Understanding and overcoming the “positive profits with negative surplus-value” paradox

This paper explains the “positive profits with negative surplus-value” example of Steedman (1975) and shows that while in joint production systems individual labour values can be negative, the claim that the total labour embodied in the surplus product of the economy (surplus-value) can also be negative is based on assumptions that have no economic meaning (such as negative activity levels). The paper also provides a way to measure the surplus-value of joint production systems which overcomes the problems of the traditional concept and restates the proposition that a positive amount of surplus labour is a necessary condition for positive profits. KEYWoRDS: surplus value; labour value; rate of profit; joint production. JEL classification: B12. * Respectivelly, Department of Economics and Statistics, Università di Siena, Italy. E-mail: gustavodlucas@ gmail.com; Instituto de Economia, Universidade Federal do Rio de Janeiro, Brazil. E-mail: franklinserrano@gmail.com. Submitted: 13/November/2015; Approved: 19/May/2016. Brazilian Journal of Political Economy, vol 37, no 3 (148), pp 587-604, July-September/2017 587 http://dx.doi. org/10.1590/0101-31572017v37n03a07 Revista de Economia Política 37 (3), 2017 • 588 Brazilian Journal of Political Economy 37 (3), 2017 • pp. 587-604 INTRoDUCTIoN Steedman (1975) gave an example of a pure joint production system (i.e.,, without fixed capital or land) in which the rate of profits and their associated prices of production were positive and yet aggregate “surplus value” was negative. This example sparked a controversy related to the questions of how to define labour values in the context of joint production and particularly whether or not it implied a refutation of the so-called “fundamental Marxian theorem”. This “theorem” states that a positive “rate of surplus value” – the ratio between the quantity of embodied labour on the physical surplus (“surplus value”) and the quantity of embodied labour in the necessary consumption of workers (“variable capital”) – is a necessary and sufficient condition for a positive general rate of profits. Although the literature on the possibility of individual negative labour-values quite exhaustively scrutinized the necessary and sufficient conditions for it to happen – see Schefold (1989), Filippini & Filippini (1982) and Hosoda (1993) – the same cannot be said on the literature related to the possibility of negative surplusvalue – i.e.,, the labour-value of the aggregate surplus product of the economy. Many authors tried to get around Steedman’s critique through redefinitions of the labour values of single commodities, arguments about heterogeneous labour and considerations about the problem of choice of technique. Few contributors, however, discussed the actual economic meaning and relevance of the special (implicit) assumptions in Steedman’s example. In this paper we do that by means of a critical survey and a theoretical evaluation of this literature1. We make use of Steedman’s original numerical example as basis to compare and contrast the different contributions using the activity analysis diagram2 which provides a very clear picture of some properties of a square twocommodity system3. our main conclusions are that although labour values for some single commodities can indeed be negative in the most general case (it may happen if the system is not “all-productive”, as defined by Schefold (1978)), the basic and sensible classical proposition that in the aggregate less labour would be necessary to produce only the necessary wage basket than to meet also the total final demand coming from the expenditures of the capitalists always holds, even if in some cases (as in the particular economic system depicted by Steedman) producing the neces1 We decided to discuss the so-called “New Solution” approach as potential solution to the paradox in an appendix because it was not part of the original controversy. 2 originally presented by Dorfman, Samuelson and Solow (1958). 3 It is important to note that the all the contributions presented here hold for any number of commodities. The use of the original example is just to facilitate the exposition. For instance, the graphical device could not be used at all in a system with more than three commodities and even in the case of three commodities would only makes things more complicated without adding any new conclusion.