1.1 A comment on dimensions: monetary value and labour-time

I begin with a brief comment on the ‘dimensions’ in which Marx casts his analysis of the process of production of capital. Note first his particular level of abstraction here: his analysis deals with an average production process – in regard to the quantity and quality of both the means of production used and the labour used, and in regard to their organisation.⁴ [2023 remark: Most of the time Marx indeed treats averages. However, not so in Chapter 12 (ch. 10 of the German edition). I regret that the current article neglected this. The non-average account here is treated in Chapter 2 (2019) and Chapter 15 (2017) of the current book.]

One of Marx’s greatest insights, in my view, is that he comprehends the capitalist production process as a unity of labour process and of {ideal} valorisation process.⁵ In the opening Chapter 7 of the middle part Marx writes:

Just as the commodity itself is a *unity of* use-value and value, so the process of production must be a *unity of labour process and process of creating value*. (…)

The production process *as a unity of labour process and process of creating value*, is a process of production of commodities; *as a unity of labour process and process of valorisation*, it is a capitalist process of production, or the capitalist form of the production of commodities. (F, 293 and 304 – amended;⁶ G, 201 and 211)

Thus Marx is pointing out here the specific capitalist value-form of production. Expressed otherwise, we have a unity of a process of physical production (labour process) and a process of {ideal} value augmentation (valorisation process). We have two things coinciding, as unity. As simple as this may appear in practice (it is happening all the time in capitalist enterprises), its analysis is complex especially dimensionally: we have value categories (homogenous); time (homogenous); heterogenous physical inputs and outputs; and labour that can be conceived of in terms of homogenous time, but that is itself heterogenous.

Throughout this middle part Marx, as we will see, uses two dimensions for his analysis in general and his representations/equations in particular: a value dimension and a labour-time dimension. Without exception the value entities are expressed in monetary terms (£); the same applies to all numerical examples.⁷ It is necessary to emphasise this since in some accounts of Marx’s theory, ‘value’ is itself taken to have a labour-time dimension. This is a wrong account of Marx’s Capital (those same accounts often adopt the term ‘labour values’ – one that is never used in Capital). As we will see, Marx, at the level of abstraction of Capital I, aims to explain value (monetary dimension) in terms of labour-time – therewith, of course, value is not discarded of its monetary dimension. (Value is the abstract counterpart of price, at the level of abstraction – Capital I – where the distinction between surplus-value and profit is still implicit; the distinction is also not yet relevant – Marx reaches this by presenting the average capital.)

Besides the two dimensions mentioned, Marx adopts an intuitive notion of physical labour productivity increase: increases in the number of use-values (goods) produced by a unit of labour (but he always ends up by expressing these use-values in terms of price multiplied by quantity).⁸

The main problem in understanding Marx’s texts (beginning with Part One of Capital I) is that he proceeds, step-wise, to find an endogenous dimensional reference point (or reference points), one that is (or are) internal to his object of enquiry, one that is (are) key to the functioning of his object of enquiry.⁹ Its core terms, in Marx’s view, are the monetary dimension and the time dimension. The early parts of each of the three volumes of Capital theorise the interconnection of these dimensions in increasing complexity and concretion (Volume I, Parts One and Two; Volume II, Part One; Volume III, Part One) ending up with the measure of capital, the rate of profit over time. Thus we end up with the connection of the monetary dimension with the time dimension in general, not the particular labour-time (of Capital I). However, that does not mean that labour-time becomes irrelevant at the Capital III level of analysis, just that we reach an overarching category.

The labour and labour-time category retains relevance at any level of abstraction in three respects. First, for the grand organisation of the production process (the technique adopted) and, related, the planned organisation of the intensity of labour (say ‘speed’). Second, for the common day to day organisation of production on the production floor, the management of output per labourer, i.e., per unit of labour-time. Third, the renumeration of labour-time, i.e., the wage rate. With the first and third fixed for any time being, the second determines the level of output and so profits. Earlier I wrote that Marx adopts in his analysis an ‘intuitive’ notion of physical labour productivity increase. At the point of production there is nothing intuitive about it.

