Saturday, August 14, 2021

Bibliography on Marx’s Law of the Falling Rate of Profit

I present below a bibliography on Marx’s Law of the Falling Rate of Profit. The list is not meant to be exhaustive, but includes the most important or interesting discussions.

In essence, the text of volume 3 of Capital was taken from the manuscripts of volume 3 from 1864–1865 which were in a draft and fragmentary form (Vollgraf and Jungnickel 2002: 68). Engels began editing volume 3 for publication around 1885 but it took him nearly 10 years before that volume was published in 1894 (Vollgraf and Jungnickel 2002: 40). In 1993, Marx’s main 1864–1865 manuscript for volume 3 of Capital which Engels used was published and allowed scholars to compare this with what Engels published in 1894 (Vollgraf and Jungnickel 2002: 36).

Engels’ changes to Marx’s material on the Law of the Falling Rate of Profit, including his three chapters and subdivisions, suggested that this work was much more structured and complete than it in fact was (Vollgraf and Jungnickel 2002: 47, 62). Michael Heinrich argues that Engels’ editing obscured Marx’s views on the falling rate of profit. For Heinrich, the idea that Marx’s theory of crisis was based on the Law of the Falling Rate of Profit is a misinterpretation of Marx’s thought that has arisen from Engels’ editing of the third volume of Capital. Whether this is true or not, the Law of the Falling Rate of Profit has been vehemently defended by many generations of Marxists.

However, the Law of the Falling Rate of Profit did not actually play a fundamental role in Marxist crisis theory until the work of E. Preiser (1924) and Henryk Grossmann’s book The Law of Accumulation and Breakdown of the Capitalist System (1929).

Okishio’s Theorem (Okishio 1961), which was partly based on earlier work like Shibata (1939), is often cited as a refutation of Marx’s Law of the Falling Rate of Profit, but even Okishio’s Theorem is a highly theoretical refutation which itself makes unrealistic assumptions in its model, such as constant real wages, equalised profit rates and equilibrium convergence to new prices of production. Okishio himself later admitted that his original theorem required these “questionable assumptions” (Okishio 2001: 501). Moreover, it is not difficult for Marxists to respond to Okishio’s Theorem, as Paul Cockshott does below in this video:

A much better refutation of Marx’s Law of the Falling Rate of Profit should start with the fundamental objection that, firstly, the very concept of “surplus value” is irrelevant for real-world capitalist economies, since it is based on the incoherent, undefinable notion of homogenous units of “socially-necessary labour time” that can aggregate all different forms of heterogeneous human labour. Imaginary “surplus value” does not determine the rate of profit in any sense in modern capitalist economies.

Secondly, even if one, for the sake of argument, grants that the concept of “surplus value” has validity, the “organic composition of capital” (c/v) would itself still be a flawed and often poor measure of productivity. Recall that Marx postulated that there is a rising organic composition of capital as a necessary effect of capital accumulation and productivity growth. But, as Blaug (1960) argued, rising technical innovation and productivity in capitalism involves both labour-saving innovations and capital-saving innovations. This means that capital-saving innovations can lower prices of machines and non-labour factors (see also Hodgson 1991: 34–40). So the technical composition of capital may rise, but the value composition of capital c/v, as Marx defines it, may fall as (1) both money wages and real wages rise, and (2) prices of capital goods fall. Thus it is theoretically possible for productivity growth and technological advancement in firms to occur along with a decline in the organic composition of capital, if the prices of non-labour factor inputs fall fast enough.

Attempts to empirically measure Marx’s long-run rising organic composition of capital via proxies have found that the UK – the greatest capitalist economy in the relevant period – had a falling organic composition from 1855 to 1895! (Cockshott, Cottrell, Michaelson 1995). Secondly, Gillman (1958) found a falling/stable organic composition of capital in the US from 1919 to 1952, despite a brief spike in the Great Depression.

Clearly, there is something rotten about the very concept of the organic composition of capital. One can only agree with Ian Steedman that “neither the value composition nor the organic composition is a significant concept for the analysis of capitalist economies” (Steedman 1977: 136).

It follows that, even within the terms of Marx’s own theory, the Law of the Falling Rate of Profit is fundamentally flawed if the prices of constant capital goods themselves fall to a sufficient extent.

