Since the rate of turnover of capital is unity, the capital she ties up is equal to her cost of production, p_j + p_jA_j and her profit rate, r_j, is:

A system of prices of production and wages, p, w that equalizes profit rates across sectors must satisfy the matrix equation:

p = (1 + r)(pA + wl)

If we assume that the money wage, w is determined by the condition that it just allows the workers to purchase their subsistence wage b, we have w = pb, and we can eliminate w from the expression altogether:

p = (1 + r) p(A + bl)

This expression for the prices of production is homogeneous in the prices, so that if some vector p satisfies it, any positive multiple of p will also satisfy it, and thus requires some normalization. Using prices of production we can recalculate Marx’s constant capital, cl = pAx, variable capital, _v_l = pb1x, and surplus value, _s_l = p(I - A - bl)x. This critique thus involves two system of accounts, embodied labor coefficients and prices, and has as a result been called a “dual system” interpretation of the labor theory of value.

How closely can we connect these two systems of accounts, one, _c_p _v_p and _s_p based on prices of production and the other, _cl_, _vl_ and _sl_, on embodied labor coefficients? Except in the “degenerate” case in which the sectoral ratios _pAj/pbl_j are all equal (Marx’s case of “equal organic compositions of capital” in this interpretation) the vector (_c_p _v_p _s_p) is not proportional to the vector (_cl_ _vl_ _sl_).Thus there is no monetary expression of labor, it, such that:

(m_c_l, m_v_l, m_s_l) = (cp ,vp, sp)

The adherents of this line of critique of Marx’s method take this analysis, the mathematical correctness of which is unquestioned, to show that there is no rigorous quantitative connection between the labor time account arising from embodied labor coefficients and the phenomenal world of money price accounts. Thus for them the labor theory of value is valid only in the special case of equal organic compositions of capital  Marx’s argument in Volume III of Capita1, they conclude, fails to fill the logical gap adequately so as to generalize the labor theory of value to account for the complexity of real capitalist economies.

From this conclusion the various proponents of the critique draw quite different lessons. Some, like Michio Morishima, attempt to retail’ a kind of shadowy underworld after-life for the labor theory of value by showing that the embodied labor accounting system reflects some aspects of capitalist reality, even though it distorts the picture qualititatively. Thus Morishima puts forward a “funda­mental Marxian theorem” that the rate of profit in the price accounting system is positive if and only if the rate of exploitation in the embodied labor accounting system is positive. These interesting mathematical discoveries, however, fail to motivate the analysis of the embodied labor coefficients system by showing what explanatory power it has over observable phenomena.

Others, like Ian Steedman and John Roemer, retain a commitment to the historical materialist perspective, Find the logical case against the relevance of the labor theory of value unanswerable. This leads them to the positive re­search program of finding an alternative analytical structure in which to situate the theory of exploitation ill more modern conceptions of price theory, either Walrasian general equilibrium theory or Sraffa’s theory of pricing.

Still others, like Paul Samuelson, prefer to see what they take to be the logical inconsistency of Marx’s labor theory of value as a fatal flaw in the historical materialist theory of exploitation as a whole.

For my own part, I would remark on two points. First, this critical line of inquiry appears to establish that an interpretation of the labor theory of value based on imputed embodied labor coefficients does not lead at the purely theoretical level to a progressive research program. Second, this line of thinking somehow manages to ignore completely the monetary aspect of Marx’s labor theory of value.

6. The Empirical Approach to Embodied Labor

The last 25 years have seen fertile and interesting empirical work stimulated by the embodied labor coefficients interpretation of the labor theory of value. This work, pioneered by Ed Wolff (for example, 1975 and 1987) and Anwar Shaikh, has been developed by Shaikh and E. Ahmet Tonak (1994) and other associates, among them Ed Ochoa (1988), and more recently extended by Paul Cockshott and Allin Cottrell and their collaborators (for example, Cockshott, Cottrell and Michaelson, 1995).

This line of empirical work uses Leontief’s input-output tables to calculate imputed embodied labor coefficients and prices of production for real-world economies. The focus of analysis is to study how much empirical deviation there is between the embodied labor coefficients system of accounts and either price of production or market price systems.

