to left determination)Â [derived explanation] (29)
(The explanation is derived from the set of equations (1)â(4) and (16)â(28).)
We also aggregate equation (25) into:
R = S + UÂ [aggregation] (30)
Because theoretical priority is given to (29) we have:
U = 0Â [theory decision] (31)
Finally, the sector uiâs are determined via the rate of profit criterion. From (24)â(26) we have:
r´i = r´ = (s´vi + ui)/ki [implication] (32)
Hence:
ui = r´ki â s´vi [implication] (33)
§3.6 Some conclusions and a preview
1. The last equation (33) is the âtache de beautéâ of this CP set up. The uiâs are determined by the âgeneral rate of profitâ, instead of the rate of profit being fully determined by explanatory entities. Two objections may be raised against this alleged blemish. One is that we have a simultaneous determination. The other, as argued by Marx, is that, at a still lower level of abstraction, the uiâs are determined by competition (see §4.3).
2. Remind Marxâs equation (15**) from CC-2 that I qualified as âmethodologically illegitimateâ (a qualification that I maintain, that is within the Concretion Method). We had:
r´i = r´ = [(s´vi)+
δ i]/ki (15**)
Its outward appearance is similar to (32).
3. In Variant (b) of CC-2, i.e., my reconstruction of Variant (a), we have the rate of profit fully determined without any transformation âproblemâ:
r´i = r´ = (s´ivi)/ki (15*)
4. In my view CC-1 is the better interpretation of Das Kapital I, published by Marx in 1867!, and revised shortly before it. In my view CP-2 is the better interpretation of Marxâs manuscript for Part Two of Das Kapital III, written in 1864/65! (at least up to some point of the manuscript â see §4.4).
5. How is this so? This is methodologically inconsistent! Yes. Because of this problem, the following section (§4) is rather complex. My hypothesis is as follows. The 1864â65 manuscript for Part Two initially followed the path of the 1861â61 manuscript, which is in line with CP-2 â i.e., the âchapter 9â transformation procedure (see §4.3). Then, reflecting on this transformation procedure in Marxâs âchapter 10â, Marx got increasingly worried about what he had been doing in terms of his manuscript for Das Kapital I (see §4.4).14 (Engels, however, in his editing of the 1864/65 manuscript for âhisâ Das Kapital III polished away these worries whence we have the âCP-2â result.)
6. Each of [CC-1 with CC-2] and [CP-1 with CP-2] is consistent. The usual post-Marx solutions to the transformation problem obviously took Engelsâs version of Das Kapital III for granted, and then combined the âtheoretical domainâ of CC-1 with that of CP-2, which is methodologically inconsistent. If one would want to use the âdomainâ CP-2 (not only for a solution to the transformation problem but also for any other quantitative matters) then one is bound to CP-1.
§4 The 1864â65 manuscript and the text of âCapital IIIâ Part Two
§4.1 General outline
Regarding Part Two (originally one âchapterâ) of the 1864â65 manuscript Engels left unchanged the main chapter structure of the text for his Capital III edition (chapters 8â12); however, there are changes of order within the chapters as well as texts that have disappeared altogether. For the readerâs convenience, I therefore refer in this section to the Capital III chapters.
At the very opening of Part Two (Chapter 8) we immediately find the crucial assumption of a uniform rate of surplus-value, for all of Part Two (M:212; E:151; F:241).15 It is repeated regularly throughout the part. According to this manuscript it is not just a simplifying assumption but rather a law. In âChapter 10â Marx writes that competition between labourers gives rise to:
a general rate of surplus-value â tendentially that is, as for all economic laws; we posit it as a theoretical simplifying presupposition; in fact it is the actual presupposition of the capitalist mode of production even if inhibited by practical frictions â¦; in theory we assume that the laws of the capitalist mode of production develop in their pure form {rein}. (M:250-mt; cf. E:184, F:275)
Given this assumption/law the terrain of the problematic for Part Two is defined by the prevalence of non-uniform compositions of capital (ratios of k/v) between sectors of production, or also non-uniform turnover times of capital â which offers the same problematic (M:216). Thus whereas Capital I, Parts Four, Five and Seven treat the diachronic change of the capital composition (with any divergences between sectors âbracketedâ) the current part makes the reverse assumption: constant though diverging.