But, from a Post Keynesian perspective, a straightforward empirical refutation of the Law of the Falling Rate of Profit is simply that most profits are attained as a mark-up on total average unit costs, and many capitalists will charge whatever profit mark-up they can get away with, sometimes very large mark-ups indeed. Moreover, there is no strong evidence that the rate of profit has a tendency to equalise throughout a capitalist economy (Glick and Ehrbar 1990; Zacharias 2001; Gschwandtner 2005; Cable and Jackson: 2008; Zachariah 2006: 18), and even if one granted hypothetically that surplus value existed, it would not govern the rate of profit given the use of persistent, divergent profit mark-ups on costs by capitalists.

In the long-run, we should expect the average rate of profit to rise or fall randomly. The profit rate would be mainly reduced by money wage rises in many industries. Any long-run falling trend – even if it could be demonstrated – would not even vindicate Marxism, but would have to have another explanation, because Marx’s theory of profit is profoundly and inescapably both theoretically and empirically flawed.

The bibliography below is presented in chronological order, not alphabetical order, since I think a chronological order from the earliest discussion to most recent is more useful. I include occasional comments about the significance of certain articles or books.

Croce, Benedetto. 1899. “Una obiezione alla legge marxistica della caduta del saggio di profitton,” Atti dell’Accademia Pontaniana 29 (May 1899).
Remarkably, Croce already in this 1899 paper pointed out that, as technical progress and productivity increase under capitalist production, this is likely to decrease the value/price of constant capital, which effectively refutes Marx’s law of the falling rate of profit. See the English translation in Croce (1914).

Baranovsky, Michael Tugan. 1901. Studien zur Theorie und Geschichte der Handelskrisen in England. G. Fischer, Jena. pp. 230–231.

Baranovsky, Michael Tugan. 1905. Theoretische Grundlagen des Marxismus. Duncker & Humblot, Leipzig. Chapter 9.
Tugan-Baranovsky concluded that the falling rate of profit law was questionable in the face of capital-saving innovation.

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.
In this paper, Bortkiewicz agreed with the argument of Tugan-Baranovsky and questioned why capitalists would introduce labour-saving machines if the profit rate fell.

Charasoff, Georg von. 1909. Karl Marx über die menschliche und kapitalistische Wirtschaft: eine neue Darstellung seiner Lehre. H. Bondy, Berlin.

Charasoff, Georg von. 1910. Das System des Marxismus: Darstellung und Kritik. Hans Bondy Verlag, Berlin.
Charasoff rejected the law of the falling profit rate in this book as erroneous, for reasons similar to those of Tugan-Baranovsky and Bortkiewicz.

Croce, Benedetto. 1914. “A Critique of the Marxian Law of the Fall in the Rate of Profit,” in Benedetto Croce, Historical Materialism and the Economics of Karl Marx (trans. C. M. Meredith). The Macmillan Company, New York. [article first published in 1899].

Preiser, E. 1924. “Das Wesen der Marxschen Krisentheorie,” in R. Wilbrandt, A. Löwe, G. Salomon (eds.), Wirtschaft und Gesellschaft. Beiträge zur Ökonomik und Soziologie der Gegenwart. Frankfurter Societäts-Druckerei, Frankfurt am Main. 47–76.
Preiser appears to have been one of the first early Marxists who emphasised the falling rate of profit as the fundamental cause of capitalist crisis.

Grossmann, Henryk. 1929. Das Akkumulations- und Zusammenbruchsgesetz des kapitalistischen Systems: Zugleich eine Krisentheorie. C. L. Hirschfield, Leipzig.

Moszkowska, Natalie. 1929. Das Marxsche System: Ein Beitrag zu dessen Aufbau. Verlag Hans Robert Engelmann, Berlin.

Shibata, K. 1934. “On the Law of Decline in the Rate of Profit,” Kyoto University Economic Review 9.1 (17): 61–75.
Along with Shibata 1939, this was an important theoretical discussion of the falling rate of profit.

Bauer, Otto. 1936. Zwischen zwei Weltkriegen?. E. Prager, Bratislava. In this book, Bauer discussed the relationship he postulated between the business cycle and the falling rate of profit.

Shibata, Kei. 1939. “On the General Profit Rate,” Kyoto University Economic Review14.1 (27): 40–66.
This paper was an important theoretical discussion of the falling rate of profit. Shibata concluded that innovations that are capital-saving (that is, that reduce the price of constant capital) can lead to a rising profit rate, as long as real wages are constant. His work was developed by Okishio 1961.

