Prices, profits and rhythms of accumulation GILBERT ABRAHAM-FROIS University of Paris X at Nanterre AND EDMOND BERREBI University of Paris X at Nanterre Translated by SONIA BEN OUAGRHAM CAMBRIDGE UNIVERSITY PRESS Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge CB2 1RP 40 West 20th Street, New York, NY 10011-4211, USA 10 Stamford Road, Oakleigh, Melbourne 3166, Australia © Cambridge University Press 1997 First published 1997 Printed in Great Britain at the University Press, Cambridge A catalogue record for this book is available from the British Library Library of Congress cataloguing in publication data Abraham-Frois, Gilbert. [Prix, profits et rythmes d'accumulation. English] Prices, profits and rhythms of accumulation / Gilbert Abraham- Frois and Edmond Berrebi; translated by Sonia Ben Ouagrham. p. cm. Includes bibliographical references (p. ) and index. ISBN 0 521 39532 1 1. Prices - Mathematical models. 2. Profit - Mathematical models. 3. Saving and investment - Mathematical models. I. Berrebi, Edmond. II. Title. HB221.A1913 1995 336.5'2-dc20 94-42383 CIP ISBN 0 52139532 1 hardback SE Contents Preface page ix 1 The golden rule of accumulation and prices 1 1.1 Typology of activities 2 1.2 Choices of methods of production and satisfaction of demand 4 1.3 An analysis of the golden rule of prices 13 1.4 The accumulation-consumption conflict under 'simple' production 15 1.5 The accumulation-consumption conflict under strong joint production 22 1.6 Separately reproducible goods and strong joint production 35 2 Systems of production prices 38 2.1 A world of robots: production for subsistence 38 2.2 Sharing out the surplus 42 2.3 Wage prices and wage-profit relations 47 2.4 Reduction to dated quantities of labour 52 2.5 'Advanced' wages and wages paid 'post factum' 55 3 Irregular and decomposable systems 59 3.1 Decomposable systems 59 3.2 Irregular systems 85 Mathematical appendix 96 4 The analysis of joint production 100 4.1 Prices in joint production 101 4.2 Basic and non-basic systems 105 4.3 Antibasic and non-antibasic systems 119 vii viii Contents 4.4 Various partitions of an indecomposable system 123 Mathematical appendix 126 5 Standards and blocking goods 127 5.1 Seeking the invariant standard of value 127 5.2 Duality and standards 139 6 Labour values and the problem of transformation 148 6.1 Marx's analysis: formal presentation 148 6.2 Reformulation 153 6.3 Peculiar cases when Marx's statement holds 157 6.4 Marx's solution: an incomplete iteration(?) 160 6.5 Non-basic goods and luxury goods 165 6.6 Joint production and negative values 167 6.7 Consumption and accumulation 174 7 Switch in methods of production 176 7.1 Truncation of the system and choice of methods of production 176 7.2 Single-product industries and circulating capital 180 7.3 Joint production: new problems 187 7.4 Depreciation of machines 199 7.5 Optimisation and production prices 206 8 The dynamic evolution 217 8.1 Accumulation and distribution with constant returns 217 8.2 Accumulation and increasing difficulties to produce 229 8.3 Intensified use of natural resources 243 8.4 Technical improvement and distortion of the system of prices 259 Notes 263 References 271 Index 277 Preface How are the prices of reproducible goods determined? Can the analysis of the distribution of the gross national product and the determination of production prices ignore wants, the level and structure of demand? How does the choice of techniques, a switch in the methods of production, interfere with the accumulation process, the distribution of the gross national product, and therefore with the structure of prices? What kind of relationship is there between market prices and production prices? How should the contemporary analysis contemplate the problem of exploitation and the relation between labour-values and production prices? What is the meaning of the 'standard commodity'? Can the analysis of accumulation limit itself to permanent regimes with constant returns to scale? What is the importance of the 'golden rule' of accumulation? How is the dynamic evolution to be analyzed? . These are the main topics we intend to address in the present book. We shall more specifically analyse the problems generated by the accumulation and the prices of the so-called 'reproducible' commodities, assuming first that there are constant returns to scale; then we will contemplate the increasing costs of production, the appearance of different kinds of rents, and the determination of natural resources' prices. We shall assume that commodities are reproduced by means of heterogeneous commodities and labour, the supply of which is taken to be unlimited. Production which is, so to speak, pulled by demand, is supposed to be disposed of without any difficulties. At each period, the stocks of the means of production, the available (heterogeneous) commodities that can be used for production, appear