Part Two comprises three main chapters (chs. 8â10) that in my view should be considered together (the two smaller chapters (11â12) may be regarded as âaddendaâ). I begin with a brief outline of these three chapters before discussing some of the details.
In Chapter 8 Marx sets out the constellation that results from the assumptions just indicated. These together with the assumption that commodities are sold âat their valuesâ [presumably equation (5)] would result in differing rates of profit between sectors (M:223â4) [cf. equation (10)]. This constellation, however, does not exist in reality (M:229â30). Hence the presentation is insufficient.
Therefore the next chapter (Chapter 9) must widen the theoretical terrain. Marx introduces a new concept âproduction priceâ; âits presupposition is the existence of a general rate of profitâ (GRP) (M:234). Thus Marx posits in Chapter 9 the âproduction priceâ [cf. equation (11)/(22)]. He indicates that this is âa transformation of valueâ (âeine verwandelte Form des Werthsâ â M:239; E:173) but nevertheless carries out a quantitative substitution between the two levels of abstraction! This is a problem if his method is the Method of Concretion (§3.2â§3.3), which is the hypothesis from which I start.
The point is that the status of this transformation is very different from the purely conceptual one that Marx presented in Part One and in which no quantitative differences are involved. Consider e.g. the following quotation from its Chapter 2:
while surplus-value and profit are in fact the same â they are numerically identical â profit is still for all that a transformation {verwandelte Form} of surplus-value ⦠(M:64; cf. E:58, F:139)
Or from Chapter 1:
Materially {Stoff; stofflich} considered ⦠the profit ⦠is not different from the surplus-value itself. Hence its absolute magnitude is not different from the magnitude of the surplus-value (â¦) it is however a transformation {verwandelte Form} of the latter ⦠(M:8â9-mt)16
For the Part One transformation, no new quantitative determinations come in. However, as Marx is well aware, for his Part Two transformation we do have different quantities (
It is especially in Chapter 10 that Marx reflects on, and questions, what he accomplished in the previous chapters, including the consequences for his self-interpretation of the concept of value set out in his manuscripts.
§4.2 Chapter 8: the problematic
I now move on to the relevant details. I begin by recapitulating the important point about Chapter 8 that was been made above. This chapter sets out the following five assumptions/theses (M:223â4, 229â30):
| [A] |
assume commodities are sold âat their valuesâ [presumably |
| [B] |
assume equalised rates of surplus-value [s´i = s´j]; |
| [C] |
we have diverging compositions of capital [(k/v)i â (k/v)j]; |
| [Da] |
hence [A-C] equal capitals produce unequal surplus-value or profit [(s/k)i â (s/k)j]; |
| [Db] |
therefore we have diverging rates of profit [r´i â r´j]; |
| [E] |
in fact, however, we have (tendentially) equalised profit rates [r´i = r´j]. |
These five assumptions/theses are inconsistent. At least one of them must be wrong, it remains to find out which one(s). Analytically, I repeat analytically, this set up might make sense. (Chapter 8 makes sense generally â also in that there are no deviations from the later Capital I terminology.)
§4.3 Chapter 9: a cheerful accommodation for the inconsistency
Chapter 9 sets up a possible constellation accommodating for the inconsistency (this is my interpretation); however, in any case it is obvious that the text is investigative (Forschung) not presentational (Darstellung).18 As it turns out Marxâs set up is much along the lines of his earlier 1861â63 manuscript.
The chapter starts by repeating the assumption about the rate of surplus-value [B above]. Marx also introduces a number of simplifying assumptions such as the full and linear depreciation of fixed capital within the year, and equal turnover times (M:230â1).
Next he sets out the famous three schemes (M: 231â3). (The first and the second scheme apply assumptions/theses [A]-[D];19 the third scheme is the one were Marx introduces prices of production as diverging from value [equation (11)/(16)]). He drops sales at value [A], introduces (instead) production prices and so gets rid of diverging profit rates [Db]. He does so without hardly any argument:
Their presupposition [i.e., of production prices] is the existence of a general rate of profit ⦠In reality the very different profit rates ⦠are by way of competition equalised into a general rate of profit ⦠(M:234-mt; cf. E:167, F:257)
Note that he maintains the disproportional production of surplus-value [Da] (M:234â5).
