(1) The law of value in volume 3 of Capital
Many Marxists followed volume 3 of Capital and gave up the view that commodity prices tend to equal pure labour values (which was the theory in volume 1). Instead, they defended the view of volume 3 that the “law of value” only ultimately and indirectly explains prices, and defended Marx’s three aggregate equalities:(1) the sum of surplus value = sum of profits;These aggregate equalities were asserted as true as Marx’s attempt to transform labour values into prices of production.
(2) the sum of values = sum of prices, and
(3) the value rate of profit = the money rate of profit.
Böhm-Bawerk later usefully summarised Marx’s various attempts to salvage the law of value in volume 3 of Capital as follows:“First argument: even if the separate commodities are being sold either above or below their values, these reciprocal fluctuations cancel each other, and in the community itself—taking into account all the branches of production—the total of the prices of production of the commodities produced still remains equal to the sum of their values (III, 188).It is curious that many Marxists forgot about the Third Argument: that commodities tended to exchange at their true labour values in pre-modern forms of commodity exchange. This was defended by Engels in his “Supplement and Addendum” to volume 3 of Capital of 1895 (Engels 1991 ), and also defended by a few Marxists after his time as I note here.
Second argument: the law of value governs the movement of Prices, since the diminution or increase of the requisite working time makes the prices of production rise or fall (III, 208, 211).
Third argument: the law of value, Marx affirms, governs with undiminished authority the exchange of commodities in certain ‘primary’ stages, in which the change of values into prices of production has not yet been accomplished.
Fourth argument: in a complicated economic system the law of value regulates the prices of production at least indirectly and in the last resort, since the total value of the commodities, determined by the law of value, determines the total surplus value. The latter, however, regulates the amount of the average profit, and therefore the general rate of profit (III, 212).” (Böhm-Bawerk 1949: 32).
At any rate, this interpretation of Marx, from volume 3, dominated Marxist thought both in the West and in Russia until WWII (Nitzan and Bichler 2009: 99).
(2) Simultaneous Dual System Interpretation
A revolution came with the work of Ladislaus von Bortkiewicz (1868–1931), Vladimir Karpovich Dmitriev (1868–1913) and Mikhail Ivanovich Tugan-Baranovsky (1865–1919).
We turn again to Marx’s three aggregate equalities:(1) the sum of surplus value = sum of profits;The work of Ladislaus von Bortkiewicz showed that two of the three aggregate equalities defended by Marx in volume 3 of Capital fail, and that the sum of surplus value = sum of profits quality cannot be defended unless under very special assumptions (see Bortkiewicz 1906; 1907a; 1907b; 1907c; English translations in Bortkiewicz 1949 and 1952; see also here). Even worse, Bortkiewicz’s work suggested that the tendency to a falling rate of profit is wrong too (Kliman 2006: 47).
(2) the sum of values = sum of prices of production, and
(3) the value rate of profit = the money rate of profit.
Bortkiewicz’s new model adopted a dual-system view that contended that labour values and prices of production are determined entirely separately, so that the transformation problem is avoided (Nitzan and Bichler 2009: 108).
When the work of von Bortkiewicz was translated and become known in the West, a number of Marxists adopted his view. Paul M. Sweezy (1910–2004), the author of The Theory of Capitalist Development. Principles of Marxian Political Economy (1946, London), was the most influential.
The reformed interpretations of Marx by both Ladislaus Bortkiewicz (1868–1931) and Paul M. Sweezy (1910–2004) have been seen by some as proto-Sraffian and having anticipated aspects of Sraffa’s own re-interpretation of Classical Political Economy (Mongiovi 2002: 395).
However, Ian Steedman (1977), building on the work of Sraffa, demonstrated that labour value itself was not only redundant since physical quantities of commodities can determine the profit rate, but also, in a devastating point, capable of being negative in joint production process even when prices and profit rates are positive (Nitzan and Bichler 2009: 101). The Dual System interpretation, and indeed the very labour theory of value itself, is destroyed under such a critique (Keen 2011: 426–443; Nitzan and Bichler 2009: 101).
(3) Temporal Single System Interpretation (TSSI) Marxism
This emerged in the 1980s as a new generation of Marxists surveyed the wreckage of previous interpretations of Marx’s economic theory.
Temporal Single System Marxists argue that Bortkiewicz’s criticisms of Marx apply only to a Classical long-period equilibrium interpretation of Marx’s value theory, and that this long period interpretation is wrong and a misrepresentation of Marx’s views (Mongiovi 2002: 409).
TSSI also treats factor input prices in a temporal and not simultaneous manner (Nitzan and Bichler 2009: 106). The orthodox “simultaneous” treatment of the prices of factor inputs holds that they should be measured by current prices at the time of final production of the output commodity and not at their prices when purchased. The TSSI instead holds that prices and labour value of factor inputs should be measured at the time at which they were purchased (Nitzan and Bichler 2009: 107).
However, the TSSI simply assumes labour value equal prices, as Nitzan and Bichler argue:… the single system articulated by the TSSI does not have prices and values. It has prices as values. The distinction is crucial. The conventional Marxist approach argues that labour values are the cause of prices. This causal link is meaningful because the definitions of the two magnitudes are different. Prices are counted in money, whereas values are counted in labour time. The two magnitudes could be used interchangeably – but only if the theory is correct.If the TSSI simply defines labour values as equal to price by definition then it badly misunderstands Marx, who derived prices from labour values, whether (1) in volume 1 of Capital where commodity prices tend to equal labour values, or (2) in volume 3 where labour values are transformed into prices of production.
The setup of the TSSI is completely different. Here, there is no point in asking whether or not prices are equal to values, simply because values are defined by market prices.” (Nitzan and Bichler 2009: 107–108).
