Garegnani on Sraffa and Marx, with an intro by Petri

The Review of Political Economy has done a great service to those interested in political economy, and in particular those concerned with the revival of the surplus approach. It has published the manuscript of Pierangelo Garegnani's unpublished paper.

From Fabio Petri's introduction:

In the last year of his life, Pierangelo Garegnani (1930–2011) worked on revising a paper on Marx’s labour theory of value drafted 30 years before, which had remained unpublished. This revised paper is what is reproduced below. 

The paper had been read at a 1980 Conference on Marx in Bielefeld, Germany. It was a new version, in English, of the paper ‘La teoria del valore: Marx e la tradizione marxista’, published, together with an early Italian version of Garegnani (1984) as well as some other material, in Garegnani’s Marx e gli economisti classici (1981: pp. 55–90); the project had originated in a series of articles published in the Italian weekly Rinascita in 1978 and 1979. In the opening page of an essay on ‘The Labour Theory of Value: ‘Detour’ or Technical Advance?’, Garegnani (1991: pp. 97 and 113, endnote 4) announced the present work as forthcoming, but in fact the paper did not go to print. In September 2010 Garegnani resumed working on the paper, to add to it a further Section IX concerning more recent discussions on Marx and the labour theory of value. He intended to co-author this additional Section with me, and it is from the ensuing collaboration that I have obtained the typescript of the Bielefeld paper, dated 1981, titled ‘The Labour Theory of Value in Marx and in the Marxist Tradition.’ On why this 1981 paper was still unpublished 10 years later, what went wrong with its publication in 1991, and why then the paper remained dormant for nearly 20 more years, Garegnani supplied little information. About these questions one can only wait for when an examination of his papers and correspondence – a vast task yet to be commenced – will possibly allow for a well-founded historical reconstruction of his choices. 

Unfortunately Garegnani passed away in October 2011, before a draft of the additional Section IX could be achieved (see Petri [2015] for further details). But in that last year he also worked on revising the Bielefeld paper, that is the first eight sections of the intended new paper. The result of the revision is presented here. Although not a final version ratified by the author, it is a fully autonomous paper, and quite definitive: the draft contains no incomplete sentences or notes by Garegnani indicating that certain points might need further work. Relative to the 1981 version, it contains additional observations and stylistic improvements, but no changes in the basic arguments. 

The aim and contents of the paper were summarized at some length by Garegnani himself when announcing it in the opening page of the 1991 essay. In that summary, which can now be read as an introduction to the arguments contained in the paper here submitted to the public, Garegnani (1991: p. 97) stresses that the paper is devoted to further confirming the thesis, advanced in Garegnani (1984), that the role of the labour theory of value in the classical approach and in Marx was the ‘technical’ one of providing a ‘measurement independent of distribution, of product, wages and means of production,’ thus allowing a determination of the rate of profits as the ratio of net social product to capital advances, surmounting, in the only – albeit imperfect – way concretely available at the time, the (apparent) vicious circle of a rate of profits dependent on relative prices in turn dependent on the rate of profits. With particular regard to Marx, Garegnani explains, the confirmation is achieved by showing that the traditional interpretations that attribute other roles to the labour theory of value ‘have little foundation in Marx’s own work. This applies in particular to the readings often made of some characteristic concepts of Marx, like his distinction between ‘inner’ and ‘apparent’ relations of the bourgeois system, the distinction between ‘abstract’ and ‘concrete’ labour, the representation of the wage as ‘value of labour power’, or the sense in which Marx refers to labour exploitation – a sense which, as he explicitly states, has little if anything to do with the labour theory of value.’ These interpretations ‘have indeed made it difficult to comprehend a large part of Marx’s theoretical work’. No attempt at diplomacy here! The published 1991 essay is then presented as an appendix to that still unpublished paper, defending the latter’s arguments against the views on Marx’s labour theory of value expressed by Samuelson, Baumol, Myrdal, Meek, Morishima, and Sen. 