In Marx’s choice of categories and dimensions, and especially in the particular way he phrases his theory, there are undoubtedly also other issues at stake. For one, Marx (1867¹;1890⁴) intervenes in the discourse of the Ricardian economics of his day (with its ‘labour-embodied’ theory of value), at times radically breaking away from it (his value-form theory), at others operating within it or at least at its margins. An additional problem here is that Marx sometimes, misleadingly, speaks about values (the explanandum) as “expressions” of labour (the explanans). (In the same vein a neoclassical economist might, also misleadingly, speak about prices as “expressions” of utility or preferences.) Apart from the few remarks in the next paragraph, I will not comment on these aspects in the remainder of this essay (for more see my 1993, Murray’s 2000a comment on it, my 2000 reply, and Murray’s 2002 rejoinder).

I take the circuit of capital {M – C … P … C´ – M´}, i.e., its growth via the stages of investment (M–C), production (C–P–C´) and sales (C´–M´), to be an interconnected process. From the perspective of the valorisation (i.e., augmentation) of capital, the ‘moments’ of the circuit (M–C; C–P–C´; and C´–M´) can be distinguished but not separated. Thus valorisation of capital, the ‘production’ of capital, is the unity of this process. To stress this is in part a value-form theoretical development from Marx (i.e., with Marx beyond Marx – see e.g. Reuten and Williams 1989 and much of the work of Christopher Arthur, Tony Smith and Patrick Murray; see also Nicola Taylor 2004).¹⁰ This development builds on one of the theoretical lines in Capital. On the other hand, Marx often tends, so it seems, to attribute a predominance to the ‘moment’ of production, especially when he is discussing production. His terminology of ‘production’ of surplus-value and ‘production’ of capital (apparently in abstraction from the other moments) seems to reflect this attributed predominance. In face of the unity of this process, I consider Marx’s terminology misleading. For the value-form theoretical view, more specifically, there is properly speaking no production of ‘value’; we have value inputs (M–C) and the valorisation result in C´–M´, i.e., when commodities are validated and commensurated in the market in terms of money. In between (C–P–C´) this result is anticipated upon, hence in production we merely have an ‘ideal’ pre-commensuration, or an anticipated imputation of value.¹¹ Hence we have no production of value, but physical production in terms of value. Having said this, I will for the purposes of this essay – and apart from a few reminders in footnotes – just report Marx’s own terminology in this respect.

1.2 The terrain of the middle part of ‘Capital I’

In this subsection I briefly survey the general terrain of the middle part of Capital I (Parts Three to Six, over 400 pages), against the background of Part Two.¹²|¹³

Capital, writes Marx in Part Two of Capital I, is “the unceasing movement of profit-making” (F, 254). We have a movement from money (M) into more money: M … M+ΔM. But “unless it takes the form of some commodity, it does not become capital” (F, 256). Marx expresses this in the formula M–C–M´ (where C is the value of a commodity, or of commodities, and M´=M+ΔM). This is a formula of exchange, derived from the simpler M–C–M. The latter is a strange act, namely buying (M–C) in order to sell (C–M). It is an ‘inversion’ of C_i–M–C_j, i.e., selling C_i in order to buy a qualitatively different C_j (F, 258). Here, money is merely a facilitator – it does not really matter. In the strange, inverted, form M–C–M, though, money is all that matters; however, it makes sense only as M–C–M´, that is, when the end result is an increment (ΔM), a ‘surplus-value’ as Marx calls it. In M–C–M´ value is

the subject of a process in which, while constantly assuming the form in turn of money and commodities, it changes its own magnitude, throws off surplus-value from itself considered as original value, and thus valorises itself independently. For the movement in the course of which it adds surplus-value is its own movement, its valorisation is therefore self-valorisation. (F, 255)

So capital is a movement of self-valorising value, of throwing off surplus-value.¹⁴ Part Two is closed off with the introduction of a particular commodity and commodity market, that of labour-power. The existence of this market is predicated on the workers’ lack of means of production. We also have a brief introduction of the value of labour-power, i.e., the wage, which in principle should be sufficient to reproduce labour-power. How much is ‘sufficient’ depends on physical, historical and moral elements (F, 272–5).