In calculating prices of production from input-output tables care must be taken over the fact that the Leontief’s A table records the flows of commodities between sectors, not the stocks of commodities tied up in production, which give rise to the denominator in the rate of profit. In order to calculate the prices that would equalize rates of profit on invested capital, these must be weighted, as Marx points out, by the appropriate rates of turnover for different classes of commodity. Some of the studies in this literature have failed to take account of this methodological point.

Considerations of space prevent me from reviewing the richness of empiri­cal detail revealed by this literature, but its main finding is that by a number of statistical measures embodied labor coefficients are closely correlated with both prices of production and market prices across sectors in real capitalist economies. The main methodological question these studies raise is the appropriate statistical measure of correlation to use in this comparison.

Since replicable empirical regularities are rather rare in economics, the strong evidence these studies offer for a widespread coherence between embodied labor coefficients, prices of production and market prices is of indubitable scientific interest. Its exact theoretical significance and explanation, however, remains obscure. Some of the key figures in this tradition, for example, Shaikh, have not yet to my knowledge publicly discussed their views of the theoretical significance of this work in detail in relation to the issues addressed in this paper.

Other workers in this tradition, Cockshott and Cottrell, for example, argue that this empirical regularity provides the foundation for the scientific role of the labor theory of value. In this view, the empirical correlation between market prices and embodied labor coefficients supports the idea that embodied labor coefficients determine market prices, and motivates economic interest in the embodied labor coefficients and their evolution over time. This position raises some troubling questions from the perspective of Marx’s own work. Suppose, for example, that the correlations between embodied labor coefficients and market prices had turned out to be much lower, or to fall over time, or to be low in certain capitalist economies. Are we to conclude that the labor theory of value does not hold, or is weakening over time, or holds only in some capitalist economies?

The empirical approach to reconciling embodied labor coefficients with real prices echoes to a considerable degree Ricardo’s position that embodied labor is a good first approximation to ‘in understanding of value and labor flows in real economies.

7. The “New Interpretation”

In the late 1970s Gerard Dumenil and I independently from each other suggested a reconstruction of Marx’s labor theory of value emphasizing the relation be­tween money and labor time that preserves the rigorous quantitative relation between paid and unpaid labor on the one hand and the aggregate wage hill and aggregate gross profit (including interest, rent, and business taxes) on the other.[3. See Duménil (1980, 1983), and Foley, (1982b, elaborated in 1986a and 1986b.) Dumenil’s work was brought to my attention and to the English-language literature through the article of Alain Lipietz (1982).****  ] This approach was rather uninformatively described as “The New Solution” to the transformation problem, and, after Dumenil’s observation that it actually abolished the “transformation problem” as such, and thus wasn’t really a solution to anything, equally uninformatively as “The New Interpretation”.

Our intervention centered on the monetary expression of labor. We argued that the important issue for Marx was the idea that money represents social labor time, and that he can therefore use a measure of the monetary expression of labor appropriately defined at the level of the aggregate system of commodity production to translate flows of money in real-world capitalist accounts into flows of labor-time and vice versa. This way of looking at the labor theory of value dispenses with the need for a separate accounting system based on embodied labor coefficients.

We argued that the core content of Marx’s labor theory of value was that the expenditure of living labor in production adds money value to the inputs to production. (Marx reiterates the point that the money value of inputs to production is merely preserved by living labor in the production process, and reappears unchanged in the price of the commodity.) The value added in production in an economy over any time period is a familiarly measured statistic, the net domestic (or national) product. Thus we concluded that the appropriate definition of the monetary expression of labor was the ratio of the net domestic product at current prices to the living productive labor expended in an economy over a period of time.

There are further important issues involved in applying this definition in practice. The measurement of net domestic product depends on deducting un­reliable estimates of depreciation of fixed capital from the more precisely mea­sured gross domestic product. (In practice the use of the GDP in place of the NDP in estimating the monetary expression of labor leads to an overestimate of the MEL, since GDP exceeds NDP by the amount of depreciation, but will not distort the time profile of the measurement very much as long as the share of depreciation in GDP is changing slowly.) Accepted national income accounting practice includes imputations of non-market transactions (such as the rental value of owner-occupied housing) that should in principle be removed from mea­sures of NDP for the purpose of calculating the MEL. There are also issues of measurement of the denominator of the MEL, the living labor expended. In principle it is necessary to adjust total hours worked for the skill levels of work­ers, A variety of methods, some based on relative wage weights, and others on more direct measures of skill, have been proposed to make this adjustment. Not all employed labor in capitalist economies is productive in Marx’s sense, so that in principle an adjustment should be made to deduct unproductive labor from the total living labor expended.[4. See Edward Wol® (1987), Fred Moseley (1990) for a further discussion of this issue.  ] In the rest of this paper I will assume (contrary to reality) that some agreement has been made on these measurement issues, so as to focus on the conceptual, definitional and interpretational problems of the monetary expression of labor.