However, [A] is not really dropped. At this point in the text Marx posits one of the famous two aggregate equalities â that is, that of âvaluesâ and production prices (perhaps
As indicated, from the point of view of the Method of Concretion (§3.3), these equalities make no sense. Not so much because of an analytical mistake (the standard critique), but because of a methodological mistake: the âvaluesâ [
Finally, for Chapter 9 I draw attention to the passage where Marx seems quite happy about what he has achieved so far, declaring that the current presentation âreveals for the first time ⦠the inner connectionâ between value and production price, and between surplus-value and profit (M:245; cf. E:178 and F:268).
§4.4 Chapter 10: gloomy reflection
In Chapter 10, however, the scene seems much more gloomy and dismal. After two pages connecting the two chapters, Marx posits two research questions, one immediately after the other (I call these Question 1 and Question 2):
{Question 1} The really difficult question here is this: how does this equalisation of profits or this emergence {Hertstellung} of the general profit rate come about, since it is evidently a result and cannot be a point of departure.
It is clear first of all that an assessment of commodity values, e.g. in money, can only be the result of their exchange, and that, when we presuppose such assessment, we have to consider them as the outcome of actual exchanges of commodity value against commodity value. {Question 2:} But how could this exchange of commodities against their actual values have come about? (M:250-mt; cf. E:183â4, F:274â5)
It is especially at this point in the text that the reader (I) may start doubting if Marx indeed aims to adopt (remember this is a research manuscript) the Method of Concretion. Note the âactual exchangesâ (âwirklicher Austauscheâ), which especially for a Hegel inspired scholar cannot leave room for compromises. So do we bid â
Marx devotes about 20 pages to Question 2, before he gets to the first. The answer to Question 1 (M:269â70; E 205â7; F:297â8) is rather limited. We learn mainly that capital moves from low to high profit rate spheres and that the thus affected supply in relation to demand establishes the transformation of values into production prices. This answer is far more problematical than it might perhaps seem at first sight. (The process briefly described here is not problematical â such movement of capital and labour is also part and parcel of classical political economy, and of many economics paradigms after it.) The problem is that Marx must rely, so it seems, on a historical process to set out a systematic problem! The movement of capital is a continuous systemic process. However, the implication of Marxâs set up is that the GRP âtransformationâ is of the past. Marx is aware of this, as we can infer from the fact that he realises that Question 1 cannot properly be answered before Question 2.
By this time â that is, when he finally gets to Question 1 (page M:269) â I guess that Marx had run out of steam as a result of being disillusioned by the consequences of his Chapter 9 outline (1864â65) â that is, the answer to Question 2.
On to Question 2: how could the actual exchange of commodities against their actual values {
The âtry outâ of the historical transformation especially is inconsistent with the Chapter 9 procedure.24
On page M:267 (E:203; F:294) Marx finally arrives at a systematically and thus methodologically relevant statement. Note that he uses the kind of 1859 (or 1867) terminology of exchange (Engels puts the following in the past tense suggesting an even more direct reference to Capital I, Chapter 1):
In considering money, it is assumed that commodities are sold at their values, because there is no foundation {Grund} to consider prices deviating from value since the concern is just the changes in form that commodities have to undergo when they are turned into money and then transformed back into commodities again. ⦠it is completely irrelevant for them as such [the commodities] whether the realised commodity price is below or above their value. The value of the commodity as groundwork {Grundlage} remains important, since money can only be developed conceptually from this foundation {Fundament}, and price, in its general concept {seinem allgemeinen Begriff nach}, is only valeur monetisie [monetised value; the two words appear in French]. (M:267-mt; cf. E:203, F:294â5)
Methodologically this is fine. I believe this sheds light on what Marx (with the 1859, or later, text in his mind) intended to do in the 1867 text. It is a conceptual presentation in stages of complexity. So, finally, it seems that Marx leans back to the Method of Concretion?
In fact, Marx shows here himself (implicitly that is) that the Chapter 9 procedure makes no methodological sense. An abstract magnitude of value cannot be put into quantitative equality with the magnitude of some concretum.
I round off this section with a comment on Engelsâs editorial work. Quite apart from all my methodological critique on Chapter 9 as addressed above, Engels seems to have misjudged Marxâs own critique on that chapter in his Chapter 10 manuscript (and Engelsâs polishing work made all this worse). Thus Engels provided intelligent people like Böhm-Bawerk with plentiful opportunities to point out inconsistencies, inconsistencies that Marx himself in fact laid bar.