In the middle part of Capital I (Parts Three to Six) we see “not only how capital produces, but how capital is itself produced” (F, 280). That is, how surplus-value (ΔM) is produced – thus the (potential) expansion of capital. How can surplus-value be explained? Reconsider M–C–M´. “The change in value of the money … cannot take place in the money itself … The change must therefore take place in the commodity …” (F, 270). Hence the key to M–C–M´ lies in C. In an analysis of the production process, Marx next shows how this is the site were the value of C is turned into C´.

In the exchange M–C, capital in money-form is turned into capital in commodity-form: means of production and labour-power. Means of production bought are static elements; they have on average a fixed technical lifetime and have their value transferred to the product, whence Marx terms the part of capital laid out on it constant capital (F, 311–17).¹⁵ Labour-power, or labour capacity, is exchanged against the wage; so the labourer sells its capacity to labour (for the time agreed by contract). A change in C can only be engendered by this active living element, labour. And since this capacity is in principle variable, both in time (length of the working day) and in intensity – as we will see in more detail later on – Marx terms the part of capital laid out on it variable capital. During production, labour is “subordinated” to capital: “the worker works under the control of the capitalist … the product is the property of the capitalist and not that of the worker” (F, 291–2). In labour resides the potential to produce a surplus-product, or, in value-terms: surplus-value. Thus labour potentially generates a surplus-value beyond the wage – or, from the point of view of the capitalist, a surplus-value beyond the capital advanced. Marx calls the ratio between the amount of surplus-value and the capital laid out in wages the “rate of surplus-value” or the “degree of exploitation of labour-power by capital” (F, 320–7).

Part Three is on “The production of absolute surplus-value” (Chapters 7–11, about 150 pages). Central to it is the increase in the rate of surplus-value through extension of the working day. In my view this part serves didactic purposes, similarly to Marx’s recurrent procedure of starting with “simple reproduction” (stationary state) before setting out “expanding reproduction”. In this case it allows Marx to introduce systematically both the concept of “the value of labour-power” and the drive for increase in the rate of surplus-value. This didactic procedure of Marx also has a surprise effect. How could we still have – as happened in Marx’s day – an increase in the rate of surplus-value, or perhaps a constant rate, when we have a decrease of the working day?

This question is the core issue treated in Part Four on “The production of relative surplus-value” (Chapters 12–15, some 215 pages). Both regular “revolutions in the productive forces” and increases in the intensity of labour (each with very different effects as we will see in §2) allow for a constant or even an increasing rate of surplus-value along with a decreasing length of the working day. Both of these are core to the capitalist mode of production.

The synthetic Part Five bears the dull but appropriate title of “The production of absolute and relative surplus-value” (Chapters 16–18; it is a relatively short part, extending to 30 pages).

In sum, for the explanation of surplus-value (and the rate of surplus-value), Marx posits four factors:

1. The magnitude of the value of labour-power;

2. The length of the working day;

3. The productive force of labour;

4. The intensity of labour.

He deals with the first two in Part Three (see §2.1 below) and the next two in Part Four (see §2.2 and §2.4). Sections 2.3 and 2.5 provide reconstructions of Marx’s formal explanatory treatment.

2.1 The rate of surplus-value

Part Three, “The production of absolute surplus-value”, begins with two chapters setting out the distinctions between the ‘Labour process and the valorisation process’ (Chapter 7) and between ‘Constant capital and variable capital’ (Chapter 8) – briefly discussed in §1.2 above.¹⁶ In Chapter 9 Marx formalises these distinctions, decomposing capital advanced (Z) into constant capital (c) laid out on means of production, and variable capital (v) expended on labour-power (F, 320–1).¹⁷ The starting point for his formalisation (equations M–1 to M–5 below) is a (stylised) empirical reference:

The surplus-value generated in the production process by Z, the capital advanced, i.e., the valorisation of the value of the capital Z, presents itself to us first as the amount by which the value of the product exceeds the value of its constituent elements. (F, 320 – C amended into Z, cf. the previous note)

Capturing this, Marx formally starts with a number of identities and definitions.

Z = c + v [accounting identity] (M–1)

As valorised Z is ‘transformed’ into:

Z´ = (c + v) + s [accounting identity] (M–2)

where s is surplus-value. Thus in Z-Z´ we have the abbreviated formula of the production by and of capital.