It is important to notice that this definition of the monetary expression of labor, though it clearly links money and labor time, does not depend on any assumption about the particular monetary system operating in the economy. In particular, it works equally well for a commodity-money system like the gold standard, or for state-credit based monetary systems like those common in the late 20th century. This point underlines the fact that the definition of the monetary expression of labor in this way does not commit us to any particu­lar theory about the definition of the MEL. In a gold standard economy the MEL could be determined by the price of newly produced gold relative to that of other commodities, for example, and in a state credit money system by speculation on the prospective solvency of the state. These determining mechanisms are quite different, but in each case money can be viewed as functioning (in part) to express social labor time quantitatively.

The monetary expression of labor permits us to resolve a wide range of other issues in the labor theory of value. Dumenil and I, for example, proposed that in general the “value of labor-power” should be measured as the ratio of the money wage to the monetary expression of labor, not as the labor embodied in the commodities workers consume. With this definition the problem of the identification of surplus value in the capitalist system as a whole with the unpaid labor of productive workers simply vanishes, since the paid and unpaid portions of the total expended labor are definitionally equal to the wage and gross profit share in the net domestic product. As a result, the rate of exploitation measured as the ratio of the gross profit share hi national income to the wage share in national income coincides with the corresponding ratio expressed in labor­time equivalents. A moment’s thought shows, in fact, that this definition of the monetary expression of labor and of the value of labor-power are the only definitions that will generally preserve the quantitative relation between surplus value in the form of the aggregate gross profit and unpaid labor.

To put the matter in a slightly different light, the New Interpretation proposes to define the relevant categories of the labor theory of value so that what we regarded as the key Marxian insight, the quantitative equivalence between capitalist gross profit and unpaid labor, holds. The “dual” approach to the labor theory of value outlined in the last section, in contrast, considers whether it is possible to deduce Marx’s equivalence from other assumptions (such as the iden­tification of the value of labor-power with the labor embodied in the workers’ consumption). It is in this sense that the New Interpretation is an “interpre­tation” , not a “solution”, since it proposes a particular definitional ordering of the key abstractions of the labor theory of value.

The New Interpretation definition” has some significant methodological ad­vantages. It is completely general, ill that it is consistent with any theory of price formation (including, but not restricted to theories of profit-rate equalizing prices of production.) It opens the way to an interpretation of the substantive parts of Marx’s theory (his discussions of relative surplus value, induced techni­cal change in capitalism, and the long-term tendencies of capital accumulation, or his theory of the circuit of capital, for example) as testable empirical hypothe­ses that can be confronted with widely available statistical data. It opens up new avenues of empirical-theoretical work ill the Marxist tradition, such as an examination of the relation of national exchange rates to relative monetary expressions of labor. (See Mark Glick and Hans Ehrbar, 1987, and Simon Mohun, 1994 for further discussions of these points.)

In our initial attempts to explain the New Interpretation, Duménil and I both spent quite a bit of effort showing how it would work in the context of special models of production such as the pure circulating capital model of the last section. These expositional efforts unfortunately have misled some of our readers into thinking that these examples are all an inherent pa. t of the New In­terpretation itself, which they are not. The point of the New Interpretation is that it proposes an operational and (pace the measurement problems mentioned above) unambiguous method of measuring the monetary expression of labor in any real economy, no matter how complex its production system in terms of times of turnover or joint production activities. Since the New Interpretation only proposes definitions of a restricted set of labor theory of value theoreti­cal concepts (the monetary expression of labor and the value of labor-power) it can consistently be combined with a wide range of other definitions or hy­potheses constituting particular theories of capitalist production (for example, theories about class struggle, induced technical change, international trade and imperialism, and the like.)