§5 Notes on a small 1878 ms.: diverging rates of surplus-value
My suggestion that Marx was not happy with the Chapter 9 manuscript is sustained by the fact that Marx kept returning to the matter in manuscripts from much after the publication of Capital I (see §1) even if without substantial progress (that is, in the MEGA II/14 manuscripts). However, I should like draw attention to a hint in Marxâs final manuscript on the issue (Marx 2003f/1878?).25 This is a small manuscript of six pages dating probably from 1878 (see Vollgraf and Roth 2003, p. 697). Consider the following passages:26
For [the] calculation of the rate of profit that the social capital yields it was assumed {angenommen}, 1) that the rate of surplus-value uniform for the different heaps of capital {Kapitalmassen} in different branches of industry, 2) and neglecting turnover, i.e., the turnover of the social capital over the year posited = 1.
In fact for the different heaps of capital different rates of surplus-value and different turnover times. (158-mt)
The clarification following it (after seven, printed, lines on the calibration of turnover times) is very interesting. Note Marxâs usage of the term pure (rein) which he reserves for law-like entities.
These are just differences {Differenzen} emerging from the pure economic conditions, namely different {verschiedne} magnitudes of the capitals invested in business sectors, different rates of exploitation of labour-power, different turnover times. However [there are] other aspects of the equalisation such as unattractiveness, danger and standing of the work. (158-mt)
This text is ambiguous. With some hesitation I opt for the interpretation that the text emphasised by Marx in the last quotation, sums up the pure conditions. (In the alternative interpretation the two assumptions of the first citation would presumably be the âpure conditionsâ. However, it would then be most puzzling how these could turn in their exact opposite.)
Remember the first quotation in §4.1 [p. 294 of the current book] from the 1864â65 manuscript (its p. 250) where Marx posited the uniform (general) rate of surplus-value as part of the âpureâ constellation. Thirteen years later, if my interpretation above is correct, non-uniform rates of surplus-value are seen to be part of the theoretically pure constellation â whereas the competition between labourers has become a subordinate factor. Then even Marxâs reason for the troubling 1864â65 Chapter 9 type of procedure evaporates.
Conclusions
We have seen that the assessment of Marxâs GRP transformation procedure in Chapter 9 of his 1864â65 research manuscript for Das Kapital III hinges on the interpretation of the general method that he adopts for the three volumes of Capital. If the adopts the Method of Concretion (cf. §3.3) then the procedure is illegitimate. The problem centres on the two equations for âvalueâ and âprice of productionâ, each posited at a different level of abstraction. Then the mistake is to transpose quantities between these levels. If Marx adopts the Method of Completion (§3.5) the procedure is legitimate, though not without problems. More important, it would make much of Capital I problematical.
We have seen that in the course of writing Chapter 10 of the research manuscript for Das Kapital III, Marx becomes increasingly worried about the consequences of Chapter 9. For over 15 pages it seems that Marx is leaning towards the Method of Completion. However, towards the end of Chapter 10, Marxâs apparently reverts to the Method of Concretion, so leaving the Chapter 9 procedure in the air. This conclusion applies to the manuscript. On basis of âEngelsâsâ text (as well as his interpretation of Part One of Capital I) the Method of Completion is fairly consistent for most of Part Two of Capital III.
The problem for the interpretation of Marxâs work, and for the further development of Marxian theory after Marx, is not that Marx encountered a big problem that he did not solve. The problem is that Engels in his editorial work polished away most of Marxâs worries and so made it appear as if Das Kapital III was a near to final texts instead of a research manuscript on this issue.
We also saw (§3.3) that the very reason for Marxâs troubling 1864â65 Chapter 9 type of procedure is in fact the thesis of a uniform rate of surplus-value. If that thesis is dropped there is in fact no transformation âproblemâ. In reference to Marxâs brief last manuscript on the issue (§5), we saw that there is some (thin) evidence that Marx might have been about to set on this track.
I am grateful for the comments and discussion provided by the participants of the 2006 ISMT meeting in Bergamo â esp. Christopher Arthur, Riccardo Bellofiore, Roberto Finelli, Roberto Fineschi, Rolf Hecker, Michael Heinrich, Fred Moseley, Patrick Murray, Regina Roth, Tony Smith, and Massimiliano Tomba. I have also added the completely new section 4 (against which, due to space limits, other parts of the original paper were removed).