There remains to indicate why publishing this paper today is deemed important. The main reason is that Garegnani’s understanding of the role of the labour theory of value in Marx (and of the correct reading of those ‘characteristic concepts of Marx’) appears to be scarcely known outside Italy [1], a fact that has helped the frequent placement of his overall approach in the ranks of an allegedly anti-Marx ‘Sraffian school’. This reaction is hardly surprising in the light of the substantial diversity of Garegnani’s theses from the long-dominant ones. So dominant was the tradition attributing to the labour theory of value indispensable roles other than the one indicated by Garegnani – for example, the role of proving labour exploitation – that it is not difficult to understand that the spontaneous reaction of scholars steeped in the traditional interpretation may have been one of skepticism, if not of hostility, toward a view which, by claiming that nothing is lost by replacing the labour theory of value with Sraffa’s equations, seemed to reject fundamental elements of Marx’s assessment of the nature of the capital–labour relation. The absence of a detailed exposition in English of the arguments Garegnani supplies in support of his views has made it difficult to give those arguments the attentive consideration warranted by the recognized depth of thought of the author. The publication of the present paper aims at making such adequate consideration possible [2]. 

The criticism, in the last sections of the paper, of two Italian scholars absent from recent debates does not seem to be outdated either, because views similar to those they expressed are still present today. The near identification one finds in Lucio Colletti’s (1924–2001) writings of the concepts of fetishism, alienation, and abstract labour continues the long (and still alive) tradition stressing the ‘qualitative’ roles of Marx’s labour theory of value, and has been influential outside Italy too (see, for example, Foley 1982: p. 46, fn. 5). The argument put forward by Claudio Napoleoni (1924–1988), that outside the labour theory of value one cannot view profits as the fruit of exploitation [3], is representative of a widely shared view that helps us to understand the reluctance of many Marxists to replace the labour theory of value with the correct analysis of prices as provided by Sraffa. 

Independently of how convincing it will be found, this paper questions the idea of a so-called ‘Sraffian school’ antithetical to Marx. Leaving aside the analytical and even philological legitimacy of referring to Sraffa’s work and its later developments as any new particular ‘school’ distinct from the modern reappraisal of the classical approach to value and distribution, the paper shows that no such counterposition is applicable to a scholar highly representative of that line of thought, in whose view Marx’s overall approach actually turns out to be strenghtened, rather than challenged, by the correct determination of rate of profits and prices achieved with Sraffa.

Notes

[1] The publication in 1985 of a French version of the Bielefeld paper (Garegnani 1985), also containing a short appendix criticizing Rowthorn (1974), does not seem to have been widely noticed: I have found it cited in only one (unpublished) paper concerned with Marx’s theory of value, Chattopadhyay (2000).

[2] And at supplying at last the needed background to the 1991 essay.

[3] Napoleoni’s argument is available in English in Napoleoni (1991). Garegnani does not cite this article, presumably because of the little time he had to work on the last three Sections, which have remained almost unchanged from the 1981 version.

Most of these issues were briefly tackled in this old post.  Read paper by Garegnani here.

H/T to Franklin Serrano and Sergio Cesaratto for bringing the paper to my attention.

The Passage of Time, Capital, and Investment in Traditional and in Recent Neoclassical Value Theory

New paper by Fabio Petri published in Œconomia. From the abstract:

With the shift from traditional analyses where capital is a single value factor of variable ‘form’ to the neo-Walrasian versions, general equilibrium theory has encountered new problems pointed out by P. Garegnani (1976, 1990): impermanence problem, price-change problem, substitutability problem radically question the right to consider neo-Walrasian equilibria as approximating the actual path of real economies. The paper briefly summarizes these problems and then concentrates on a fourth problem, the savings-investment problem, arguing that neo-Walrasian general equilibrium theory assumes that investment is adjusted to full-employment savings but cannot justify this assumption. The attempt to justify it in intertemporal general equilibrium through the tâtonnement is subjected to a new criticism: it is shown that the tâtonnement assumes Says’ Law all along the adjustments, and determines investment in a way that would crumble if it were not assumed that consumers determine their demands for consumption goods on the basis of an assumption of full employment incomes, which is not justified outside equilibrium, and was not assumed in traditional analyses. This reinforces the absence of reasons to view neo-Walrasian equilibrium paths as sufficiently approaching actual paths. It is concluded that behind the reference to intertemporal equilibrium as the microfoundation of macro analyses there is a continuing faith in traditional neoclassical time-consuming adjustment mechanisms, based on the old and untenable conception of capital that the shift to neo-Walrasian equilibria intended to do without.

