In all social circumstances, material reproduction involves the generation and disposition of particular products (specific use-values, in appropriate quantities) by means of an allocation of available resources—natural and produced physical resources, but also, crucially, human labors. Each particular use-value is produced because a portion of available social labor takes the form of the specific activities it requires. So in all times and places, each qualitatively distinct use-value is inherently associated with a qualitatively specific cluster of human laboring activities.
When Marx takes capitalist social relations as his focus, he confronts further dimensions of social reproduction. Capitalist production is production for exchange: outputs are consciously and intentionally produced as commodities, produced in order to be exchanged, and thus production and exchange are interacting phases of the broader process of social reproduction. When outputs are produced as commodities, they are no longer simply use-values with particular characteristics, but also “bearers” of exchange-value since they are exchangeable in certain proportions with all other commodities. Commodities thus have a dual nature: as use-values, each is defined by the particular and unique qualitative characteristics that make it useful in consumption or production, but as exchange-values, those characteristics are irrelevant and all that matters is their common property of exchangeability: as an exchange-value, a commodity represents simply a quantitatively specific part of aggregate social output which, via exchange, can enable the acquisition of some other equal portion of that aggregate.
Given his focus on the social (class) relations of capitalism, Marx immediately poses this dual nature of commodities in relation to a parallel “two-fold character” of the labors engaged in their production.1 On the one hand, as noted above, the commodity as a qualitatively specific use-value is associated with the qualitatively specific labor activities needed for that use-value: “the totality of heterogeneous use-values … reflects a totality of similarly heterogeneous forms of useful labour” (Marx 1976, 132). On the other hand, as a bearer of exchange-value, each commodity is qualitatively homogeneous yet quantitatively distinct, and so “as exchange-values they represent the same homogeneous labour, i.e., labour in which the individual characteristics of the workers are obliterated” (Marx 1970, 28). In Marx’s terminology, the heterogeneous labors associated with the use-value dimension of commodities are concrete labors, unique and distinct; the homogeneous labor associated with the exchange-value dimension is instead abstract labor, human labor in general, abstracted from its various concrete forms. Concrete labors as such give the commodity its use-value, but those same concrete labors simultaneously represent the abstract labor that gives the commodity its value: as “congealed quantities of homogenous human labor, … as crystals of this social substance … common to them all, [the products of labour] are values—commodity values” (Marx 1976, 128). And value is the category with which Marx then proceeds to analyze the exchange-value relations established between commodities in the market.
As initially presented at the beginning of Capital 1 (prior to any mention of money), value is measured in units (hours) of abstract labor-time. As a magnitude, commodity value counts only the labor-time that is “socially necessary,” the time required to produce “under the conditions of production normal for a given society and with the average degree of skill and intensity of labour prevalent in that society” (Marx 1976, 129). So differences (in skill, productivity, intensity, etc.) among the individuals producing any one specific commodity by performing a particular type of labor are disposed of by averaging, i.e., counting only labors done under average social conditions. All other dimensions of difference between concrete labors, including those presented by qualitatively different skills (i.e., “complex” rather than “simple” labors) are presumably accounted for in some fashion (“obliterated”) through what Marx refers to as a “reduction” process that commensurates disparate individual labors and creates the homogeneous (abstract labor) unit of account for value.2
In several passages Marx says more about this reduction process through which concrete labors are homogenized as abstract labor, and his repeated invocation of the role of exchange within that process has proven to be an issue where different interpretations are possible. Marx writes (with emphasis added):
The point of departure is not the labour of individuals considered as social labor, but on the contrary the particular kinds of labour of private individuals, i.e., labour which proves that it is universal social labour only by the supersession of its original character in the exchange process. Universal social labour is consequently not a ready-made prerequisite but an emerging result. ... on the one hand, commodities must enter the exchange process as materialised universal labour-time, on the other hand, the labour-time of individuals becomes materialised universal labour-time only as the result of the exchange process.
(Marx 1970, 450)
[T]he specific social characteristics of [producers’] private labours appear only within ... exchange. In other words, the labour of the private individual manifests itself as an element of the total labour of society only through the relations which the act of exchange establishes between the products, and, through their mediation, between the producers.… It is only by being exchanged that the products of labour acquire a socially uniform objectivity as values ...