to be a constraint, limiting production; this constraint is relaxed as time goes by, owing to accumulation. The link with the classical approach is thus obvious, the classical school focussed its analysis on 'such commodities only as can be increased in quantity, by the exertion of human industry' (D. Ricardo, 1984, chapter 1) and tended to put aside those for which the quantity could not be increased. Ricardo referred to these as follows. IX x Preface There are some commodities, the value of which is determined by their scarcity alone. No labour can increase the quantity of such goods, and therefore their value cannot be lowered by an increased supply. Some rare statues and pictures, scarce books and coins, wines of a peculiar quality, which can be made only from grapes grown on a particular soil, of which there is a very limited quantity, are all of this description. Their value is wholly independent of the quantity of labour originally necessary to produce them, and varies with the varying wealth and inclinations of those who are desirous to possess them. These commodities, however, form a very small part of the mass of commodities daily exchanged in the market. By far the greatest part of those goods which are the objects of desire are procured by labour: and they may be multiplied, not in one country alone, but in many, almost without any assignable limit, if we are disposed to bestow the labour necessary to obtain them. This approach is not only due to Ricardo; many other classics1 adopted it and it was approved by Marx (XXXX) in the first pages of The Poverty of Philosophy. Production of Commodities by Means of Commodities by Sraffa (1960) follows on the same line. However, this considerable work is limited to the price theory while the scope of the classical analysis is much broader, including, among other things, the problems of growth and accumulation of capital which are at the heart of the general equilibrium model due to J. von Neumann (1945-6). The latter introduced the first characteristic of the system he intended to analyse as follows: 'Goods are produced not only from "natural factors of production", but in the first place from each other. These processes of production may be circular, i.e., good G, is produced with the aid of good G2, and G2 with the aid of G,.' In von Neuman's model, consumption is limited to the subsistence level. Such a limitation will be cleared in the very first chapter of the present book. The problems arising from the satisfaction of wants, or demand, are mentioned from the very beginning, and this will allow us to draw a typology of the structures of production and of goods. The accumulation/ consumption conflict is indeed quite different, depending on whether joint production prevails and whether it is 'strong' or 'weak'. The determination of production prices under 'simple' production will be developed in chapter 2; we shall temporarily assume that the choice of the methods of production has been previously made, so that there are as many methods of production as there are commodities to produce. The analysis of production prices is continued in chapter 3 which deals with peculiar structures of production, the decomposability and irregular- ity of production systems. Chapter 4 is devoted to a prior study of price systems under joint production; indeed, the decomposability of productive systems brings about some new problems. Joint production cannot be addressed independently of the problems of viability and efficiency of the system, problems that we shall develop in chapter 7. Preface xi The meaning and the determination of the invariant standard of value are developed in chapter 5. We shall more particularly emphasise the treatment of decomposable systems where the notion of a blocking sector appears to be relevant. We will show that under joint production there is always a standard of prices. This is to be linked with the existence of a solution to von Neumann's model. Finally, we shall address the standard of activity levels which appears to be the dual of the standard of prices. Chapter 6 is totally devoted to the analysis of the problems developed by Marx, i.e., the relation between labour values and production prices, as well as between the rate of profit and the rate of exploitation; the reformulation that we shall suggest allows us to maintain a relation between the rate of profit and the rate of exploitation through a specific commodity, or rather, through a combination of activities similar to Sraffa's standard of prices. This will lead us to deal with the problem of luxury goods and the decomposability of productive systems; we shall also examine the difficul- ties arising from joint production systems where some commodities may have negative labour values; this demonstrates the interest of the notion of separately reproducible goods, defined in chapter 1.