Full paper available here.

Dvoskin and Petri on the relevance of the capital debates

Ariel Dvoskin and Fabio Petri just got their paper published in Metroeconomica. From the abstract:

Among the recent interventions in the capital controversy, the debate between Paola Potestio and Kurz & Salvadori has raised important issues. We agree with Potestio's rejection of the legitimacy of a value endowment of capital but we disagree with her dismissal of the relevance of reswitching and reverse capital deepening: these phenomena are very important because they undermine the demand-side role of the conception of capital as a single factor. For the marginal approach to be plausible, this demand-side role had to imply the stability of the savings-investment market even in shorter time frames than those required by a complete adaptation of the ‘form’ of capital; this was taken by Marshall to authorize doing without a given endowment of value capital, which opened the door to the shift to the modern neo-Walrasian versions of the marginal approach. With proof from Hayek, Hicks, Malinvaud, and Lucas we argue that a continuing belief in traditional time-consuming marginalist disequilibrium adjustments based on capital-labour substitution is the hidden reason why the claim often made by contemporary marginalist economists, that the economy can be assumed to be all the time on the equilibrium-growth path, is not found patently unacceptable. The true microfoundation of DSGE macromodels is not intertemporal equilibrium theory, but the time-consuming adjustment mechanisms on whose basis the marginal approach was born and accepted, and on whose basis monetarism was then able to re-assert a pre-Keynesian view of the working of the economy.

You can read the preliminary version at the Siena working paper series here. The idea that the capital debates is a central issue in macroeconomics has been discussed recurrently in this blog.

Fabio Petri on non-substitution theorems

Sometimes there is simple and right

New paper by Professor Petri, which is always worth reading, titled "Nonsubstitution Theorem, Leontief Model, Netputs: Some Clarifications." From the abstract:

The nonsubstitution theorem concerns long-period technical choice and relative prices, and was so understood in its first (1951) formulations, but the modern advanced micro textbooks that present it do not make this clear, rendering the theorem impossible to understand for students. These modern presentations derive from a reinterpretation of the Leontief model as a ‘timeless’ economy in Walrasian equilibrium, capable of positive production in spite of zero initial endowments of all inputs except labour: an unacceptable interpretation, made possible by a use of netputs, to describe the economy’s production possibilities, that is illegitimate in this case even from a strictly neoclassical perspective. The notion of a ‘timeless’ economy disappears from the textbook presentations of the Leontief model and of the nonsubstitution theorem, but the result is that the nature of the model and of the prices to which the theorem refers is not clarified, inevitably leaving students utterly confused. This note remembers the true nonsubstitution theorem, points out that it had been correctly enunciated by Samuelson (1961), and suggests that the current inability to present it in a correct way is due to the absence of the notion of long-period prices from the theoretical horizon of contemporary neoclassical value theory. The paper opens with clarifications on the meaning of the Leontief model which prepare the ground for the discussion of the problem with netputs.

 Read full paper here.

Petri on Say's Law

Profs. Serrano and Petri

I somehow missed this paper so far. It explain the several additional problems with Say's Law even if one does not rely on the capital debates to show the limitations of the downward-sloping investment curve.

From the abstract:

Neoclassical capital-labour substitution correctly understood is unable to prove a tendency toward the full employment of resources because it leaves investment indeterminate if the full employment of labour is not assumed to start with; then Say's Law loses plausibility because of the inevitable presence of accelerator-type influences on investment, even neglecting the inconsistencies of neoclassical capital theory; and wage decreases cause a decrease of investment, undermining the 'neoclassical synthesis' criticism of Keynes. The way a negatively interest-elastic investment function is obtained by Romer without assuming the full employment of labour, that is through adjustment costs, relies on several grave mistakes. The recent DSGE models which directly assume that investment equals savings are not supported by general equilibrium theory because the latter theory is admitted by the specialists not to be a positive theory, nor can those models rely on the neoclassical synthesis or monetarism because of the critique of this paper (besides the capital critique), so they must be discarded too.

Read rest here.

Heterodox Microeconomics

Tae-Hee Jo, Fred Lee, Nina Shapiro, and Zdravka Todorova have compiled a list of readings in Heterodox Microeconomics that deserves attention and praise (available here). The only classic book that was central in my formation that I see missing is Paolo Sylos-Labini's Oligopoly and Technical Progress (1962). My favorite graduate textbook still is the one by Fabio Petri here.