(Marx 1976, 165–6)
The equalization of the most different kinds of labor can be the result only of … reducing them to their common denominator, … human labor in the abstract, and only exchange brings about this reduction, opposing the products of different forms of labor with each other on the basis of equality.
(Marx, quoted in Rubin3 1972, 148)
It is only the expression of equivalence between different sorts of commodities which brings to view the specific character of value-creating labour, by actually reducing the different kinds of labour embedded in the different kinds of commodity to their common quality of being human labour in general.
(Marx 1976, 142)
Clearly Marx sees a relationship between the commensuration of heterogeneous commodities as equivalents in exchange and the commensuration of heterogeneous concrete labors that occurs when commodity value is expressed in terms of abstract labor. But the nature of the relationship has been differently interpreted. Is the relationship simply one of “reflection” or “expression,” or is it more complex and causal?4 Do the results of exchange simply “manifest” or “bring to view” quantitative relations already determined when labors are performed in production, or is exchange more deeply constitutive of how production labors “count,” how they are weighted, in determining values? Or are there perhaps implications for the very possibility of quantitative measurement of value in terms of labor-time?
Some have argued that abstract labor can only be expressed in terms of money, and that therefore there is no need to pursue a reduction that would allow value to be expressed in a labor-time unit of account. Pursuing the method of “systematic dialectics,” members of the loose-knit group of authors favoring the “value-form” approach (e.g., Reuten (1988), Reuten and Williams (1989), Arthur (2004)) seek to break from any “substance” conception of value, even that found in Marx. Labor is viewed as the source of value, but not its substance and not its measure: “only in the market is the product constituted as a commodity and the labour that produced it constituted as abstract labor in the form of money,” and so “money as it appears in the market is the only expression of value. There are no pre-market value entities (such as labour-embodied in a Ricardian conception of value…)” (Reuten 1988, 53–4). Commodity producers of course anticipate the market’s outcomes and make advance calculations (an “ideal precommensuration”), but “it is only the validation of labour and its products in the market that determines where and how much value(-added) is actualized” (Reuten 1988, 57). The market attaches a money measure to the commodity and so to the labors that are expressed in its value, and no other measure of the labors performed in production is necessary or even possible: “abstract labor … is a category of the social process of validation (… not a category of the individual process of production…” (Reuten 1988, 57).5 This rejection of the very possibility of an abstract labor unit of account separates the value-form approach from the quantitative concerns present in other interpretations of value categories.
Most interpreters do understand abstract labor as a quantitative measure, the original unit for conceiving commodity value, but not all view the concept as useful. Critics of Marx’s value theory are, not surprisingly, also typically critics of abstract labor as that theory’s core quantitative concept—Steedman, for example, whose treatments of heterogeneous labors are an extension of his critique of Marxian value theory in Marx After Sraffa. Steedman argues that Marx follows (and, for consistency, must follow) the practice of the classical economists in aggregating heterogeneous concrete labors into a “quantity of labor” by using weights proportional to relative wages (Steedman 1985, 560). With the real wage bundle for each type of concrete labor-power taken as data, his reading of Marx implies that a uniform rate of exploitation (e) can be present only if the value added by the labor performed by each concrete labor type is proportional to the value of each wage bundle. This allows a classical-type “wage aggregation” quantifying heterogeneous labors on a common scale as abstract labor while also determining commodity values in Steedman’s sense of the term, as the abstract labor expression for the concrete labors directly and indirectly embodied in the commodity6 (Steedman 1980, 46–8).
But Steedman considers this an empty triumph:
The concept of ‘abstract labour’ … is a metaphor for the fact that each specific labour is one part of the social division of labour. Apart from [this], the metaphor and the concept can be discarded at zero cost to Marx’s theory.
(Steedman 1985, 573)
And since this “neo-Ricardian” approach regards the calculation of commodity value as simply an unnecessary step in the derivation of competitive prices and profits, abstract labor is similarly redundant, a phrase with “no genuine explanatory content”—“just a pair of words” (Steedman 1985, 568, 573). Note that in this neo-Ricardian conception of abstract labor no reference is made to the exchange process—abstract labor is derived with reference solely to technical production conditions and the information on real wages taken as data.