Henceforth all of Marx’s equations/representations are indicated with M–. Unless made explicit otherwise, the dimension of all equations is monetary (as indeed Marx has it explicitly in terms of pounds, £; cf. also pp. F 327–29 where Marx, using empirical cases, derives s from business accounts.). All equations apply to a definite time period (a production period); I have refrained from adding on time subscripts as these would be uniform for all equations (up to equation 14). For each equation I indicate their analytical status in square brackets; the particular terms are mine (M–2, for example, is named ‘a tautology’ by Marx – F, 320).

Marx calls ‘the new value created’ (y) ‘the value-product’ and the output (x) ‘the value of the product’.¹⁸

y ≡ v + s [definition] (M–3)

x ≡ (c + v) + s [definition] (M–4)

The s over v proportion is called ‘the rate of surplus-value’ (e).

e ≡ s/v [definition] (M–5)

As a ratio of equal dimensions e ≡ s/v is, of course, a dimensionless number. Crucially from a theoretical point of view Marx (F, 324–6) casts the “same” ratio (F, 326) in terms of ‘surplus labour’ (SL) and ‘necessary labour’ (NL).¹⁹

e* ≡ SL/NL [definition] (M–6)

e = e* [explanatory device] (M–7)

Thus he posits e* as an explanation for e. There is a difficulty here. So far, there is nothing in itself wrong with positing the one ratio as an explanation for the other, or with positing surplus labour(-time) as an explanation for surplus-value. There is a problem, however, if the explanans (e*, or SL) cannot be measured independently of the explanandum (e, or s). This is not uncommon in science, but it is nevertheless a problem and far from a perfect situation.²⁰

So far we have entities (c, v, s) that are, in principle, observable and measurable. However, by themselves (in isolation from the already known s/v ratio, one that can be measured) SL and NL cannot be measured. Another observable and measurable entity might be the labour-time of workers, e.g. 10 hours a day. Given a particular length of the working day we could, analytically, divide that up into one part in which an amount of value is produced equivalent to wages (equivalent to variable capital, v) and call this ‘necessary labour(-time)’ (NL), and another part in which an amount of value is produced equivalent to the surplus-value (s) and call this ‘surplus labour(-time)’ (SL). This is in fact what Marx does (F, 329–31).²¹

Another way to think about this is that (M–6) together with (M–7) simply makes explicit the idea that at a given wage per day, an extension of the working day results, in general, in an increased value-product. On this account (M–6) with (M–7) have elementary explanatory meaning.²²

Early on in the last chapter of Part Three, Chapter 11, Marx provides a decomposition of the surplus-value in his earlier representations.²³

s = (s/v)v [definition] (M–8)

s = w(a´/a)n [explanatory device] (M–9)

where:

(Hence the underlined symbols in M–8 and M–9 are in value per time dimension; a´ and a in time dimension. This way we end up with the monetary value dimension for s – at least if we interpret Marx’s “the number of workers employed” for n (F, 418) as workers days, which can readily be inferred from the context.)

Note that as ratios we have the equalities of

e ≡ s/v = s/v = a´/a [recapitulation of explanatory device] (10)

The s in the s/v of (M–8) cannot be measured independently of s and v. Similarly the a´/a of (M–9) cannot be measured independently of s and v. (See the comment on (M–6) and (M–7) above.)

Anticipating Marx’s discussion of absolute and relative surplus-value in Part Five, I add on a definition here (equations 11 or 12 are not Marx’s):

wL ≡ v [definition] (11)

where w is the wage rate per hour and L the amount of labour hours hired. Hence we may rewrite (M–9) as

s = e*(wL) [explanatory device] (12)

Marx writes: “the mass of surplus-value {s} is determined [bestimmt] by the product of the number of labour-powers {L} and the degree of exploitation of each individual labour-power {e*} … We assume throughout, not only that the value of an average labour-power {w ?} is constant, but that the workers employed by a capitalist are reduced to average workers” (F, 418; G, 322; symbols in curled brackets added).

The advantage of this notation (12) is that the number of hours hired (L) – as well as their remuneration (w) – has been made explicit. It seems that in his representation (M–9) Marx tried to bring this in – unsuccessfully though, since the working day itself is a variable (cf. Marx’s w and n). On the other hand, in equation (12) we seem to have lost Marx’s distinction between labour-power (L) and labour (L).²⁴ Or at least, this is now merely implicit.²⁵ In that respect, representation (12) – to be found in much of contemporary Marxian theory – is defective.²⁶ Later on we will retrieve Marx’s labour–labour-power distinction (§2.3 and §2.5).