Ariel Dvoskin on the limits of Walrasian equilibrium

Here is Ariel's PhD dissertation, which is well worth reading for those interested in the evolution and limitations of the marginalist (neoclassical) models. From the abstract:

"The marginalist approach is unable to satisfactorily incorporate capital goods within the supply and demand explanation of prices and distribution, and this seems to have condemned modern general equilibrium theory to face an unpleasant dilemma: either this theory is, like Hahn, truly consistent with its own theoretical object, a notion of equilibrium that must be silent on the issue of how actual economies work; or, alternatively, the theory attempts to provide some explanation of the working of actual economies and in so doing, it must inescapably rely on traditional gravitational ways of reasoning that must presume the illegitimate notion of capital in value terms. Either way modern general equilibrium theory runs into a blind alley, with the implication that, to predict with reasonable accuracy price, quantity and distributional trends as observed in actual economies, an explanation with different theoretical foundations is necessarily called for."

The Economist thinks bubbles are rational

Or at least is what they suggest in the popular blog Free Exchange. They bring back Peter Garber's research on the Tulipmania, and more recent research by Earl Thompson, which suggests that "the market for tulips was an efficient response to changing financial regulation." They conclude by arguing that:

"It is easy to claim that bubbles are irrational. They seem to represent a deviation of prices from fundamental values—and they contradict basic economic theory. But there has been little attempt to understand how speculation actually works. The example of tulipmania shows the importance of doing that—rather than relying on lazy quips about 'animal spirits' or irrationality."

The notion is related to the idea of the Arrow-Debreu models in which short term prices (they don't have long term prices associated with a uniform rate of profit) do reflect the fundamental values associated to the preferences of agents and the given technology and factor endowments. In this context, the efficient market hypothesis (EMH) suggests that the prices of financial assets reflect all market information, and as a result those prices would not deviate from their fundamentals. In other words, according to the EMH, bubbles do not exist.

Rational bubbles assume that rational behavior may still be associated with deviations of asset prices away from their fundamental values. In general, a self-confirming belief that asset prices depend on a variable that is intrinsically irrelevant, that is, not part of market fundamentals, is assumed. Much discussion goes into the behavioral assumptions that would make rational bubbles possible. Justin Fox's The Myth of the Rational Market, which I reviewed here (subscription required) provides an accessible introduction.

John Eatwell (here; subscription required) noted that a more relevant question than the rationality or not of bubbles is whether they are useful or not. Railroads were built on bubbles, and the dot.com bubble even left some infrastructure in terms of telecommunications that has been useful. Other bubbles, like the one associated with the subprime, are less obviously useful.

Finally, note that the old capital debates are still important to understand the limitations of much of this literature. Garegnani and Petri have noted that even the short run Arrow-Debreu models must bring investment to equality to full employment savings, and as a result some notion of a natural rate of interest is implicitly needed. And then all the problems of the aggregative model apply. So it is not possible to show that long term prices do reflect fundamentals associated with preferences, technology and endowments.

PS: On the related topic of whether the Bubble Act (financial regulation), that followed the South Sea Bubble, led to lower rates of growth see here. For the capital debates go here.

The natural rate in pure exchange, intertemporal models

One more clarification on the previous discussion about the natural rate in Austrian models. In his reply,  Mr. Rallo suggests (in Spanish) that I confused the natural rate that can be derived from a barter economy with the one derived from intertemporal equilibrium model. So let's start by clarifying that barter refers to whether there is money or not, while the notion of intertemporal equilibrium is associated to the nature of equilibrium, whether it is short-term or long-term.  You can have an intertemporal model of equilibrium with barter as several Arrow-Debreu models actually are.

Traditional notions of equilibrium, like the classical authors had, are not intertemporal, but several of those were based on barter ideas. Equilibrium in classical economics is a tendency associated to the process of competition that leads to a uniform rate of profit. Some authors had the real (meaning non-monetary) rate of profit govern the system and also the rate of interest, like Ricardo, while others like Tooke suggested that the rate of interest governed the rate of profit, and arguably there are elements in Marx analysis that suggest the possibility of an independent rate of interest.*

The notion of intertemporal equilibrium is relatively new and was developed by Hayek, Hicks, Lindahl, and Myrdal (see Milgate here; subscription required)  in the 1920s and 1930s, before it become common after the capital debates on the basis of the Arrow-Debreu model. Intertemporal models do not require the notion of a uniform rate of profit, and some authors have suggested that as such they are not open to the capital critique. Because they do not require a uniform rate of profit these models are short-term.