Moreover, Mongiovi charges the Temporal Single System Interpretation with the following flaws and errors:(1) the concept of labour value, contrary to Marx, is reduced by the Temporal Single System Interpretation merely to price (Mongiovi 2002: 406, n. 20);On (2), there seems to be good evidence that Marx really did conceive his economic theories firmly in the Classical long-run equilibrium position. For example, the evidence for how Marx regarded “average price,” “cost-price” or “price of production” as the long run Classical “natural price” is superbly presented in Fred Moseley’s paper “Marx’s Concept of Prices of Production: Long-Run Center-of-Gravity Prices,” which demonstrates how the Temporal Single System Interpretation badly misunderstands Marx’s concept of the “price of production.”
(2) the Temporal Single System Interpretation’s attempt to deny that Marx’s economics was in the tradition of long period Classical equilibrium theory is wrong (Mongiovi 2002: 402, 412).
(3) the Temporal Single System Interpretation attempts to defend the propositions that the (1) sum of profits equals the sum of surplus value and (2) the sum of prices equals the sum of values by reducing this to an idiosyncratic and empirically empty pure mathematical identity that is a sleight of hand (in other words, by an analytic mathematical propositions merely true by definition) (Mongiovi 2002: 405–406, 413);
(4) Temporal Single System Interpretation Marxists focus on random passages in Marx and take these passages out of context to prove their own idiosyncratic ideas (Mongiovi 2002: 409–411).
If correct, then TSSI is fatally flawed by its own incompetent misunderstanding of Marx, and reduces to an empty tautological theory with no explanatory power and adds nothing of any importance to economic science.
(4) the New Interpretation (NI) of Gerard Dumenil, A. Lipietz, and Duncan Foley
The New Interpretation (NI) of Marx by Duncan Foley and Gérard Duménil emerged in the 1980s and appears to dispense entirely with any attempt to transform labour values into prices by conflating values with prices.
(5) Michael Heinrich’s “New German Reading of Marx.”
This is presented in Michael Heinrich’s book An Introduction to the Three Volumes of Karl Marx’s Capital (2012).
Heinrich’s interpretation, however, disputes that there is any tendency for the rate of profit to fall in capitalism and seems in some respects to morph into Keynesianism, as analysed here. How Heinrich understands labour values is unclear to me.
I am unsure if Anwar Shaikh, Fred Moseley, Alan Freeman, Makoto Itoh and Dominique Levy are also followers of the New Interpretation (NI), but I have read that they share similar views on the transformation problem.
John Barkley Rosser, “He’s Baaack! Karl Marx and The Transformation Problem,” March 2, 2015, Econospeak
Matias Vernengo, “Sraffa and Marxism or the Labor Theory of Value, what is it good for?,” Naked Keynesianism, August 14, 2012.
Böhm-Bawerk, Eugen von. 1949. “Karl Marx and the Close of His System,” in Paul. M. Sweezy (ed.), Karl Marx and the Close of His System and Böhm-Bawerk’s Criticism of Marx. August M. Kelley, New York. 3–120.
Bortkiewicz, L. von. 1906. “Wertrechnung und Preisrechnung im Marxschen System I,” Archiv für Sozialwissenschaft und Sozialpolitik 23: 1–50.
Bortkiewicz, L. von. 1907a. “Wertrechnung und Preisrechnung im Marxschen System II,” Archiv für Sozialwissenschaft und Sozialpolitik 25: 10–51.
Bortkiewicz, L. von. 1907b. “Wertrechnung und Preisrechnung im Marxschen System III,” Archiv für Sozialwissenschaft und Sozialpolitik 25: 445–488.
Bortkiewicz, L. von. 1907c. “Zur Berichtigung der grundlegenden theoretischen Konstruktion von Marx im 3. Band des ‘Kapital,’” Jahrbücher für Nationalökonomie und Statistik 34: 319–335.
Bortkiewicz, L. von. 1949. “On the Correction of Marx’s Fundamental Theoretical Construction in the Third Volume of Capital,” in Paul. M. Sweezy (ed.), Karl Marx and the Close of His System and Böhm-Bawerk’s Criticism of Marx. August M. Kelley, New York. 197–221.
Bortkiewicz, L. von. 1952. “Value and Price in the Marxian System,” International Economic Papers 2: 5–60.
Engels, F. 1991 . “Supplement and Addendum” to Volume 3 of Capital,” in Karl Marx, Capital. A Critique of Political Economy. Volume Three (trans. David Fernbach). Penguin Books, London.
Keen, Steve. 2011. Debunking Economics: The Naked Emperor Dethroned? (rev. and expanded edn.). Zed Books, London and New York.
Kliman, Andrew. 2006. Reclaiming Marx’s ‘Capital’: A Refutation of the Myth of Inconsistency. Lexington Books, Lanham.
Mongiovi, G. 2002. “Vulgar Economy in Marxian Garb: A Critique of Temporal Single System Marxism,” Review of Radical Political Economics 34.4: 393–416.
Moseley, Fred. “Marx’s Concept of Prices of Production: Long-Run Center-of-Gravity Prices”
Nitzan, Jonathan and Shimshon Bichler. 2009. Capital as Power: A Study or Order and Creorder. Routledge, Abingdon, UK and New York.
Samuelson, Paul A. 1971. “Understanding the Marxian Notion of Exploitation: A Summary of the So-Called Transformation Problem between Marxian Values and Competitive Prices,” Journal of Economic Literature 9.2: 399–431.
Steedman, Ian. 1977. Marx after Sraffa. NLB, London.
Sweezy, Paul M. 1946. The Theory of Capitalist Development. Principles of Marxian Political Economy.. Dennis Dobson, London.