2.2 The ‘productive force’ of labour

Part Four of Capital I presents “The production of relative surplus-value”. In its first Chapter 12 Marx introduces a key factor into his presentation: “change in the productive force of labour”.²⁷ Before going into this, a note on translation is required. In the context of production we will generally need to differentiate between changes that have to do with the exertion of labour only, or mainly, and changes that have to do with the interconnection of changes in the means of production, technology and the exertion of labour. It seems to me that in the German text Marx makes important differentiations in this respect. Fowkes translates the German Produktivkraft by “productivity”.²⁸ This is unfortunate, as Marx sometimes also uses the term Arbeitsproduktivität (labour productivity) – this will be seen to be especially important in the context of his presentation of ‘intensity’ of labour, discussed in the next subsection. In all of the following texts I will amend the translation for Produktivkraft into ‘productive force’ (marked *…* – I use the same mark for any other amendments, as specified in footnotes).²⁹

In Chapter 12 Marx writes:

Hitherto, in dealing with the production of surplus-value … we have assumed that the mode of production is given and invariable. … The technical and social conditions of the process and consequently the mode of production itself must be revolutionized *so as to increase the productive force of labour* …. (F, 431–2 amended;³⁰ G, 333–4).

Introducing this by way of an example Marx wrote:

increase in the *productive force* of labour … cannot be done except by an alteration in his [the labourer’s] tools or in his mode of working [Arbeitsmethode], or both. Hence the conditions of production of his labour, i.e., his mode of production, and the labour process itself, must be revolutionized. By an increase in the *productive force* of labour, we mean an alteration in the labour process of such a kind as to shorten the labour-time socially necessary for the production of a commodity, *hence a smaller quantity of labour acquires the force* of producing a greater quantity of use-value. (F, 431 amended;³¹ G, 333)

Productivity (it seems to me) has an imprecise meaning.³² I am pretty sure that Marx always reserves his term Produktivkraft (productive force) for – as he says in this quotation – the production of a greater quantity of use-value by a smaller (or by the same) quantity of labour (and it usually goes along with price decrease). My hypothesis is that the notion of ‘socially necessary labour-time’ – see the quotation – is associated with this notion of productive force and that, in this context, ‘productive force’ must be taken as average.

In the subsequent chapters of Part Four (13–15) Marx further conceptualises the development of productive force by way of a historical description of the development of ‘tools’, via manufacture, into (Chapter 15, section 1) ‘machinery and large-scale industry’. Generally Marx associates an increase in productive force with changes in the organisation of the labour process (e.g. related to scale and division of labour and to changes in the composition of capital).³³

2.3 A formal and immanent-reconstructive intermezzo on capitalist revolutions in the productive force of labour

It is not until Chapter 18 (i.e., the last chapter of Part Five) that Marx returns to his formulas for the rate of surplus-value, however, without improving on the previous ones – i.e., those discussed in §2.1 above. Nevertheless, in view of the conceptual progress made by Marx so far (Chapter 11 to Chapter 15, section 2), there is reason to do so. (Marx does not do it here and does not return to it in similar contexts later on.)

We saw that the potential of labour for producing use-values (the potential use-value productivity) is affected by the productive force; today economists would say: the state of technology and its implementation. Thus given that state, any labour is potentially exerted at a particular productive force.

A revolution in the productive force of labour can be envisaged as a change in technological trajectory (T) – think of grand technologies such as that of steam engine, electricity, petrol motor, computer. They get started in particular branches and then are gradually diffused throughout all or most of the branches in the economy. Let us simplify a trajectory (i) into a certain value c of specific means of production that could potentially be worked up by an amount of average labour (measured in time).

