Marx's analysis of the falling rate of profit in the first version of Volume III of capital

Abstract

This paper provides an analysis of the Hodgskin section of Theories of Surplus Value and the general law section of the first version of Volume III of Capital. It then considers Part III of Volume III, the evolution of Marx's thought and various interpretations of his theory in the light of this analysis. It is suggested that, as late as the 1870s, Marx had hoped to be able to provide a demonstration that the rate of profit must fall. The main conclusions are that (1) Marx's major attempt to show that the rate of profit must fall occurred in the general law section, (2) Part III does not contain a demonstration that the rate of profit must fall and (3) Marx was never able to demonstrate that the rate of profit must fall and he was aware of this.

Acknowledgments

This paper first appeared as Universitat Autònoma de Barcelona working paper 297.95. I have benefited from the comments of Giovanni Bono, Tony Brewer, Gerard Duménil, Duncan Foley, Heinz Kurz, David Laibman, Costas Lapavitsas, Jordi Massó, Lefteris Tsoulfidis, the participants of the UAB macroeconomics workshop, the Congress Marx International III and the European Society for the History of Economic Thought 2002 Conference, and several anonymous referees. I am grateful for their help. The usual disclaimer applies. Financial support from the Spanish Ministry of Education and Science and the European Fund for Regional Development through grant SEC 2003-00306 and from the Barcelona economics program of the Centre de Referència en Economia Analitica is gratefully acknowledged.

Notes

¹What this paper calls the Hodgskin section is in Marx (1862–63, pp. 263–319). The 350 notebook pages have been published in two parts, in Marx & Engels (1989, pp. 449–543) and Marx & Engels (1991, pp. 7–252), while the general law section is in Marx & Engels (1991, pp. 104–152). See Marx & Engels (1989, p. 560, n. 121) for the editors' view of the relation between the 350 notebook pages and Volume III of Capital.

²A justification for not calling this the organic composition of capital is given in footnote 5 below.

³Marx habitually used the phrase ‘the tendency for the rate of profit to fall’. This has two interpretations: first, that the rate of profit must fall in the long run but might rise during short periods and, second, that it is probable that it will fall in the long term but that it might not. When it is clear that Marx has in mind the first interpretation the paper will refer to ‘must fall’, whereas in the other case it will be ‘might fall’.

⁴In designating k and l as measures of productivity the paper is deviating from conventional notational practice.

⁵This could be called the organic composition of capital. However, the issue is complicated. First Marx used the phrase ‘the ratio of variable to constant capital’ in both the Hodgskin and general law sections, which are the focus of this paper. Second, since the model only has one good, the technical, value and organic compositions of capital are all equivalent. Third, there is a large literature on the roles of the different compositions (see Sadd-Filho, 2002, Chapter 6) and the reader might easily think that it was significant that this paper has chosen the organic composition. It seems best to follow Duménil & Lévy (2003) and avoid these issues by simply calling C/V the composition of capital.

⁶In the Hodgskin section Marx slid over the link between the rising K/L ratio and the rising C/V ratio. In the general law section he just started with the rising C/V ratio. However, in the Cherbuliez section of Theories of Surplus Value (Marx, 1862–63, pp. 362–398), he studied the link. In the two sections covered he appeared to suppose that it is the change in K/L that causes the change in C/V.

⁷ [ltilde]  ^′ = d [ltilde]/d (C/V) and similarly for [ktilde] ^′ below.

⁸Marx had ‘and’ rather than ‘by’.

⁹I have deleted the rise in the productivity of capital from the condition. This must have been a slip by Marx since if the productivities of both capital and labour rise, the rate of profit must also rise. This is obvious but can also be seen from equation (10).

¹⁰The actual quote reads ‘if, as in the above example, the value of 12 hours is 75 then that of 24 hours adds up to 2 × 75 or 150. And since a worker must live he can never produce 150 profit much less 200’ (Marx, 1862–1863, Part III, p. 304). This paper has corrected two slips to ease the reader's task. The first is of translation: ‘as … is’ is clearly wrong because in the above example the value of 12 hours is 25. The second is in Marx's calculation. Clearly he was thinking that the rate of profit in the above example was 100% while it was actually 50%.

¹¹In Marx's notation here c and v are the constant and variable capital, with C = c + v.

¹²The edges of these pages have been damaged so that the transcription has such frequent gaps that Marx's argument is impossible to follow. The author reconstructed the pages. The complete reconstruction is in Appendix II of Petith (2001). The quotes that follow are taken from this reconstruction; the phrases in square brackets are the ones that have been added.

¹³In Table 2, p′ is the rate of profit and s′ is the rate of surplus value.

¹⁴This example suffers from the same problem as that of section 3.2. However, proposition 3 has shown that the problem the example illustrates is a real one.

¹⁵The manuscript has 50.

¹⁶Marx's calculation is slightly awry since the undepreciated amount is 333. The correct calculation would be (37 + 150 + 80 + 0.05′333)(1.05)=326. By this method the price in the first case would be 600 × 1.05 = 630. These details do not alter the thrust of Marx's calculations.

¹⁷There are sketches of multi-sector arguments that are usually based on resource scarcity, but these are outside the scope of the paper.