The New Interpretation has, I believe, had some effect in opening up Marxist economics to a more vigorous and fertile empirical/theoretical development in the last 15 years  A promising beginning has been made in measuring the monetary expression of labor, the rate of exploitation, and other parameters of the circuit of capital in the work of Senchak (1983), Azari (1996), Matthews (1995), Alemi (1997) and Dumenil and Levy (1994)

In anticipation of later sections of the paper, let me point out that it is possible (as Fred Moseley particularly has emphasized) to extend the use of the monetary expression of labor defined by the New Interpretation to the transla­tion of money measures of constant capital and stocks of invested capital into labor-time equivalents. We could, for example, take the money flow of pur­chases of intermediate inputs (which is netted out from firm accounts to create the national income accounts, but is preserved in census-based statistics like the U.S. Census of Manufactures) and divide it by the MEL to arrive at a num­ber, denominated in labor time units, representing the labor time equivalent of the flow of constant capital. If we did this for an economy with a unit rate of turnover, then these labor time equivalents of constant capital would sat­isfy Marx’s claimed quantitative equivalence between total price and value of output, and also between the average price and value rates of profit.[5. To see this in the circulating capital model of the last section, consider that the monetary expression of labor, m, will in this context be defined as:m = p(I ? A)x/lx If we now define the labor-time equivalents of constant capital, cm = pAx/m, variable capital, vm = wlx/mand surplus value sm = (p(I– A) – wl)x/m, then we have: cm + vm + sm = (pA + p(I – A) – wl +wl)x/m = px/m rm = sm/(cm + vm) = (p(I – A) – wl)x/(pA + wl)x = r: Note that: cm = pAx/m ? lAx = cl]At the time, however, there seemed to be 110 plausible interpretation of the labor time equivalent of the constant capital or invested capital (since these measures will in general be equal neither to the historical labor embodied in the means of production, nor to the labor that would be required to reproduce them with contemporary technology). In order to clarify the relation of the proposed New Interpretation to the “dual” system that had preceded it, Duménil and I both pointed out the quantitative incongruity between the embodied labor coefficient accounts rate of profit and the rate of profit at market prices arising from the difference between the labor embodied in the means of production and the labor-time equivalent of the money spent on the means of production using the monetary expression of labor. Fred Moseley has argued that this lacuna represents an inconsistency in the New Interpretation, which “transforms” variable capital, but does not “transform” constant capital in the same way. I personally see no objection to using the New Interpretation definition of the monetary ex­pression of labor to derive labor-time equivalents of constant capital. In effect, Marxist empirical and theoretical studies based oil the circuit of capital do this by looking at the dynamics of the money values in the circuit.

8. Criticisms of the New Interpretation

The New Interpretation has been criticized on various grounds.

Anwar Shaikh and E. Ahmet Tonak criticize the relevance and originality of the New Interpretation in the following terms:

As just defined, the value of money… is the living labor commanded in exchange by the net product. This means that the value of labor power … is the living labor commanded by the money wage bill of productive workers, and that surplus value … is simply the living labor commanded by the existing mass of profit. Marx argued that price and profits were monetary forms of value and surplus value. The new approach abandons this altogether by defining surplus value to be a form of profit! The whole relation between surplus value and profit is turned on its head. Moreover, tills approach does not even have the virtue of being new, since it is really nothing more than Adam Smith’s second definition of labor value as living labor commanded by price.  Ricardo and Marx decisively rejected this approach, with good reason. (1994, p. 179)

Shaikh and Tonak here reveal a misunderstanding of either the New In­terpretation or of Smith’s conception of value as labor commanded. Smith’s definition identifies the amount of what he called “labor” and what Marx called ‘labor-power” the price of the commodity could command on the market, in algebraic terms p/W where ;) is the money price of the commodity and w the money wage. Ricardo’s and Marx ‘5 reasons for rejecting Smith’s conception are good, and rest on the point that Smith’s definition confuses the effects of tech­nology and distribution on the value of commodities. Ricardo and Marx correct this by regarding value as being produced by the expenditure of labor in the production process, and therefore determined logically before the distribution of the value of net product between wages and profit. The New Interpretation is completely consistent with Ricardo and Marx’s argument on this point, since the definition of the monetary expression of labor as the ratio of the value of the net product at market prices to the living labor expended in a period does not involve the level of money wages (and this is not Smith’s conception)

One of the virtues of the New Interpretation is that it finally links the value of the net product at market prices to the expenditure of living labor and profit to unpaid labor time.  It is true that the New Interpretation identifies the phenomenal forms of price to the categories of the labor theory of value, but it is hard to see why this turns the relation on its head. The New Interpretation locates the source of new value in the expenditure of living labor in production, not in market exchange, the relation Marx insists on.