T_i ⊇ «c/L» [definition of approximation] (13)

Thus c/L stands for a certain value (£) of means of production that could be worked up by a particular amount of labour in a definite period of time. (Analytically we might put L to unity, e.g. an hour, whence we have, e.g., £10 per labour hour.) The guillemets here, indicate the specificity of means of production and labour; ⊇ is the sign for ‘contains or equals’. Within a trajectory we have bounded variations in c/L ratio’s coming about in tranches (blocks) of diffusion (variations say of a range of 40% – in the analytical example ranging from £10/hr to £14/hr, coming about in e.g. 5 tranches). We call any one such tranche a state of the technological trajectory (ST), or a state of the development of the productive forces:³⁴

ST_i(t) ⊇ «c/L»_(t) [definition] (14)

The subscript (t) stands for that particular state of trajectory (i) – it also stands for a definite period in time (e.g. 1850–1860) in a region (e.g. Great Britain and France).

Let us now consider production (recall that the accounting dimension of the production process is a monetary one).³⁵

x = «c/L»_(t) L^β[β>1]³⁶ [determination; step of heuristic

 approximation] (15)

Hence, as before, x is the gross output in value terms (e.g. £). «c/L» is the quantity of means of production in value terms that could, potentially, be worked up by a quantity of labour (hours). The c is some value of means of production at the point when workers enter the business gate (at the point where they enter ‘the hidden abode of production’ – F, 280). Thus «c/L» is for example (£40mln)/(4mln potential labour hours).³⁷ The outer right-hand L in representation (15) is the actual labour employed (measured in hours), i.e., actual labour-time. The factor β in L^β is the actual exerting power of labour (per hour). For the time being we take β to be a (stylised) constant, as attached to the productive force «c/L»_(t).

I make a strict distinction between, first, the productive force of labour («c/L»_t), second, labour-power in the conventional sense (the L in «c/L»), i.e., a potential, and third, the ‘actual exerting power of labour’ (L^β) – this distinction is returned to in §2.5.³⁸ Apart from the value of labour-power (see §2.5) we have herewith collected all of the main variables that Marx adopts in his Part Four analysis of relative surplus-value. [2023 note: except the ‘potentiated’ (or ‘empowered’) value-productivity of labour – cf. chapters 2 and 15 of the current book.]

Before further commenting on β in the next subsection, we may proceed with a simple example (simple purely illustrative numbers). Let «c/L» = £40mln/(4mln labour hrs). Let β=1.16 (at L=4mln hrs). Then, because 4^1.16=5, x = £50mln. Assume the average wage rate to be £1.50. From Marx’s equation (M–4) and definition (11) we have the accounting identity:

s = x − (c + wL)

s = £50m − [£40m + (£1.50)(4m)] = £50m − [£40m +£6m] = £4m

x = c + wL + s = £60m + £6m + £4m

So this gets us back to Marx’s type of example. In fact my statement ‘let β=1.16’ is analogous to statements of his, such as ‘if 1 hour’s labour is exhibited in 6d’, where d is a monetary unit.³⁹

Indeed all of Marx’s formulas are results. The advantage of a representation such as (15) is that we see some more of the explanatory dynamic behind those results; an explanatory dynamic that Marx sets out in his text.

As indicated, in Parts Three to Six of Capital I all of Marx’s focus is on the rate of surplus-value. In terms of the formalisation of the current subsection we have for that rate:⁴⁰

Thus at the prevailing productive force of labour «c/L»_(t), the rate of surplus-value depends positively on the ‘actual exerting power of labour’ β, and negatively on the wage rate w. So far β is a constant power. Note that it cannot be directly measured independently of surplus-value (s).⁴¹

According to Marx the main concomitant of revolutions in the productive forces is a decrease in the value of commodities. To the extent that these are wage goods, such revolutions allow for nominal wage decrease at any level of real wages. Thus between states of technological trajectories we have, ceteris paribus (specifically the factors affecting the subsumption of labour), the rate of surplus-value pushed up. Indeed this, for Marx, is the heart of the production of relative surplus-value. Thus we have

w = w* + f(ΔST_(t))    [f´ < 0] (17)

where w* summarises the labour market aspects of the general state of subsumption of labour.⁴²

2.4 Degree of intensity of labour

We now proceed from the point where we left Marx’s text prior to the reconstructive intermezzo of the previous subsection. Note first that Marx up to this point – as he reminds us early on in the section now under discussion – conceptualised increase in the production of relative surplus-value as being engendered by increase in the use-value productivity of labour. “The same amount of labour-time adds the same value as before to the total product, but … is spread over more use-values. Hence the value of each single commodity falls” (F, 534 – italics added).⁴³