So the relevant point is the notion of equilibrium and not whether it is a barter or credit system [additionally that would bring about the way money is introduced in the economy, as mere toke for exchange, or as a unit of account in which agents want to accumulate, but that is a different issue]. Mind you, one might think that Mr. Rallo is suggesting that in a short-term model (with no tendency ot a uniform rate of profit) there is no need in marginalist models for a natural rate of interest (although we'll see that's not his point).

Yet, the point made by Garegnani and Petri is that in an intertemporal model with disaggregated means of production (capital goods), it is still necessary for the equilibration of aggregate investment to full employment savings, and that requires a measure of the quantity of capital, and that means, and by necessity a rate of interest. That rate of interest that equilibrates savings and investment is a natural rate.

Mr. Rallo seems to believe that there is a difference between a situation in which there are "lenders (savers) lending at 5% for a year, and investors that demand 5% for 30 years" (or in Spanish "ahorradores que prestan al 5% a 1 año e inversores que piden prestado al 5% a 30 años"), which would be different if both lenders and borrowers had the same time period in mind, but different rates.
Again, this involves not the intertemporal nature of the model, but the term structure of interest rates.

So taking away the adjustment for risk associated to the longer-term that financial capital would be tied to investment, in the neoclassical theory arbitrage should still work. So presumably the rate would be more than 5% for the 30 year loan. This has nothing to do with the necessity in Austrian theory, as in any type of marginalist model, of a quantity of capital and a natural rate of interest. Neither barter nor the term structure of the rate of interest (or the more relevant discussion of the short-term nature of intertemporal models) relieves the marginalist (and Austrian) theories from a need for a natural rate of interest.

The only consistent way to get rid of the notion, is to abandon the marginalist approach, and like Sraffa assume that one distributive variable, in his case the monetary rate of interest, is given exogenously. Savings then is adjusted to investment by the multiplier process (i.e. Keynes and Kalecki's Principle of Effective Demand).

* Panico (1980, p. 269 here; subscription required) argues that: "Marx's analysis of the factors determining the rate of interest, he rejected any attempt to explain the determination of the average rate of interest on the basis of'laws of necessity'. He proposed instead, to investigate it by means of qualitative description, of those economic, conventional and institutional factors that, from time to time, affect this variable." So while its clear that Marx thought that the rate of profit determined the rate of interest, it is also reasonable to argue that there are contradictory propositions that suggest a determination of the normal rate of interest that is independent from the rate of profit.

PS: Thanks to Franklin Serrano for pointing my mistake on Quesnay (deleted; yes there is money in the Tableau as there is in Marx's simple reproduction system, derived from Quesnay) and the causality in Marx. Also, forgot the link to Milgate's paper, which is now in place.

Sraffa and Marxism or the Labor Theory of Value, what is it good for?

An old, but not completely closed, debate revolves around whether Sraffa was a Marxist or instead he should be seen as Ricardian, hence the term Neo-Ricardian used derisively by Bob Rowthorn (subscription required) and other Marxists authors (and also by Frank Hahn, again subscription required). From a personal point of view there is little doubt that Sraffa identified with Marxism, and close friends like Antonio Gramsci and Maurice Dobb would agree. But the important question is whether his contributions in Production of Commodities by Means of Commodities (PCMC) should be seen as a development or a criticism of Marx's theoretical tradition.

For the most part the question revolves around the relation between Sraffa's prices and the labor theory of value. Several authors tend to believe that the latter theory is central for Marx's theory of exploitation. Recent interpretations such as the so-called New Interpretation (NI) and the Temporal Single System (TSS) would agree on that point.

For example, Foley and Duménil (2008; subscription required) argue that:

"Central to Marx's framework of analysis in Capital is the labour theory of value (LTV), which defines the value of a commodity as the ‘socially necessary’ labour time required by its production, that is, the labour time required by average available techniques of production for workers of average skill. 