Dobb, Maurice Herbert. 1940. Political Economy and Capitalism: Some Essays in Economic Tradition (rev. 2nd ed.). Routledge & Kegan Paul, London. pp. 94–99, 108–114.

Robinson, Joan. 1941. “Marx on Unemployment,” The Economic Journal 51.202–203: 234–248.

Sweezy, Paul M. 1942. The Theory of Capitalist Development. Principles of Marxian Political Economy. Oxford University Press, New York.
In this book, Paul Sweezy dismissed the law of the falling rate of profit theory as a general law.

Robinson, Joan. 1942. Essay on Marxian Economics. Macmillan, London.
See the 2nd edition of Robinson 1966.

Bortkiewicz, L. von. 1952. “Value and Price in the Marxian System,” International Economic Papers 2: 5–60.

Rosdolsky, Roman. 1956. “Zur neueren Kritik des Marxschen Gesetzes der fallenden Profitrate,” Kyklos 9.2: 208–226.

Dickinson, H. D. 1957. “The Falling Rate of Profit In Marxian Economics,” The Review of Economic Studies 24.2: 120–130.
In this article, Dickinson adopted Neoclassical theory to analyse the falling rate of profit law.

Samuelson, P. A. 1957. “Wages and Interest: A Modern Dissection of Marxian Economic Models,” The American Economic Review 47.6: 884–912.
Along with Shibata 1934 and Okishio 1961, this paper was very important in technical discussions of the falling rate of profit law.

Gillman, Joseph M. 1958. The Falling Rate of Profit: Marx’s Law and its Significance to Twentieth Century Capitalism. Dobson, London.
In this book, Gillman found empirical evidence that his proxy for the US organic composition of capital had increased from 1849 to 1919, but – contrary to Marxist theory – had been stable or fallen from 1919 to 1939 (despite a rise during the Great Depression).

Robinson, Joan. 1959. “‘The Falling Rate of Profit’: A Comment,” Science & Society 23.2: 104–106.

Blaug, M. 1960. “Technical Change and Marxian Economics,” Kyklos 13.4: 495–451.

Okishio, Nobuo. 1961. “Technical Changes and the Rate of Profit,” Kobe University Economic Review 7: 85–99.
Okishio’s paper is the classic statement of Okishio’s Theorem.

Okishio, Nobuo. 1963. “A Mathematical Note on Marxian Theorems,” Weltwirtschaftliches Archiv 91: 287–299.

Robinson, Joan. 1966. An Essay on Marxian Economics (2nd edn.). Macmillan, London. pp. 35–42.

Meek, Ronald L. 1967. “The Falling Rate of Profit,” in Ronald L. Meek, Economics and Ideology and Other Essays: Studies in the Development of Economic Thought. Chapman & Hall, London. 129–142.

Steedman, Ian. 1971. “Marx on the Falling Rate of Profit,” Australian Economic Papers 10: 61–66.

Heertje, A. 1972. “An Essay on Marxian Economics,” Schweizerische Zeitschrift für Volkswirtschaft und Statistik 108.1: 33–45.

Yaffe, David S. 1973. “The Marxian Theory of Crisis, Capital and the State,” Economy and Society 2.2: 186–232.

Heertje, A. 1976. “An Essay on Marxian Economics,” in M. C. Howard and J. E. King (eds), The Economics of Marx. Penguin, Harmondsworth. pp. 219–232.

Mandel, Ernest. 1973. Der Spätkapitalismus: Versuch einer marxistischen Erklärung. Suhrkamp Verlag, Frankfurt am Main.
See Mandel 1976 for an English translation.

Hodgson, Geoff. 1974. “The Theory of the Falling Rate of Profit,” New Left Review 84: 55–82.

Mandel, Ernest. 1976. Late Capitalism (trans. Joris De Bres). NLB, London.
In this book, Mandel argued that the falling rate of profit was important in the Marxist explanation of the post-WWII boom and its breakdown.

Steedman, Ian. 1977. Marx after Sraffa. NLB, London. pp. 116–136.

Rowthorn, Bob. 1976. “Late Capitalism,” New Left Review 98: 59–83.

Croce, Benedetto. 1981. Historical Materialism and the Economics of Karl Marx. Transaction Books, New Brunswick, N.J. [reprint of the 1914 edn].

Groll, Shalom and Ze’ev B Orzech. 1989. “From Marx to the Okishio Theorem: A Genealogy,” History of Political Economy 21.2: 253–272.

