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Revisiting the Cambridge Capital Theory Controversies: a Historical and Analytical Study / Andrés Lazzarini ANDRÉS LAZZARINI Revisiting the Cambridge Capital Theory Controversies: A Historical and Analytical Study Lazzarini, Andrés Revisiting the Cambridge capital theory controversies: a historical and analytical study / Andrés Lazzarini. – Pavia : Pavia University Press, 2011. – VI, 172 p. : ill. ; 24 cm. ISBN: 978-88-96764-17-6 1. Economia – Teorie – Gran Bretagna – Sec. 19. – 20. 330.1 CDD-22 – Economia, sistemi, scuole, teorie © Andrés Lazzarini, 2011 – Pavia ISBN: 978-88-96764-17-6 Texts published by Pavia University Press in the series “Editoria scientifica” have been peer-reviewed prior to acceptance by the Editorial Board. www.paviauniversitypress.it/scientifica. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the author. The cover shows: The Mathematical Bridge, Cambridge (UK), Margarita Olivera, 2007 Publisher: Pavia University Press – Edizioni dell’Università degli Studi di Pavia Biblioteca Delle Scienze - Via Bassi, 6 – 27100 Pavia <http://www.paviauniversitypress.it> Printed by: Print Service – Strada Nuova, 67 – 27100 Pavia Contents Preface and Acknowledgements ................................................................................ V Chapter 1. Why a study on the capital theory controversies? 1.1. Capital as a factor of production and the capital theory debates .............................1 1.2. The relevance of this conflict to contemporary economic analysis .........................3 1.3. A first phase in the capital controversies ................................................................5 1.4. A second phase in the capital controversies............................................................6 1.5. Radically different views on the meaning of the critique for the contemporary versions of the theory .............................................................................................9 1.6. Sketch of this study ..............................................................................................10 PART I. Analytical and Methodological Issues in Neoclassical Economics: Setting the Ground to Understand the Capital Controversies Chapter 2. Understanding the foundations of neoclassical economics: The principle of factor substitution and the problem of capital 2.1. The data of the Marginal Theory. The direct mechanism of factor substitution....17 2.2. The indirect mechanism of factor substitution......................................................18 2.3. From ‘employment’ functions to ‘demand’ functions (I)......................................19 2.4. From ‘employment’ functions to ‘demand’ functions (II).....................................21 2.5. The capital supply function ..................................................................................23 2.6. Key role of the downward-sloping shape of factors’ demand curves....................24 2.7. Problems connected with the heterogeneity of capital goods................................25 2.8. Supply-side role of capital....................................................................................27 2.9. Persistence character of the determining circumstances: The traditional method of ‘normal positions’ ............................................................................................31 2.10. Demand-side role of capital: Conclusion............................................................34 Chapter 3. ‘Reswitching’ and ‘Reverse Capital Deepening’: Introduction to the heart of the controversies and their implications 3.1. Some premises......................................................................................................39 3.2. Economies with heterogeneous capital goods. The wage curve............................42 3.3. The wage-frontier. Economies with more than one system of production.............46 3.4. Implications for the basic premises of the theory: Conclusion..............................49 Andrés Lazzarini – Revisiting the Cambridge Capital Theory Controversies PART II. The Capital Theory Debates in a Historical Perspective and the Transformation of Dominant Theory Chapter 4. A first phase in the controversies: Samuelson’s 1962 intervention, the 1966 Symposium, neoclassical reactions and the highest point of the debates 4.1. Introduction..........................................................................................................55 4.2. Samuelson’s (1962) model with heterogeneous capital goods ..............................57 4.3. Samuelson’s ‘special sub-class of realistic cases’.................................................59 4.4. The neoclassical ‘parable’: ‘Surrogate’ capital and the ‘Surrogate’ production function ................................................................................................................60 4.5. What did Samuelson actually demonstrate?..........................................................63 4.6. There is no heterogeneous capital goods model in Samuelson’s (1962) ...............68 4.7. Levhari (1965) and the 1966 Quarterly Journal of Economics Symposium ..........70 4.8. Pasinetti (1966a)...................................................................................................73 4.9. Garegnani (1966)..................................................................................................74 4.10. The meaning of the 1966 Symposium: A turning point in the controversies.......75 4.11. Neoclassical reactions: Samuelson (1966a) ........................................................78 4.12. Further neoclassical reactions after the Symposium: Ferguson (1969) ...............80 4.13. Garegnani’s 1970 critique of the marginal theory...............................................85 4.14. Bliss’s 1970 intervention. Prelude to the shift to neo-walrasian equilibria and the beginning of a second phase in the debates.....................................................87 4.15. The zenith of the debates....................................................................................89 Chapter 5. A step back in the debates: Joan Robinson’s role in the controversies and first neoclassical reactions 5.1. Introduction..........................................................................................................91 5.2. Robinson’s critique: Aggregate production functions as her main target..............91 5.3. Equilibrium and expectations ...............................................................................93 5.4. Understanding Robinson’s way: The ‘Pseudo-production function’ and the ‘curiosum’ ............................................................................................................95 5.5. Conclusion .........................................................................................................101 5.6. Champernowne’s (1953) contribution ................................................................103 5.7. Further replies to Robinson: Solow (1955; 1956) and Swan (1956) ...................105 5.8. Robinson rejoinders............................................................................................109 Chapter 6. A second phase in the capital controversies and radical changes in the neoclassical theory 6.1. Introduction........................................................................................................111 6.2. Rehabilitation of Walras’s treatment of capital as physically heterogeneous goods and Walras’s inconsistency ......................................................................112 6.3. Walras’s way-out to the inconsistency................................................................116 6.4. Implications of the Walrasian specification of capital ........................................118 6.5. Hahn’s (1975a; 1982) and Bliss’s (1975) views on the question of capital: A first critical excursus ..........................................................................................119 II Contents 6.6. Uniform profit rates and intertemporal prices. Hahn’s ‘special case’ .................124 6.6.1. Introduction ..............................................................................................124 6.6.2. Commodity own rates of interest..............................................................124 6.6.3. Uniform rates of return on supply prices in intertemporal equilibria ........125 6.6.4. Further discussion of Hahn (1975a)..........................................................127 6.6.5. Conclusion: some obscurity in the debates ...............................................131 6.7. Do ‘reswitching’ and ‘reverse capital deepening’ bear theoretic problems on intertemporal general equilibrium? Two views: Bliss and Garegnani.................132 6.7.1. Bliss..........................................................................................................132 6.7.2. Garegnani .................................................................................................134 6.7.3. Confrontations..........................................................................................136 Chapter 7. Conclusions ...........................................................................................139 Appendixes A. The curve of the net marginal product of labour...................................................143 B. Discussion of the ‘supply-side’ of capital in Wicksell’s general equilibrium system ................................................................................................................147
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