A different quantitative understanding of abstract labor, similar in some respects to (even though deeply different from) the neo-Ricardian understanding, is the probabilistic approach of Farjoun and Machover (1983). They reject any “deterministic” relation between value and price, denying both the need for and realism of the imposition of a uniform competitive rate of profit as a part of price theory. Instead, they treat profit rates and price-value ratios as random variables, to be theorized in terms of their characteristic distributions rather than calculated from more basic data. Still, they recognize their own need to develop an empirically measurable and testable definition of the “labor content” of commodities, one independent of prices (so as to avoid any “deterministic” relation between value and price). Thus, they explicitly pose the question of how to aggregate the value added by different types of concrete labor. Marx’s approach, they note, involves distinguishing “skilled” from “simple” labor, which requires the derivation of “skill coefficients” with which to weight different labor types. But Marx, they argue, did not present a method independent of prices with which to derive these coefficients (Farjoun and Machover 1983, 216), and the authors express skepticism that there is any such method available. However, their own probabilistic approach (treating price-value ratios as random variables) does not require any such calculation: “skill coefficients are not required by our probabilistic theory, nor can we see any reasonable way of determining them”; since “all we need is a consistent way of measuring the labour-content of commodities,” they instead “opt for the egalitarian solution of the problem,” in which the contributions to value of different types of labor “count on an equal basis, so that … a baker-hour [counts] as equal to a tool-maker-hour” (Ibid., 221, 215). Each measured hour of concrete labor is assumed to count, like any other, as an hour of abstract labor.7 Farjoun and Machover regard this egalitarian method of calculation as both “appealingly simple” and “most consonant with the very notion of abstract labour” (itself regarded as “one of [Marx’s] deepest insights” into a commodity economy) (Ibid., 215, 213). In the end, although they reject the perceived determinism of the neo-Ricardian conception of price-value relations, they nonetheless have in common with Steedman the premise that “labour-content is determined solely in the sphere of production,” independent of prices and all other exchange phenomena (Ibid., 223–4).
Still another approach to quantifying abstract labor is exemplified by McGlone and Kliman (2004), operating from within the “temporal single system interpretation” (TSSI) of value theory. McGlone and Kliman read Marx on the “two-fold character” of labor as implying that “the labour of workers in capitalist production is immediately abstract as well as concrete” (McGlone and Kliman 2004, 141). This means for them that concrete labors as we observe and measure them are simultaneously abstract labor-time: “clock-hours thus measure abstract labor” (Ibid., 149, n. 4, emphasis in the original). Thus, while observed concrete labors are heterogeneous in many ways including skill complexity, for McGlone and Kliman it is still the case that “even though complex and simple labour create different amounts of value, … complex and simple labour are both abstract labour” (Ibid., 136).8 By thus “disentangling” the concept of abstract labor from the issue of skill complexity, they can then proceed to the latter issue, recognizing that “the reduction of complex to simple labour presupposes the separate and prior reduction of concrete to abstract labour” (Ibid., 139). The complex/simple issue is regarded as merely a “measurement problem, specifically an index number problem,” one that perhaps presents “measurement difficulties” but is “trivial and unnecessary” to the larger project of Marxian value analysis.9 Finally, having reduced complex abstract labor to simple abstract labor, the value created by an hour of work can be specified using Marx’s definition of “socially necessary” labor: “each hour of work of a simple labour-power, working at average intensity and under average technological conditions …, is one hour of abstract, socially necessary labour” (Ibid., 140). For McGlone and Kliman, “abstract, value-creating labour [is] the exact same real work as the concrete labour that produces use-values, and … each hour of the one is likewise an hour of the other, given only that the work is socially necessary” (Ibid., 141). Thus, in this TSSI approach, “workers’ labour in the capitalistic production process is made abstract by, and is abstract within, this [production] process” (Ibid., 135–6), and “no reference to exchange of the products is needed in order to determine either the abstract labour extracted from workers or the products’ values” (Ibid., 142). Indeed, allowing any role for exchange in commensurating different labors is said to make labor-value analysis “devoid of significance” (Ibid., 135).
The views so far considered represent two broadly distinct positions. On the one hand, value-form theory stresses the crucial role of the exchange process in constituting abstract labor, but denies the possibility of a quantitative reduction permitting an abstract labor unit of account (i.e., a non-monetary measure). On the other hand, in their very different ways, the neo-Ricardian, probabilistic, and TSSI approaches all affirm the need for abstract labor as a quantitative measure but see that measure as determined within the production sphere in a way that excludes the exchange process from any constitutive role. In addition, though, there is a third broad position, affirming both the quantifiable abstract labor unit of account and the role (suggested in the quotations from Marx above) of the exchange process in commensurating concrete labors as abstract labor.