Dietzenbacher, Erik. 1989. “The Implications of Technical Change in a Marxian Framework,” Journal of Economics 50.1: 35–46.

Catephores, George. 1989. An Introduction to Marxist Economics. Macmillan, Basingstoke. pp. 166–189.

Glick, Mark and Ehrbar, Hans. 1990. “Long-Run Equilibrium in the Empirical Study of Monopoly and Competition,” Economic Inquiry 28.1: 151– 162.

Moseley, Fred. 1991. The Falling Rate of Profit in the Postwar United States Economy. Macmillan, Basingstoke.

Hodgson, Geoffrey M. 1991. After Marx and Sraffa: Essays in Political Economy. Macmillan, London. pp. 28–55

Grossmann, Henryk. 1992. The Law of Accumulation and Breakdown of the Capitalist System: Being also a Theory of Crises (trans. Jairus Banaji). Pluto Press, London.

Howard, Michael Charles and John Edward. 1992. A History of Marxian Economics: Volume II: 1929–1990. Macmillan, London. Chapter 7 (pp. 128–148).

Cockshott, Paul, Cottrell, Allin and Greg Michaelson. 1995. “Testing Marx: Some New Results from UK Data,” Capital & Class 19.1: 103–130.

Zacharias, Ajit. 2001. “Testing Profit Rate Equalization in the US Manufacturing Sector 1947–1998,” Working Paper No. 321

Okishio, Nobuo. 2001. “Competition and Production Prices,” Cambridge Journal of Economics 25.4: 493–501.

Vollgraf, Carl-Erich and Jürgen Jungnickel. 2002. “‘Marx in Marx’s Words’? On Engels’s Edition of the Main Manuscript of Book 3 of ‘Capital,’” International Journal of Political Economy 32.1: 35–78.

Gschwandtner, Adelina. 2005. “Profit Persistence in the ‘very’ Long Run: Evidence from Survivors and Exiters,” Applied Economics 37.7: 793–806.

Kliman, Andrew. 2006. Reclaiming Marx’s ‘Capital’: A Refutation of the Myth of Inconsistency. Lexington Books, Lanham. pp.113–138.

Zachariah, Dave. 2006. “Labour Value and Equalisation of Profit Rates: A Multi-Country Study,” Indian Development Review 4: 1–20.

Cable, John R. and Richard H. G. Jackson. 2008. “The Persistence of Profits in the Long Run: A New Approach,” International Journal of the Economics of Business 15.2: 229–244.

Heinrich, Michael. 2012. An Introduction to the Three Volumes of Karl Marx’s Capital (trans. Alexander Locascio). Monthly Review Press, New York. pp. 149–154.

Wednesday, July 7, 2021

Zachariah’s “Labour Value and Equalisation of Profit Rates”: A Critical Review

D. Zachariah’s paper “Labour Value and Equalisation of Profit Rates: A Multi-Country Study” (Indian Development Review 4 [2006]: 1–20) seeks to prove Marx’s Labour Theory of Value (LTV) by examining empirical data on factor input costs and final prices of finished goods from 18 nations in a period from 1968 to 2000.

Zachariah concludes that “market prices and labour value of industry outputs are highly correlated for a fairly broad sample of economies” (Zachariah 2006: 18), and that the idea of “prices of production” (used by Marx in volume 3 of Capital) is an inferior theory to the simple Labour Theory of Value in explaining prices, especially since Zachariah finds strong evidence against a tendency to equalisation of profit rates (Zachariah 2006: 18). In essence, Zachariah also concludes that the Transformation Problem appears to be irrelevant, given his findings.

So it is clear that Zachariah is trying to defend a version of the LTV used by Marx in volume 1 of Capital.

We must remember that Marx had no single, consistent Labour Theory of Value. The “law of value” (a phrase which Marx used to refer to the LTV) in volume 1 of Capital contradicts the “law of value” in volume 3.

In order to clarify this problem, we can review Marx’s two versions of the Labour Theory of Value, as follows:
(1) The “Law of Value” in volume 1 of Capital
In volume 1 of Capital, Marx defended in his text a “law of value” in which homogeneous socially-necessary labour time units were the anchor for the price system in modern capitalism. That is to say, individual commodity prices are supposed to gravitate towards their labour values (but volume 1 contained two footnotes hinting at the different theory of price determination in Marx’s draft of volume 3, so that volume 1 was not even internally consistent).