In section 3(c) of Chapter 15, Marx presents the concept of ‘intensity of labour’.⁴⁴

… something we have already met with, namely the intensity of labour, develops into a phenomenon of decisive importance. Our analysis of absolute surplus-value dealt primarily with the extensive magnitude of labour, its duration, while *the degree of its intensity* was treated as a given factor. We now have to consider the inversion [Umschlag] of extensive magnitude into intensive magnitude, or magnitude of degree. (F, 533 amended;⁴⁵ G, 431)

Marx directs our attention here both by the terms ‘decisive importance’ and ‘inversion/break’ [Umschlag]. Thus next to the magnitude of labour (L), Marx introduces its degree of intensity. In fact part of my reason for introducing the formalisation of §2.3 is to be able to put sharp focus on this. In terms of my representation (15) or (16) a change in the ‘actual exerting power of labour’, the β in L^β, is at stake. Henceforth I will call this the ‘degree of intensity of labour’.⁴⁶ Marx – as he does often when introducing an important new concept – uses a number of adjectives to stress the concept. Here is a key formulation – it is also a key citation for the current article:

… the development of *the productive force and the economisation of the conditions of production* imposes on the worker an increased expenditure of labour within a time … This compression of a greater mass of labour into a given period now counts for what it really is, namely an increase of the quantity of labour. In addition to the measure of its ‘extensive magnitude’, labour-time now acquires a measure of its *degree of density*. … The same mass of value is now produced for the capitalist by, say, 3⅓ hours of surplus labour and 6⅔ hours of necessary labour, as was previously produced by 4 hours of surplus labour and 8 hours of necessary labour. (F, 534 amended and italics added;⁴⁷ G, 432–3)

Thus we see a crucial conceptual progress (concretisation) in comparison with the earlier simpler (more abstract) conception summarised at the opening of this subsection: no longer do we have the simple parallel between value and labour-time.⁴⁸

Marx indicates as main factors bringing about this intensity increase, an increase in the speed of the machines, and the same worker having to supervise or operate a greater quantity of machinery (F, 536). In the remainder of the section he cites reports as evidence for this process.

The issue is taken up further in the synthetic Part Five – apart from a brief passage in Chapter 16 (F, 646) mainly in its Chapter 17. Note that all along Marx’s primary problematic is not so much the determination of the magnitude of value, but rather the relative magnitudes of surplus-value and the price of labour-power.⁴⁹ At a given average real wage rate per ‘normal working day’, the latter relative magnitudes depend on:

(1) the length of the working day, or the extensive magnitude of labour, (2) the normal intensity of labour, or its intensive magnitude, whereby a given quantity of labour is expended in a given time and (3) the *productive force* of labour, whereby the same quantity of labour yields, in a given time, a greater or a smaller quantity of the product, depending on the degree of development attained by the conditions of production. (F, 655 amended;⁵⁰ G, 542)

All these three are variable, and next Marx analyses their variation in turn. I focus on the intensity of labour (section 2 of Chapter 17).

… if the length of the working day remains constant, a day’s labour of increased intensity will be incorporated in an increased amount of value, and, assuming no change in the value of money, in an increased amount of money. … A given working day, therefore, no longer creates a constant value, but a variable one …. (F, 661 – italics added;⁵¹ G, 547)

So far this repeats – though in a very clear formulation – the inversion/break indicated above. However, in two subsequent statements Marx (I think) muddles the issue for the inattentive (preoccupied?) reader. Here is the first one.

Whether the magnitude of the labour changes in extent or in intensity, there is always a corresponding change in the magnitude of the value created, independently of the nature of the article in which that value is *exhibited*. (F, 661 amended;⁵² G, 548)

Although to the letter of the text there is nothing to complain about, it might (carelessly) be read as a repetition of the conceptualisation cited at the very opening of this subsection. In fact the ‘magnitude of labour’ has now been cut loose from labour-time; labour-time no longer ‘corresponds’ to value (at least not diachronically).