The early essays of Isaak Rubin (published in English only in 1972) emphasize Marx’s repeated invocations of exchange when considering the concept of abstract labor. Rubin seeks to counter the then-prevalent “physiological interpretation” of abstract labor, insisting that abstract labor is a “social phenomenon” which “we must construct” as a social and historical category, yielding, in Rubin’s phrase, “a sociological theory of abstract labor” (Rubin 1972, 135). Individual acts can be seen as social when they are viewed as parts of a broader whole, and so a private and individual act of labor “is social if it is examined as part of the total mass of homogeneous social labor or, as Marx frequently said, if it is seen in terms of its ‘relation to the total labor of society’” (Ibid., 141). But “the equalization of labor is carried out through the equalization of things” (Ibid., 98). It is the exchange of disparate and dissimilar use-values (their commensuration as equivalent exchange-values) that allows them to be counted as parts of the whole product. At the same time, this process also accomplishes a second commensuration: although “the concrete labor of producers is not directly social labor but private, … this private labor can become social only through its equalization with all other forms of labor, through the equalization of their products” (Ibid., 98, 141). Concrete labors, the private and particular acts of separate individuals, are commensurated in and through exchange as social, general, and universal labor, simply parts of a (homogeneous) social whole expressed in terms of abstract labor.
Rubin examines Marx’s texts, stressing that “in later editions of Capital, Marx, with increasing sharpness, underlines the idea that in a commodity economy only exchange transforms concrete into abstract labor” (Rubin 1972, 148; see also endnote 2). He also explicitly seeks to counter the criticism that this amounts to the (un-Marxian) notion that abstract labor and value originate in the exchange sphere. Rubin understands Marx’s invocation of exchange in this context as referring not to a “particular phase” distinct from and subsequent to the production phase but to exchange as “a social form of the production process” which “puts its specific imprint on the entire process of reproduction” (Ibid., 149). For Rubin, value originates in production labors, not exchange relations, but the “specific imprint” of exchange is what allows production labors to be counted on a common quantitative scale:
in a commodity economy … the equality of two amounts of abstract labor signifies their equality as parts of total social labor—an equality that is only established by means of the equalization of the products of labor. … equality in the form of abstract labor is established through the process of exchange.
(Rubin 1972, 155)
However, while for Rubin abstract labor is an explicitly quantitative concept, he does not present a formal quantitative treatment.
Krause (1982) invokes Rubin in developing his own quantitative approach. Krause was the first to present a systematic formal treatment of abstract labor as an “induced relation” derived from equivalence in exchange: if two commodities are market equivalents when taken in certain physical quantities (e.g., 20 yards of linen and 1 coat), this equivalence relation “results in the ‘equating’ of certain quantities of the various concrete labours expended in [the] production” of those physical quantities (Krause 1982, 94–5). “Concrete labour viewed in terms of this equivalence relation is designated abstract labour” (Ibid., 10). Crucially, though, Krause understands the induced relation in terms of value, i.e., the abstract labor expression for the concrete labors directly and indirectly embodied in those commodities, so that relative quantities of abstract labor embodied equal relative prices, an equality he refers to as “the fundamental relation” (Ibid., 90). Krause completes his system with what he calls the “standard reduction of labour” as a way of determining the reduction coefficients (abstract labor per unit of each concrete labor performed).10 In combination, these elements of Krause’s system guarantee the equality of relative prices and relative values, since value for Krause is understood as the abstract labor expression for concrete labors directly and indirectly embodied. In effect, Krause derives coefficients to count concrete labors as abstract labor in precisely the way needed to impose a uniform capital composition, a circumstance which eliminates the price-value deviations that Marx, in Capital 3 and beyond, regards as the general capitalist case. To Krause, this is his system’s strength (it disposes of the need to engage in price-value transformation), but it brings with it some rather un-Marx-like results.11
The approach to abstract labor as an induced relation is most extensively developed by Roberts (2004, 2005, 2009), who, unlike Krause, begins from the premise that relative values and (capitalist) relative prices can and do systematically diverge. Hence, when equivalence is established in the market between commodities in particular proportions (20 yards of linen and 1 coat), this equates the concrete labors “contained in” the exchange-values of the commodities, rather than in their (generally different) values. Roberts focuses on passages from Contribution to the Critique of Political Economy (CCPE), where Marx examines the measurement of “the specific character of … labour which is embodied in exchange-value,” recognizing that when “regarded as exchange-values all commodities are merely definite quantities of congealed labour-time” (Marx 1970, 29–30). But the labor-time represented in exchange-value is explicitly social labor, and thus “equal” despite the heterogeneity of the various concrete labors performed. How is this accomplished? Marx answers by means of an analogy; concerning exchange-value as “the specific manner in which the social character of labour is established,” he says:
the effect is the same as if the different individuals had amalgamated their labour-time and allocated different portions of the labour-time at their joint disposal to the various use-values.