As to the originality of the New Interpretation, there are surely suggestions along the line of the New Interpretation in the previous literature (starting with Marx, but not with Smith, in my opinion), including passages from Shane Mage (1963), Joan Robinson (1965), Bertram Schefold (1973), and perhaps others with whose work I am not familiar. The only claim I would make for Dumenil and myself in this regard is that we were the first (excepting perhaps Marx himself, if you accept the New Interpretation as a faithful representation of Marx’s ideas) to pursue the idea and develop it into a complete and coherent interpretation of the labor theory of value.

Adherents of the dual-system interpretation of the labor theory of value tend to view the New Interpretation as a contentless “trick”, which evades rather than confronting the problem of the relation between embodied labor coeffi­cient accounts and market price accounts. The dual system framework poses the problem as proving mathematically the proportionality of profit and the wage bill measured in market prices to surplus and necessary labor the mea­sured in embodied labor coefficients, and argues that the New Interpretation makes no contribution to this project. If one accepts the mathematical correct­ness of the dual-system demonstrations, as I do, then within that framework the question is completely settled: it is impossible in general to maintain the required proportionality, and neither the New Interpretation nor anything else is ever going to come to a different conclusion without committing a mathematical error. Accepting the mathematical validity of the analysis within the dual-system framework, However, does not require one to accept that this is the only, or the most relevant, way of posing the issue.

Recent unpublished work by Robert F. Brinkman (1997), for example, ar­gues that the New Interpretation essentially complements and completes the dual-system interpretation. Brinkman points out that the original dual system analysis (rehearsed above) leaves the rate of profit calculated in terms of embodied labor coefficients, as well as the absolute level of the profit rate-equalizing money prices and wages, undetermined. He shows that taking into account the allocation of social labor time among sectors (or, what amounts to the same thing, the composition of net output) completes both systems, by determining the rate of profit in embodied labor coefficients and determining the prices of the commodities and the money wage up to a constant of proportionality which is, in fact, the monetary expression of labor is defined by the New Interpreta­tion. Brinkman proposes to distinguish ‘essential prices’ (money prices divided by the monetary expression of labor) and ‘labor values’, that is, embodied labor labor coefficients. He argues that embodied labor coefficients are the appropri­ate accounting system to distinguish in general between necessary and surplus labor time, but that essential prices are the appropriate accounting system to distinguish between paid and unpaid labor time. Profit and the wage bill are always equal to 1)aid and unpaid labor time, but paid and unpaid labor time are equal to necessary and surplus labor time only under special assumptions that guarantee the proportionality of embodied labor coefficients to prices of production.

I agree with the dual-system advocates that the New Interpretation is a set of definitions rather than an empirical Hypothesis, but I disagree with their claim that as a result the New Interpretation has no theoretical or scientific content. This disagreement arises, perhaps, from different philosophies of sci­ence. In my view the labor theory of value under the New Interpretation plays a role in political economy analogous to the role played by Newton’s Laws in mechanics. The definition of the monetary expression of labor is analogous to the stipulation in Newtonian mechanics that force is equal to mass multiplied by acceleration. Taken by itself f = ma is just a definitional relation between three theoretical terms (just as the monetary expression of labor is just a defi­nitional relation between the money magnitudes and living labor time), but in the context of a determinate mechanical system this definition decisively dis­ciplines and directs scientific in contentful and fruitful ways. Thus while the New Interpretation does not itself propose any operational hypotheses about the evolution of the monetary expression of labor or the rate of exploitation, its definitional framework allows us to measure the evolution of the monetary expression of labor and the rate of exploitation in real capitalist economies and to link these magnitudes to other aspects of capital accumulation, such as the bias of technical change, or the class relations of particular societies. The dual­system advocates, on the other hand, seem to be saying that only empirical hypotheses about the real world count as “theories”, so that the labor theory of value has to be understood as a specific contingent hypothesis which Might or might not hold in specific situations (such as the hypothesis of a ‘ugh correlation between market prices and embodied labor coefficients.)