Kopf et al. 1983, pp. 15*â16*.
[2023 note. Since 2015 there is one by Ben Fowkes: Marxâs economic manuscript of 1864â1865, Leiden: Brill.]
Relevant are esp. pp. 373â¯ff. and 434â¯ff. of the English edition.
For a comparison: the 1861â63 draft consists of 35 printed pages (MEGA); the 1864â65 draft has 285 printed pages (MEGA); the final text of Das Kapital III, as edited by Engels is 164 pages (MEGA) (220 pages in the MEW edition).
The annotations to the texts (e.g. text variations, crossing outs, dating and contextualisation) by Vollgraf and Roth are of superb scrutiny and scholarship.
Heinrich (1996) writes about the whole of the manuscript for Das Kapital III: âthere are modifications to the original text on practically each page that have not been indicated. Hardly one paragraph remained as Marx had written it. Engelsâs modifications are not confined to âstylisticâ matters. ⦠[T]he 1894 edition was an extensive adaptation of Marxâs manuscript, and Engels did not inform the readers about the true extent of his adaptation. ⦠The interventions ⦠offer solutions for problems which the manuscript left open ⦠and in some passages they even change the argumentation of the original text, if this obstructs Engelsâ interpretationsâ (pp. 456, 459, 464). See also the extensive comments by Vollgraf and Jungnickel (1994) about Engelsâs mark on the text (âEngels left only few of Marxâs sentences untouchedâ â p. 47-mt).
Relating to (uniform) turnover time, there is a problem with equation (1) that I set aside for the purposes of this essay (see Reuten 2006).
Marxâs explanation is discussed in Reuten 2004. [Chapter 8 of the current book.]
I feel constrained to stress that an interpretation may be truthful as an interpretation, but that this does not imply that the interpreter agrees with what is interpreted.
The theoretical ground for this reconstruction is in the productive force and the degree of intensity of labour (cf. Capital I, Ch. 15) as discussed in Reuten (2004, esp. pp. 136â41). [Chapter 8 of the current book, §2.4.]
That is, prior to the introduction of finance and interest.
As a corollary it may be noted that, as against CC-1, there is at this point no implication of (implicit) uniform profit rates.
Another problem is that the penultimate manuscript for Das Kapital I is missing. We just do not know to what extent â if at all â Marx adapted his text as a consequence of the worries mentioned.
I write âuniformâ; the manuscript has âconstantâ and âgivenâ. The manuscript has âchapterâ; Engels apparently forgot to change this into âpartâ.
This text appears on the opening pages (2â3) of the manuscript; apparently it is omitted in Engelsâs text.
A similar critique was made earlier by Hartmann (1970, p. 370): âThe mistake made by Marx was the mistake of viewing a transcendentally early (category) as identical to a transcendentally late one.â Smith (1990, p. 168) adds: âThis goes against one of the basic canons of systematic theories of categories.â (Hartmann is cited from Smith.)
Cf. Vollgraf and Roth 2003, p. 385.
In the second scheme the silly addition of profit rates (to 110%) is Engelsâs (F:256).
When he posits
Note that for the following 20 pages Engels maintains the structure of Marxâs text.
Instead of Capital I, Chapter 1, we can take the 1859 Critique as a reference point. On page M:257 (E:191â2) Marx refers to this work (note that the 1864â65 manuscript for Capital I is lost â see Kopf et al. 1983, pp. 15*â16*).
Böhm-Bawerk, of course, read the text as a final document â that is, as polished by Engels.
Engels, on the other hand, seems to have liked the idea. It has given rise to a historical, as against systematic, interpretation of Capital I, Chapter 1 â rightly criticised by Arthur (1997). Such an interpretation, however, cannot save the Chapter 9 procedure (even neglecting the latterâs internal problems of the two conditions).
If we neglect the 25 lines of algebra which is the content of a manuscript from probably 1877â82.
It is extremely difficult to translate these texts. Marxâs texts are unpolished and continuously mixed with shorthand phrases.
A tilde ~ before the second date means that the text, as edited by Engels, is roughly based on that manuscript.
First Engl.transl. Ernest Untermann 1909.
MEGA: MarxâEngelsâGesamtausgabe (1975â1997 Dietz Verlag, Berlin; 1998-current Akademie Verlag, Berlin).
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