(Marx 1970, 32)
Roberts (2004, 128) points out that individuals, as such, have only concrete (private, particular, individual) labors to dispose of; if they were to “amalgamate” those concrete labors, the result is the aggregate vector of concrete labors available “at their joint disposal”; if they were then to “allocate different portions” of that aggregate to particular commodities, each such portion would be a quantitatively distinct but qualitatively identical “share” of the total, a vector of labors “of uniform quality, whose only difference, therefore, is quantity” (Marx 1970, 30).
Marx here applies to the measurement of labors an analytical metaphor that appears regularly in his later work, that of an “aliquot part” economy, in which actual magnitudes (e.g., capitals or individual commodities, as well as labors performed) are replaced by equivalents derived by the same “amalgamate and allocate” procedure. As one among many possible examples, Marx writes:
The average profit which a capital … yields in a certain trade it yields not as the capital employed in this particular way, nor in the proportion, therefore, in which it produces surplus-value, but as an aliquot part of the aggregate capital of the capitalist class.
(quoted in Baumol 1974, 55)
In this and many other cases, Marx poses competitive capitalism as enforcing results identical to those derived by first amalgamating (here, taking the “aggregate capital”) and then allocating qualitatively uniform portions (an “aliquot part”) of appropriate magnitude. Here, each capital’s profit emerges as a redistributed share of aggregate surplus-value amounting to the surplus-value that would be generated by a capital of equivalent size but average composition; similarly, in the quotation from CCPE above, the same logic shows that individual acts of concrete labor become commensurable (as parts of commodities’ exchange values) when each is replaced by a socially average composite of concrete labors taken in the same proportions as (because it is an aliquot share of) the social aggregate of concrete labors.12
Roberts combines Marx’s “amalgamate and allocate” metaphor and the approach to abstract labor as an induced relation, developing a formal system in which actual inputs (commodities and concrete labors) are replaced by their aliquot share counterparts (a “standard technology”). The system has a determinate solution13 in which (1) the vectors of concrete labor hours directly and indirectly embodied in commodities under aliquot part or standard technological conditions are proportional to each other (they all have the same “average” composition as the aggregate of concrete labors) and so can be added directly to express each commodity as a magnitude of homogeneous (abstract) labor; and (2) those magnitudes (the “average labor” directly and indirectly embodied) express the commodities’ exchange values (or, in fully competitive capitalism, their production prices). This is precisely the “induced relation”: the equality of use-values as equivalents in exchange also expresses (induces) the equality of the labors that are “contained in” their exchange values. In effect, extending Marx’s aliquot part metaphor as a means of abstracting from the technological heterogeneity of actual production conditions in one stroke creates a viable (homogeneous) labor-time unit of account and applies it to the quantification of exchange value as “average labor embodied.” Moreover, viewing the commodity as it appears in competition, “as a part, both really and conceptually, of production as a whole” (Marx 1971, 112–13), highlights the intimate connection between the dual nature of commodities and the “twofold character” of the labors that produce them: the expression of each use-value as an exchangeable (aliquot) part of the social product as a whole is simultaneously the expression of the concrete labors it contains as parts of the aggregate of social (abstract) labor. So, in this reading, price formation (“gravitational” adjustment of relative prices to levels expressing exchange equivalence) is inseparable from the formation of abstract labor as the homogeneous unit of measure for the labor content of commodities. Each is an aspect of a single process that simultaneously commensurates use-values as market equivalents and commensurates concrete labors as abstract labor, so that equivalents in exchange do indeed “contain” equal amounts of abstract labor (Roberts 2005, 155–6).