By volume 3 of Capital, Marx thought this only happened in the pre-modern world of commodity exchange, but he describes the process as follows:
“The assumption that the commodities of the various spheres of production are sold at their value implies, of course, only that their value is the center of gravity around which prices fluctuate, and around which their rise and fall tends to an equilibrium.” (Marx 1909: 208–210).
For this LTV to work and be empirically proved, all human labour of different kinds must be measurable in a homogenous unit of basic socially-necessary labour time and then compared.

(2) The “Law of Value” in volume 3 of Capital
In volume 3 of Capital, Marx abandons the view that commodity prices tend to equal pure labour values. Instead, Marx defended the view that the “law of value” only ultimately and indirectly explains prices, and defended three aggregate equalities:
(1) the sum of surplus value = sum of profits;

(2) the sum of values = sum of prices, and

(3) the value rate of profit = the money rate of profit.
These aggregate equalities were asserted as true as Marx’s attempt to defend labour value. But Classical “prices of production” became the anchors for the real-world price system.
Now Zachariah in his article is essentially rejecting the “law of value” in volume 3, and trying to defend the crude LTV in volume 1.

The trick that Marxists like Zachariah use is this: by showing empirically that there is a high correlation between the labour cost of fundamentally different labour types to the prices of their respective output goods, Marxists think they have proven the LTV. But this is a spectacular non sequitur. The reason is this: Marx’s Labour Theory of Value is much more than this simple correlation.

Zachariah’s contends that it is “the need for companies to meet the wage-bill that forces market prices to gravitate around prices proportional to labour values” (Zachariah 2006: 4). But this does not follow at all, because we cannot even properly measure the objective labour values of all different goods produced by heterogenous kinds of human labour. The very concept of labour value as used by Zachariah has not been properly defined in the way Marx used it.

No Marxist has ever convincingly shown how to overcome the problem of reducing all different types of human labour-time and measuring it in a homogeneous unit. For example, one hour of labour by a highly-skilled engineer is different from one hour of labour by a brick layer on a construction site.

This devastating problem with even properly defining the LTV has been noted by economists from different schools. Joan Robinson correctly pointed out that Marx needed to reduce all heterogeneous human labour time to a meaningful homogenous unit (Robinson 1966: 12), but this “leaves open the problem of assessing labour of different degrees of skill in terms of a unit of ‘simple labour’” (Robinson 1966: 19).

Marx faced the problem of reducing all heterogeneous human labour to a homogeneous abstract socially-necessary labour time unit, but Marx did not properly explain how this happens. You cannot prove a theory when your fundamental concept cannot be empirically defined or measured.

Eugen von Böhm-Bawerk identified the same problem. Böhm-Bawerk stated:
The fact with which we have to deal is that the product of a day’s or an hour’s skilled labor is more valuable than the product of a day's or an hour's unskilled labor; that, for instance, the day's product of a sculptor is equal to the five days’ product of a stone-breaker. Now Marx tells us that things made equal to each other in exchange must contain ‘a common factor of the same amount,’ and this common factor must be labor and working time. Does he mean labor in general? Marx's first statements up to page 45 would lead us to suppose so; but it is evident that something is wrong, for the labor of five days is obviously not ‘the same amount’ as the labor of one day. Therefore Marx, in the case before us, is no longer speaking of labor as such but of unskilled labor. The common factor must therefore be the possession of an equal amount of labor of a particular kind, namely, unskilled labor.

If we look at this dispassionately, however, it fits still worse, for in sculpture there is no ‘unskilled labor’ at all embodied, much less therefore unskilled labor equal to the amount in the five days’ labor of the stone-breaker. The plain truth is that the two products embody different kinds of labor in different amounts, and every unprejudiced person will admit that this means a state of things exactly contrary to the conditions which Marx demands and must affirm, namely, that they embody labor of the same kind and of the same amount!.” (Böhm-Bawerk 1949 [1896]: 81–82).
Marxists like Zachariah cannot even defend the “law of value” in volume 1 of Capital without solving this problem, but there is no convincing solution to the problem even mentioned in Zachariah’s paper.

The normal technique used by Marxists is to correlate mere labour costs in money prices with output prices, but this is a practice that cannot possibly overcome the problem of aggregating the different types of labour with a homogenous unit. To prove that prices are determined by labour values, you would have to calculate the homogeneous socially-necessary labour time units required to produce every commodity where all skilled labour and unskilled labour can be measured in the same homogenous unit, and then compare these quantities with prices. But Zachariah and other Marxists do not do this.