Another way to make this point is that the New Interpretation definitions are ex post accounting identities, which must hold definitionally in all economies in all periods. The critics of the New Interpretation, seeking ex ante hypotheses with explanatory and predictive content, find the New Interpretation wanting in this regard. I am myself extremely interested in the development of ex ante ­hypotheses, and certainly support their investigation. The history of science, however, suggests that the discovery of successful ex ante Hypotheses is much aided by the establishment of appropriate heuristic ex post definitional frameworks, like Newton’s mechanical laws.

Some scholars find the connection between money and labor time asserted by the New Interpretation to he arbitrary and unsupported. For example John Roemer (1990) criticizes the lack of economic motivation in the identification of social labor time with money.

This criticism seems to me to be closely connected with that of the dual-system advocates. As I have explained earlier in this paper, I think the main motivation for Marx’s labor theory of value was the relation he perceived between it and the theory of  historical materialism and class society. In Roemer ‘5 terms this motivation is not “economic”, that is, directly connected to the anal­ysis of commodity market relations. Roemer’s failure to find much resonance in the New Interpretation may also be connected with his commitment to the Walrasian model of market equilibrium as a vehicle for the analysis of com­modity relations. The Walrasian approach is in striking contrast to Marx’s in its inability to integrate money, which is precisely the point on which the New Interpretation definitions rest.

Alfredo Saad-Filho (1996) in a well-informed and balanced appraisal of the New Interpretation (which he calls the “New Approach”), makes two critical points, one more persuasive than the other.

The less persuasive concerns the role of the net product in the analysis. Saad-Filho appreciates the issue of double-counting if the value of gross output at market prices rather than the value of net output at market prices is used to define the monetary expression of labor (p. 126). The full complexity of this problem is obscured by our thinking in terms of period models, in which the accounting period and the production period coincide. In real capitalist economies, we account in periods such as years that may span more than one turnover of some elements of constant capital in some production processes. The value of the gross product in market prices over a year, for example, may count some parts of constant capital more than twice. This point emphasizes the ambiguity of the concept of gross output in real capitalist economies as opposed to period models.

Saad-Filho sums this discussion up, however, by saying: “…the New Approach argues that only the value of net product should be the subject of the transformation….” As we have seen above, one can use the value of the net output at market prices to define the monetary expression of labor, and still use the resulting monetary expression of labor to “transform”, that is, convert into abstract social labor equivalents, the flow of constant capital.

Saad-Filho persuades me more by his criticism of the New Interpretation for being excessively reductionist:

This conception of price is methodologically questionable. Its main drawback is that this is simply a circulation-based view of price. It is correct as far as it goes, but it fails to give analytically priority to conceptually more fundamental processes such as the performance of labor in production, vis-a-vis more superficial phenomena such as the relations between supply and demand for each commodity or monopoly power. The internal structure of the New Approach leads it to address the appearance from  the start…, but this apparent advantage exacts a heavy toll: it becomes very difficult to develop the theory further without making use of arbitrariness in the choice of phenomena to be explained, the judgement of their importance and their relation with other features of reality (1996, p 128)

I think this criticism has some merit. For example, there may be a real role for a concept of the value of labor-power independent of the ex post realized wage share In a fully developed Marxist theory. The approach of Brinkman outlined above, which retains a separate role for the concepts of necessary and surplus labor and paid and unpaid labor may suggest a way to address this issue.

9. The Temporal Single-System Approach

At the same time that Dumenil and I were publishing the New Interpretation (and in some cases in the same issues of the same journals), a nuinber of scholars, including Richard Wolff, Antonino Callari and Bruce Roberts (1982), and John Ernst (1982), began a critical re-examination of Marx’s labor theory of value which has developed into an embryonic school (see for example, Alan Freeman and Guglielmo Carchedi, eds., 1996.)

Wolff, Callari and Roberts emphasize, as 1 have here, class and exploitation as the context of Marx’s interest in the labor theory of value. They go on to propose that Marx used the word “value” in a different technical sense in his discussions in Volume III of Capita1 from Volume I. In Volume I, according to their reading, Marx used the word “value” to mean “abstract social labor directly and indirectly expended in producing the commodity”, and therefore consistently with the mathematical definition of the vector A above. But in Volume III, Marx changed the meaning of the word “value” to mean the sum of the direct labor expended in producing the commodity with the abstract social labor-time equivalent of the means of production use(l up calculated by dividing the money price paid for the means of production by a monetary expression of labor. In a stationary economy with no technical change, they define these “values” as the vector V in terms of the prices of production p (determined in the same manner as in the dual-system approach described above) by the relations:

p=(1 +r)p(A+bl)

py= lx

v = pA +1

This amounts to the extension of the New Interpretation outlined above, in which the monetary expression of labor is taken to be titlity, as is evident from the second equation above. As I have already shown, if we regard the abstract social labor time equivalents of the constant capital as their money prices di­vided by the monetary expression of labor rather than the labor directly and indirectly embodied in them, as this approach proposes, then in addition to the proportionality of the money value of the net product to living labor expended, of surplus value to unpaid labor time, and of the wage bill to paid labor time, the price of the gross product will be equal to the value of the gross product and the price and value rates of profit will be equal. Wolff, Callari and Roberts argue exegetically that this interpretation seems to correspond to Marx’s conception as expressed in Volume III, but offer no economic motivation or interpretation of the “value” coefficients, V. Fred Moseley, as I have remarked, has emphasized the desirability of making this extension of the New Interpretation.

Alan Freeman (1996a), Ted McGlone and Andrew Kliman (1996), and Alejandro Ramos-Martinez and Adolfo Rodriguez-Herrera (1996) call this a “single-system” interpretation of the labor theory of value, since in it the embodied labor coefficients A of the dual-system analysis disappear altogether. Ramos Martinez and Rodriguez-Herrera marshal considerable textual evidence supporting the claim that this interpretation is consistent with Marx’s method of analyzing the relation of prices and values in Volume III of capital

I do not see any inconsistency between the New Interpretation and a single system interpretation of the labor theory of value, as long as the single-system interpretation consistently (either explicitly or implicitly as in Wolff, Callari and Roberts) defines the monetary expression of labor as the ratio of the money price of the net product to the living labor expended, as it must do in order to conserve value added, surplus value and variable capital in the analysis.

John Ernst’s paper (1982) raises a further issue, the generalization of the labor theory of value to realistic situations where technology is changing over time. Ernst, working In a single-commodity model in which there can be no disproportionality of money prices and embodied labor coefficients, calculates two profit rates, a “visible” profit rate calculated as the ratio of surplus value to the sum of variable capital and constant capital reckoned in terms of the commodity as numeraire (or, in this case, equivalently in terms of money), and a “value” profit rate in which the constant capital is valued in terms of the labor historically expended to produce it. (In Ernst’s paper lie examines a one-period circulating capital model so that only one older “vintage” of labor, last period’s, is involved.) Since there is technical change, the labor embodied in each vintage of the commodity diverges from that contained in the constant capital used up to produce it, so that the “value” rate of profit is generally lower than the “visible” rate of profit.

Alan Freeman (1996b) argues vigorously for an interpretation of the labor theory of value general enough to embrace situations in which there is ongoing technical change, 50 that technology is not stationary, as it is assumed to be in many of the examples and models in the literature. Since ongoing technical change is a key feature of capitalist economic reality, it is hard to quarrel with this goal.

As I showed in (Foley, 1982a) and elaborated in (Foley, 1986b), the New Interpretation can provide such a framework. The key analytical simplification is once again the definition of the monetary expression of labor as the ratio of the value of the net product at market prices to the living labor expended in each period, an unambiguously defined magnitude. With this definition, it is possible to analyze capitalist economies undergoing any complex patter of technical change in the average money prices of commodities into a part representing changes in the productivity of labor.

If, on the other hand, we were to try to define the monetary expression of labor as the ratio of the price of the gross product to the total labor expended in producing the gross product in the context of ongoing technical change, we would confront the problem that the gross product contains means of produc­tion of various vintages, produced under different technical conditions, and em­bodying labor of different vintages and different productivities. This the labor embodied in the gross product is under these circumstances a vector of labor of different vintages. The definition of the monetary expression of labor as the ra­tio of a scalar (the contemporary value of the gross product at market prices) to a vector (the labor embodied in the gross product) is incoherent mathematically.

The attempts to develop a ‘temporal single-system” interpretation of the labor theory of value in the Freeman-Carchedi volume fail to put forward a sin­gle, consistent definition of the monetary expression of labor, which is necessary to carry out their purpose. It appears to me that this definition should coincide with the New Interpretation definition, as in the Wollf, Callari and Roberts paper: otherwise the temporal single-system interpretation that results will not preserve the proportionality of wage bill and gross profit with paid and unpaid labor.