The LTV is central to Marx's theory of exploitation, a term he uses to describe a situation in which one individual or group lives on the product of the labour of others."

On the similar claims by the TSS Marxism see Mongiovi (2002; subscription required). [Vienneau provides a list of readings on the TSS topic here.]

The question then is what was the role of the labor theory of value in Marx and the classical authors, i.e. for the surplus approach. The initial problem that Smith was trying to deal with the LTV was to determine the rate of profits independently of prices, since profits were considered essential for capital accumulation. Note that one needs the prices to determine profits, in particular the price of the means of production advanced for production, but one needs the rate of profit (the normal uniform rate of profit) to determine long term normal (or production) prices.

Smith (1776, book I, chapter 6) makes the value of commodities depend on the quantity of labor required to produce them is where there has been no accumulation of capital or land. In his words:

"In that early and rude state of society which precedes both the accumulation of stock and the appropriation of land, the proportion between the quantities of labour necessary for acquiring different objects seems to be the only circumstance which can afford any rule for exchanging them for one another."

But when profit and rent make their appearance alongside the worker's income, the rule is no longer applicable. The price of a commodity is then obtained by 'adding up' its component parts, namely: wage, profit and rent. The adding up theory implied that profits and wages had an independent determination. Hence, if profits went up, and prices too, real wages might not decrease. As a result, one cannot determine profits independently of prices.

Ricardo saw the limitations of the adding up theory. In his early writings he solved the problem by presuming that the economy produced corn (grain) with corn and labor, and the surplus was a physical amount of corn, so the rate of profit could be measured as ratio of corn (the surplus) to corn (the means of production advanced for production). He, then used, the labor theory of value as an approximation to the solution in his Principles, knowing that prices were not exactly proportional to the amounts of labor directly and indirectly used in production.

That was, also, essentially the role of the LTV in Marx's volume I of his masterpiece Capital. That is, the LTV allows Marx to determine the rate of profit independently of prices. Note that Marx was also aware that relative prices determined by the amounts of labor directly and indirectly incorporated are incorrect once you have produced means of production. However, Marx thought that embodied labor redistributed by the process of competition meant that in the aggregate total surplus value  corresponded to total profits, even if prices of production deviated from embodied labor. As a result, on the basis of the LTV it was still possible to obtain the correct rate of profit. As it turns out, there is no reason for positive and negative deviations of prices of production from the labor values to cancel out. You cannot argue with the algebra.

Marx had no way of knowing this. Only with Bortkiewicz, Dimitriev and Tugan-Baranovsky's work, early in the 20th century, this was clearly understood. If in general commodities do not exchange at labor values, then there is no reason why that should be correct for two composite commodities that make the total physical surplus and the physical advanced means of production.

Sraffa's solution, based on the standard commodity (to be discussed in another post), shares with Ricardo's corn model the idea that one can measure the rate of profit as a share of a particular commodity (Sraffa's being a composite commodity, that is, composed of several goods). It also shares with Ricardo the fact that only basics (commodities that enter the production of all goods including their own production), which for simplicity can be related to subsistence goods, affect the rate of profit, while non-basics, or luxury goods, are not relevant. Further, as noted by Sraffa too, his solution resembles Smith's since the standard commodity can be seen as akin to the former's idea of labor commanded, that is relative prices are proportional to the amount of labor that they can command (buy). In that sense, Sraffa's prices are firmly based on a certain notion of the labor theory of value.

Mind you, in the central issues Marx's theory was correct. Once you determined exogenously the real wage, and the technical coefficients of production are given, one can determine the rate of profit, and it is inversely related, everything else constant, with the real wage. Hence, the theory of distribution based on class conflict which is the central element of the surplus approach, including Marx, is logically consistent [which is more that can be said about marginalism, as showed by the capital debates].

But does the Sraffian system mean that exploitation as interpreted by Marx is not valid anymore, since, as noted above, some Marxist authors think that the LTV (narrowly interpreted as prices of production proportional to embodied labor) is essential for that part of the Marxian project? Petri (2012)* has published an excellent review of the limitations of the NI and TSS. He clearly states (p. 3) that:

"The proof that labour is exploited, in particular, does not lie in the validity of a quantitative correspondence of surplus exchange value with surplus labour time; this is a misconception that derives from a mistaken acceptance of the argument that the inability to prove such a correspondence might mean that the capitalists contribute to production, that profits reflect their contribution, and that this is the reason why commodities do not exchange in proportion to labours embodied – the argument of the ‘vulgar’ economists and then of the marginalist critics of Marx" (emphasis added).