What Zachariah has proven is that there is, indeed, a very high correlation between labour factor input costs and prices, since labour costs are, generally speaking, a huge part of total production costs in most sectors. But Post Keynesian economics also accepts this, as do all non-Marxist cost-based theories of price determination.

The problem with all these Marxist attempts to empirically prove the LTV is identified by Nitzan and Bichler:
“The other problem with [sc. Marxist] empirical studies has to do with values – or rather the lack thereof. To our knowledge, all Marxist models that purport to correlate prices with values do no such thing. Instead of correlating prices with values, they in fact correlate prices with . . . prices!

The reason is simple enough. Recall that, according to Marx, the value of a commodity denotes the abstract labour time socially necessary for its production. Yet, as we already mentioned …, this quantum is impossible to measure. And so the researcher makes assumptions.

The most important of these assumptions are that the value of labour power is proportionate to the actual wage rate, that the ratio of variable capital to surplus value is given by the price ratio of wages to profit, and occasionally also that the value of the depreciated constant capital is equal to a fraction of the capital’s money price. In other words, the researcher assumes precisely what the labour theory of value is supposed to demonstrate. ….

Since values are forever unknown, we need to first convert prices into ‘values’ and then correlate the result with prices. It seems reasonable to expect the outcome to be positive and tight. After all, we are correlating prices with themselves. What remains unclear is why one would bother to show this correlation and, more puzzling still, how the whole excise relates to the labour theory of value.” (Nitzan and Bichler 2009: 96–97).
Apart from labour-time data from Sweden, Zachariah states clearly that the rest of his data simply uses monetary “labour costs... as a proxy for labour input” (Zachariah 2006: 6), so that virtually all Zachariah’s data is subject to the critique above.

While some Marxists have in fact used labour hours or labour time in trying to calculate value, not even this proves Marx’s LTV, because the Marxists never calculate the homogeneous socially-necessary labour time units necessary for comparing different types of labour.

In reality, the finding that labour costs are strongly correlated with output prices is actually one of many strong proofs of the Post Keynesian cost-based mark-up theory of pricing, which has no need for a Labour Theory of Value at all.

And one can only note that when Marxists try and prove the crude LTV in volume 1 of Capital, they are in effect admitting that the aggregate identities that constitute the “law of value” in volume 3 must be false, which Zachariah effectively does.

However, one very interesting finding from this paper, as noted above, is that Zachariah found strong evidence against a tendency to equalisation of profit rates (Zachariah 2006: 18). It logically follows that Classical “prices of production” cannot be anchors for the real-world price system, because a tendency towards an equal profit rate is a necessary condition of “prices of production.” So the Classical, Sraffian and Marx’s theory of price determination as used in volume 3 of Capital cannot be true.

Further Reading
“The Critical Responses to Volume 3 of Marx’s Capital and the Early Development of Marxism,” February 9, 2016.

“Joan Robinson on Marx’s Labour Theory of Value: A Few Points,” August 11, 2015.

“Marx’s ‘Law of Value’ in Volume 1 of Capital,” February 4, 2016.

“Why Marx’s Labour Theory of Value is Wrong in a Nutshell,” June 28, 2015.

“Empirical Studies showing that Prices are Correlated with Labour Costs do not Prove the Classical Marxist Labour Theory of Value,” December 23, 2015.

“Böhm-Bawerk on Marx’s Problem of Aggregating Heterogeneous Human Labour,” March 7, 2016.

“Marx’s Capital, Volume 1, Chapter 11: A Critical Summary,” February 7, 2016.

“Alexander Gray on the Two Contradictions in Marx’s Theory of Surplus Value in Volume 1 of Capital,” February 8, 2016..

Böhm-Bawerk, Eugen von. 1949 [1896]. “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.

Marx, Karl. 1909. Capital. A Critique of Political Economy (vol. 3; trans. Ernst Untermann from 1st German edn.). Charles H. Kerr & Co., Chicago.

Nitzan, Jonathan and Shimshon Bichler. 2009. Capital as Power: A Study of Order and Creorder. Routledge, Milton Park, Abingdon, UK and New York.

Robinson, Joan. 1966. An Essay on Marxian Economics (2nd edn.). Macmillan, London.

Zachariah, Dave. 2006. “Labour Value and Equalisation of Profit Rates: A Multi-Country Study,” Indian Development Review 4: 1–20.