Like other variants of the Marxian tradition, Roberts sees value as generated in production, not exchange—its substance derives from labors performed, while the act of exchange, in and of itself, creates nothing (neither use-value nor value itself originates in the act of property transfer). But “universal social labour” is not immediately quantifiable in production—it is “not a ready-made prerequisite but an emerging result” (Marx 1970, 45). Hence, Roberts argues, like Rubin (“the equalization of labor is carried out through the equalization of things”), that value is only measurable (concrete labors are only commensurable as abstract labor) through the combined impact of production-and-exchange. In this reading of Marx, labors only become “labor” through the same market equivalences that turn use-values into “income.”
Overall, there are clearly unsettled issues remaining for Marxists working in this area of value theory, particularly concerning the role (if any) for the exchange process in the determining the quantitative unit of account for value: is abstract labor determined fully in production, with exchange merely providing a visible expression or manifestation of quantitative relations determined prior to it, or do the concrete labors deployed in production become quantifiable as abstract labor only in the broader context of exchange, as the consequence of exchange equivalence?
1 Indeed, Marx referred to his treatment of “the two-fold character of labour” as one of “the best points in my book [Capital 1],” in a letter to Engels, August 24, 1867 (Marx 1987, 402).
2 Whether abstract labor should be approached through a single reduction encompassing all aspects of heterogeneity, or through a process with analytically distinct reductions (treating complex versus simple labor as a separate problem), has been a matter of dispute among interpretations; see below. The most extensive early discussion of complex and simple labor is Hilferding [1904] 1949.
3 The quoted passage is translated from the fetishism section of the French edition of Capital, vol. 1 [1872]; Rubin stresses that the final part of this sentence, containing the explicit reference to exchange, was inserted by Marx into the French edition as a conscious effort to clarify the meaning of the prior German editions.
4 As Rubin (1972, 147) recognized, the issue here “borders on a very serious and profound question of the relation between production and exchange. … On one hand, value and abstract labor must already exist in the process of exchange, yet on the other hand, Marx in several passages says that abstract labor presupposes the process of exchange.”
5 Fred Moseley has much in common with this “value-form” group, including the insistence on the primary importance of measuring value magnitudes in terms of money. However, Moseley differs in that he does treat labor performed as measurable at the level of “the individual process of production”—he takes as data “the quantity of the current socially necessary labor-time (L) (in units of abstract labor hours)” (Moseley 2015, 31). But he never interrogates how the different concrete labors underlying his L are aggregated—with regard to the needed “reduction coefficients,” he sees it as sufficient to note that “Marx simply took the reduction coefficients as given, as did Smith and Ricardo before him” (Moseley 1997, 3), so that concrete labors “are assumed to be converted” into abstract labor (Moseley 2015, 31)—and so Moseley, like the value-form group, has little to say about abstract labor as a unit of account.
6 The coefficients expressing abstract labor per unit of each concrete labor emerge from the (normalized) eigenvector derived from the matrix showing the various concrete labors directly and indirectly embodied in the wage bundles, with (1/1 + e) as the corresponding maximal eigenvalue.
7 While this “egalitarian solution” dispenses with the need for skill coefficients, it actually goes further to dispense with any need to consider any and all other factors beyond skill differences that might differentiate concrete labors.
8 McGlone and Kliman’s idiosyncratic usage of the term abstract labor here differs from that of other commentators (and arguably from Marx as well) since abstract labor hours in their sense are apparently not homogeneous: they note, for example, that “if the abstract labour of [weavers] is, on average, more or less complex than the abstract labor of [tailors],” then “the amounts of abstract labour extracted differ across industries” (McGlone and Kliman 2004, 140–1).
9 McGlone and Kliman, like Marx, present no “rule” for the quantitative reduction of complex to simple labor (their numerical example assumes that “one can somehow determine” the coefficients), but they suggest in passing that the reduction of complex to simple labor would use information on the training time necessary for creation of skilled labor-power; this approach to determining skill coefficients is dismissed by both Steedman (“impossible to take … seriously”) and Farjoun and Machover (“we know of no reasonable way of determining them”) (McGlone and Kliman 2004, 138–9).