Why is that the case that there is no correspondence between the LTV and whether labor is exploited or not? Note that for Marxists this is a necessary condition because workers work more time than what is needed for their reproduction, and that is the supposed basis for exploitation. It is worth quoting Petri at length here:

"Imagine an isolated market economy where production is carried out by self-employed artisans and cooperatives, and the rate of profit is zero: prices of production are proportional to labours embodied. One day Gengis Khan’s army invades this community, but instead of killing everybody Gengis Khan announces that he will be content with collecting a yearly monetary tax at a rate r=20% on the value of the capital employed in each productive activity, a tax he will then use to buy goods on the market. The community is obliged to accept, and prices of production come to include a 20% tax on the value of capital which has the same effect on relative prices, and on real wages, as a 20% rate of profit. Relative prices are no longer proportional to labours embodied, Marx’s r=S/(C+V) does not work, but production is still performed by the same labourers, and the goods appropriated each year by Gengis Khan with the income deriving from the tax do not reflect any productive contribution of the oppressors. One would have little hesitation, it would seem, to say that Gengis Khan is exploiting this community. But if Gengis Khan had imposed the tax as a given percentage of wages, with the rate of profit remaining zero, then relative prices would have remained proportional to labours embodied, but exploitation would be still there. On the other hand, imagine that the 20% tax rate on the value of capital is imposed not by Gengis Khan but by unanimous popular vote because it is decided to use it to help for some years another community struck by an earthquake: in this case the surplus product would again be associated with an impossibility to explain prices with the labour theory of value, but few would call the surplus product the fruit of labour exploitation. All this shows that the proportionality or non-proportionality between exchange values and labours embodied reflects, not the absence or presence of other productive contributions besides that of labour, but only the specific way the mode of appropriation of the surplus product affects relative prices; the origin of the surplus remains to be ascertained" (emphasis added).

Hence, as the simple example shows one might have exploitation without the LTV, and no exploitation with the LTV, which should be a black swan for those that think that Marxism stands or falls with the narrow definition of the LTV. For our purposes what matters is that the correct solution of the problem of the determination of the rate of profit independently of prices, provided by Sraffa, actually strengthens and is a development of the theories of Marx and the other authors of the surplus approach. Sraffa is the author that makes Marx's conclusions possible.**

Notes:

* Petri provides a critique of NI and TSS solutions of the transformation problem too. A different solution, that is more Ricardian in assuming that embodied labor provides a good empirical approximation to production prices, is provided by Shaikh (1977).

** Interestingly Petri quotes several passages in which Foley tends to suggest that Marxism and marginalism are not necessarily incompatible.

References:

Foley, Duncan and Gérard Duménil (2008). "Marxian transformation problem." The New Palgrave Dictionary of Economics. Second Edition. Steven N. Durlauf and Lawrence E. Blume. (eds.), The New Palgrave Dictionary of Economics. Palgrave Macmillan.

Mongiovi, Gary (2002). "Vulgar Economy in Marxian Garb: A Critique of Temporal Single-System Marxism," Review of Radical Political Economics, 34(4), pp. 393-416.

Petri, Fabio (2012). "On Recent Reformulations of the Labour Theory of Value," Quaderni del Dipartamento di Economia Politica e Statistica, Università degli Studi di Siena, No. 643.

Shaikh, Anwar (1977). "Marx's Theory of Value and the Transformation Problem,"in Jesse Schwartz (ed.), The Subtle Anatomy of Capitalism. Goodyear Publ. Co.

On General Equilibrium (GE)

Nice post (and rare, since this kind of topic is often not dealt with) on GE by Alejandro Nadal at TripleCrisis.  In my view, the problem is less that equilibrium per se does not exist, as Nadal seems to suggest, but the particular notion of equilibrium that has come dominate economics after Arrow-Debreu and the Capital Debates.  I highly recommend the paper by Fabio Petri (here) for those interested on the subject.