New aspects of Marx's economic theory in MEGA: Marx's original six-sector model

ABSTRACT

Marx's Reproduction Scheme is widely known as one of the first two-sector economic models in the history of economic theories. However, a close investigation into Marx's original shows that his multi-sectoral analysis contains not (only) two-sector models but six-sector ones, which were totally omitted by Engels in his editing the manuscripts for Capital, Volume II. Taking up two interesting theoretical episodes in the ignored six-sector analysis, this paper attempts to make sense of Marx's treatment on the price of production and the dynamic process of traverse between two equilibria.

KEYWORDS:

• Marx
• MEGA
• six-sector model
• non-basic good
• traverse

Acknowledgments

Earlier versions of this paper were presented at the 21th Annual Conference of the European Society for the History of Economic Thought at University of Antwerp, 18–20 May 2017 and at the conference “Marx 1818/2018. New Developments on Karl Marx's Thought and Writings”, Lyon, 27–29 September 2017. I would like to thank the participants for useful comments. I am particularly grateful to two anonymous referees for careful reading and constructive criticism. The usual caveat applies. Mori's research was supported by JSPS KAKENHI Grant Number 16K03572.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ In Ms. II, the text related to Part 3 of Volume II of the edited Capital begins on manuscript page 130 (Marx 2008b, 340) and ends on manuscript page 202 (Marx 2008b, 522). The pages 167–202 (Marx 2008b, 443-522) were omitted by Engels.

² Note that Marx used in his original somewhat awkward notations IIα, IIαα, Ia, IIβ, IIββ and Ib, which we substitute in this paper with A1, A2, A3, B1, B2 and B3 respectively.

³ The first and second issues were presented in Marx's original, respectively, in MEGAII/11 (Marx 2008b, 481–503) and MEGAII/11 (Marx 2008b, 443–481). For the sake of convenience, we changed the original order here.

⁴ See Footnote 2.

⁵ On the similarity between Marx's and Shibata's construction, see Mori (2007).

⁶ Marx (2008b, 483, 493, 495).

⁷ Marx (2008b, 483, 488, 490, 494).

⁸ Marx (2008b, 488–491, 493, 495).

⁹ Marx (2008b, 481–484, 494).

¹⁰ Marx (2008b, 484-488, 494).

¹¹ Marx (2008b, 492–494).

¹² “The money of 300₤ that is initially advanced in the class I(Ia and Ib), (IIαα + IIα) and (IIββ + IIβ) as variable capital and then spent by workers as means of purchase, means of circulation of their revenue on necessary means of consumption, has returned everywhere to its starting point in order to begin then with its course anew” (Marx 2008b, 469).

¹³ “The same amount of money of 50₤ figures here alternately as money form of variable capital (IIβ)..., then money form of labours’ revenue..., money form of constant capital (Ia)..., money form of constant capital (IIαα)..., money form of capitalists’ revenue (IIα)..., money form of constant capital (Ib)..., money form of constant capital (IIββ)..., and finally returning money form of variable capital (IIβ)” (Marx 2008b, 463–464).

¹⁴ “It is therefore the variable money capital that mediates all these transactions. However, there remains as rest (Ueberschuß) a part of surplus value = I(b), II(ββ + β) which is not circulated by it, and for whose circulation own amount of money must be advanced” (Marx 2008b, 491). “The sum of value of total circulation is divided into two independent parts of which the one is advanced for circulating variable capital and surplus labour, and the other circulates within constant capital reproduced in their various natural forms. It is a big mistake to think that the amount of money outlaid by consumers (i.e. wage + capitalists’ revenue) purchases and circulates the whole product” (Marx 2008b, 481).

¹⁵ If there is a group of non-basic goods I_i (i >1) such that the Frobenius root of B_ii is not less than that of B₁₁, i.e. λ_i ≥ λ₁, then one of the following two alternatives must occur. Either basics’ prices are zero while some non-basics’ prices are positive with a (possibly) lower rate of profit. Or basics’ prices are positive while some prices are negative with a higher rate of profit. The problem was recognised by several authors besides or even before Sraffa (1960, 90–91, Appendix B). Gautam Mathur (1965) treated as a non-basic good a heavy equipment (e.g. dam) in its accumulation process which is being expanded before it can be employed as a means of production for other (machinery) industries in future (Mathur 1965, 115–116). More than 30 years before Sraffa (1960), a mathematician Robert Remak (1929) was well aware of the problem of non-basic system. Adapted to the assumptions and notations in this section, his rather abstract algebraic analysis can be summarised in the following way. First, he assumed an input coefficient matrix whose quantity (column) eigenvector is the aggregation vector ι and the associated Frobenius eigenvalue is unity, i.e. Bι = ι. Then, for this input matrix B, he proved that there exists a non-negative price eigenvector p such that p = pB, and examined how zeros are located in p. Defining I_n0 as “the highest group (höchste Gruppe)”, he concluded that all prices except the highest group must be zero. Obviously, this implies that the prices of all basic goods in I₁ must be zero. This result is true because in Remak's matrix B, we have 1 = λ_n0 > λ_j for all j < n₀.

¹⁶ Sector indices in square parentheses were changed from the original in order to be consistent with our definition.

¹⁷ Obviously, there is a difference in the “paralysis” which is directly meant by Marx and Lowe. For Marx, it is the transfer of capital and labour from B-sectors and A-sectors which would be hindered and paralysed while it is the transfer, say, from A/B2 (and A/B3) to A/B1 for Lowe. However, further consideration should be given to what Marx specifically thinks is the hindrance and paralysis in the transfer from B-sectors to A-sectors which is immanent in the capitalist production. It cannot be found in the technically given fact that means of production or workers’ qualifications are not compatible between A and B due to the division of labour. Such incompatibility would not be immanent only in the capitalist production at all. What is explicitly meant by Marx in the text is rather a characteristic phenomenon that the employment of workers in A-sectors does not increase fast enough, let alone as fast as their release in B-sectors could be absorbed (Marx 2008b, 502). And Marx regards this inertial delay in the growth of employment in A-sectors as “resistance (Widerstandskraft)” which is “immanent in the mechanism of capitalist production” (Marx 2008b, 503). Here is the point where the arguments of Marx and Lowe meet. Although it is focused on A-sectors, Marx pointed out as well as Lowe the difficulty of speedy (efficient) growth of the whole system consisting of consumption goods, secondary equipment and primary equipment. Both considered this difficulty or impossibility as immanent in capitalism (or free market) where they commonly referred to the adverse price incentive. It is true that Marx did not elaborate so much on the specific reason why such a failure of growth in A-sectors must inevitably occur in the capitalist production, as Lowe did in view of the transfer from secondary- to primary-equipment sector. However, as a matter of fact, Marx was well aware that the problem does not lie in the consumption-good sector alone, but it must vertically reach its “root”, i.e. the (primary) means-of-production sectors (Marx 2008b, 742–743).

¹⁸ The efficient traverse in B-sectors, which subsequently occurs to A-sectors, can be treated in the analogous way, which elaboration we omit in this paper.

¹⁹ Lowe admitted that the three phases may not necessarily proceed successively (or “horizontally”) but parallel (or “vertically”) as shown in Figure 1.

Additional information

Funding

JSPS KAKENHI [grant number 16K03572].