The language that surrounds this issue in these papers is somewhat obscure, so that I may be misunderstanding what is being said. But it appears to me that the temporal single-system program needs to distinguish clearly between the change in the value imputed to stocks of commodities from  one period to the next and the value of the net product in the period. In a model economy with stationary technology, so that prices of production (and embodied labor coefficients) remain constant over time, the net product in a period equals the change in stocks plus consumption in use-value terms, and as a result the value of the net product (in either a market price, prices of production, or embodied labor coefficient accounting system) is equal to the change in the value of stocks plus the value of consumption. But in an economy undergoing technical change, market prices, prices of production, and embodied labor coefficients will all be changing from period to period. As a result, the value of the net product in any accounting system will not necessarily equal the change in the values of stocks plus the value of consumption. In fact, in national income accounting language, the value of the net product is equal to the change in the values of stocks plus consumption reduced by an “inventory valuation adjustment” representing the change in the value of inventories due to price changes through the period and a “capital consumption adjustment” representing the change in the value of fixed capital (Due to price changes through the period.

This problem  arises, for example, in the examples that Andrew Kliman (1996) puts forward as “refutation” of the Okishio theorem. He makes the explicit assumption that the monetary expression of labor is constant on the paths they examine (often in the form of a stipulation that $1 remains equivalent to 1 unit of labor on the paths studied). Then in order to calculate a path of prices (in order to derive the path of profit rates), Kliman equates the change in the value of stocks plus the value of consumption to the living labor expended in the period. But from the point of view of the New Interpretation definition, this equation does not hold the monetary expression of labor constant, since under the assumed conditions of changing technology and prices the value of the net product deviates from the sum of the value of consumption and the change in the value of stocks through the period. Kliman’s equation attributes the changes in the value of inventories and fixed capital due to price change to the living labor expended, which seems counter to the Marxist interpretation of the labor theory of value. On the resulting price paths in the example, the monetary expression of labor in the New Interpretation sense is not constant, and the falling monetary rate of profit in the examples reflects this changing monetary expression of labor. When this aspect of the examples is corrected, the resulting price and profit rate paths do not contradict the Okishio theorem.

10. Conclusion

I would like to conclude by emphasizing what I see as a large degree of practical and operational agreement on the labor theory of value emerging despite the doctrinal disagreements we have reviewed. All the interpretations lead to the practical use of market price data in empirical studies based on the categories Marx’s labor theory of value such as the rate of profit, the composition of capital, and the rate of exploitation, and hypotheses concerning these categories. Single system interpretations, including the New Interpretation (extended to use the monetary expression of labor to impute abstract labor time to constant capital), all link the labor-value categories directly to money and thus establish observed monetary accounts as the appropriate operational equivalents of the theoretical concepts.

It is interesting that the empirical work of Shaikh, Tonak, Ochoa and their students and collaborators and Cockshott and Cottrell showing a high degree of correlation between embodied labor coefficients and market prices, leads to a similar practice within the dual-system interpretation.[6. I do not mean to attribute a dual-system interpretation of the labor theory of value to these scholars, only to point out an implication of the empirical results for dual-system practice.  ] The point is that these results suggest that the choice of an embodied labor coefficients or a market price accounting system doesn’t make much practical difference to estimates of Marxian categories like the rate of exploitation, or the ratio of unproductive to productive labor in real economies. Given the much wider availability of market price accounting data in financial and government sources, and the expense, dif­ficulty and possible error involved in reconstructing embodied labor coefficients for many periods and economies from input/output tables, most empirical work, even by people who hew to the dual-system interpretation, will use market price data as a first approximation to an embodied labor-coefficient system of accounts. Thus single and dual-system theorists will find themselves pursuing similar and comparable empirical investigations.

I think this is a hopeful development, since my own interest is more in what Marx’s interpretation of the labor theory of value can tell us heuristically about the structure and evolution of real capitalist economies than in what close reading and ingenious speculation can tell us about the consistency of Marx’s unwritten thoughts. I also think this convergence of empirical method carries with it some hope for Marxist economic pedagogy. It should be possible for adherents of these different positions to teach their own and the alternative in­terpretations of Marx’s labor theory of value honestly and clearly as alternative theoretical foundations for a unified empirical practice that can yield important insights into capitalist reality. The release of scholarly energy into the empiri­cal investigation of the development of world capitalism need not wait on the resolution of every knotty interpretative and theoretical issue in the labor theory of value.