Such a (careless) reading and its implication might be reinforced by the next, and final, text of this section in Chapter 17:

If the intensity of labour were to increase simultaneously and equally in every branch of industry, then the new and higher degree of intensity would become the normal social degree of intensity, and would therefore cease to count as an extensive magnitude. (F, 661–2; G, 548)

Again, to the letter this is fair enough – as well as consistent with Marx’s general approach. However, it seems to de-emphasise the conceptual progress “of decisive importance”.⁵³ To the extent that over time (diachronically) we have recurrent increases in the “normal social degree of intensity”, the value-producing potential of labour cannot be measured diachronically by labour-time independently of the value produced.⁵⁴ (By itself this does not make the explanatory power of the theory useless; it makes it more problematical.)

As indicated, Marx returns to his formula for the rate of surplus-value in the final Chapter, 18, of Part Five. It is a mystery why he, after making subtle distinctions in the previous chapters, relapses into the simple s/v result and its ‘surplus-labour’ over ‘necessary labour’ counterpart.

The intensity matter is returned to in Chapter 25 of Part Seven, “The general law of capitalist accumulation”, however, without much further development (F, 788–9 and 793).⁵⁵

It is obvious that in terms of the reconstructive formalisation of the previous subsection Marx’s new “normal social degree of intensity” of labour would be posited in terms of changes in the degree β in L^β associated with a state of the ‘productive forces’ or the state of a trajectory. Of course, this does not increase the explanatory power of the theory; it does focus, though, on the conceptual development (and it may help developing it further).

2.5 Once again, the value of labour-power and the wage rate

From all of the middle part of Capital I – indeed all of the book – it is obvious that Marx always conceives of wages, and the value of labour-power, in terms of days or weeks. Indeed this directs all his theorising about absolute and relative surplus-value. Theoretically this seems as poignant as an engraved Gestalt (in the sense of Kuhn). On the one hand this is understandable historically, that is from the perspective of the practice of the second half of the nineteenth century (including struggles over the length of the working day and the working week); the perspective of if, and how well, one can live off a day’s or a week’s wage. On the other hand, however, this is difficult to understand given that it is Marx’s aim to set out ‘capital’ and its development from its perspective, i.e., immanently.

Whereas Marx’s conceptualisation of labour-power is fine as and when he introduces it in Part Three (absolute surplus-value), there is a problem when he moves to Part Four (relative surplus-value) and introduces shortening of the working day. The daily value of labour-power is by itself not of interest to capital, but rather the value of labour-power per hour of labour-time (that is the value of labour-power relative to the actual time of employment).

Reconsider Marx’s equations (cf. §2.1)

s = (s/v)v (M–8)

s = w(a’/a)n (M–9)

and the added

wL ≡ v (11)

s = e*(wL) (12)

Recall that the underlined symbols are in per day terms, and w and L in per hour terms. If s would be measured over a year (for example), n would have to be the ‘number of workers times the number of labour days in a year’. (If s would be measured over one turn-over time of capital, n would have to be the ‘number of workers times the number of days of turn-over time’.)⁵⁶

Let the value of labour-power per day, VLP-d = w; the length of the working day = WD (i.e., a number of hours). Recall that w = the wage per hour, and L the number of hours worked. Thus we have:

w ≡ w/WD [definition] (18)

L ≡ n(WD) [definition] (19)

hence

wL = wn [implication] (20)

Thus there is no problem to translate wL into Marx’s terminology of ‘the value of labour-power’. But what is labour-power in these ‘different’ frames? Labour-power is the potential to perform labour (for a day says Marx) at some definite extensity (i.e., a number of clock hours) and intensity. What do we lose if we reduce this to intensity per hour? Nothing (note that for Marx a substitution between extensity and intensity is possible). Then we can interpret L as a number of labour-power per hour (labour potential) and L^B as labour actually exerted at some degree of intensity.

Here is the rephrase. Workers sell their labour-potential L (= labour-power) by the hour.⁵⁷ In production it is exerted at a prevailing productive force (Produktivkraft) with a certain degree of intensity L^β (= labour).

All this merely makes more explicit what is in Marx’s text. It also makes more explicit that the only directly measurable entities are all value entities, as well as total labour-time (extensity). All other ‘labour’ entities, including the intensity of labour (L^β) cannot be directly measured independently of the value entities and of labour extensity.