10 The coefficients emerge from the left-hand eigenvector corresponding to the maximal eigenvalue of the matrix of input-output coefficients (commodity inputs per unit of output).
11 In addition to the imposition of definitional proportionality between prices and values, there are further issues: Krause must then derive wage rates consistent with those prices and the implied rate of profit, rather than, a la Marx, treating (real) wages as data describing the reproduction of labor-powers, determined presumably by factors including the state of class struggle.
12 “[A] ‘socially average’ hour of work is literally a composite hour incorporating all the various concrete labors in the proportions in which each type enters into the social aggregate … [and] the value created by such an average composite hour [can be] set equal to 1 (one abstract labor hour)” to define the unit for measuring value, with the scale for value added by living labor thus set by the aggregate of clock-hours of labor performed (Roberts, 2004, 118).
13 Determinate, using Marx’s typical assumption of a uniform rate of exploitation e; that e is derived without reference to or prior solution for prices, from the usual data on production conditions and real wages, given only the “rule” for exchange equivalence (equal values changing hands in Capital 1, profit rate uniformity in Capital 3, etc.). Reduction coefficients for particular concrete labors then follow, along with values and prices (Roberts 2009, Appendix). Note that “value” here is understood in the sense of the term developed by “single system” interpretations (see “Value and Price,” this volume).
Arthur, C. 2004. The New Dialectic and Marx’s Capital. Leiden: Brill.
Baumol, W. 1974. “The Transformation of Values: What Marx Really Meant (An Interpretation).” Journal of Economic Literature 12(1): 51–62.
Farjoun, E. and M. Machover. 1983. Laws of Chaos: A Probabilistic Approach to Political Economy. London: Verso.
Hilferding, R. [1904] 1949. Böhm-Bawerk’s Criticism of Marx. New York: Augustus M. Kelley.
Krause, U. 1982. Money and Abstract Labour. London: Verso.
Marx, K [1859] 1970. A Contribution to the Critique of Political Economy. New York: International Publishers.
Marx, K. 1971. Theories of Surplus-Value, Part 3. Moscow: Progress.
Marx, K. [1865] 1976. Capital, vol. 1. London: Vintage.
Marx, K. [1867] 1987. Marx & Engels Collected Works, vol. 42. London: Lawrence & Wishart.
Marx, K. [1872] 2012. Le Capital, vol. 1. Paris: Hachette Livre-BNF.
McGlone, T. and A. Kliman. 2004. “The Duality of Labour.” In The New Value Controversy and the Foundations of Economics, A. Freeman, A. Kliman, and J. Wells, eds., 135–150. Cheltenham: Edward Elgar.
Moseley, F. 1997. “Marx’s Concept of Abstract Labor: Substance or Form? A Critique of the ‘Value-Form’ Interpretation of Marx’s Theory.” International Symposium on Marxian Theory, Mexico City.
Moseley, F. 2015. Money and Totality. Leiden: Brill.
Reuten, G. 1988. “Value as Social Form.” In Value, Social Form and the State, M. Williams, ed., 42–61. London: Macmillan.
Reuten, G. and M. Williams. 1989. Value-form and the State. London and New York: Routledge.
Roberts, B. 2004. “Value, Abstract Labor, and Exchange Equivalence.” In The New Value Controversy and the Foundations of Economics, A. Freeman, A. Kliman, and J. Wells, eds., 107–134. Cheltenham: Edward Elgar.
Roberts, B. 2005. “Quantifying Abstract Labor: ‘Aliquot Part’ Reasoning in Marx’s Value Theory.” In The Capitalist State and Its Economy; Democracy in Socialism, P. Zarembka, ed., 137–169. Bingley: Emerald Group Publishing.
Roberts, B. 2009. “Ricardo : Standard Commodity :: Marx : __?__.” Review of Political Economy 21(4): 589–619.
Rubin, I. [1923] 1972. Essays on Marx’s Theory of Value. Detroit: Black & Red.
Steedman, I. 1977. Marx After Sraffa. London: New Left Books.
Steedman, I. 1980. “Heterogeneous Labour and ‘Classical’ Theory.” Metroeconomica 32(1): 39-50.
Steedman, I. 1985. “Heterogeneous Labour and Marx’s Theory.” History of Political Economy 17(4): 551–574.