I have received a few questions about what one can read on the topic. I suggest the recent book by Andrés Lazzarini, which is based on his PhD in Rome under Ciccone and Garegnani. From the preface:
This book is the result of my research on the post-war Cambridge capital theory controversies conducted at the Department of Economics, Roma Tre University, to obtain my Ph.D. in Economics (Dottorato di Ricerca in Economia Politica), which I eventually achieved in April 2008. Since then I have presented and discussed several works drawn from my original dissertation which immensely helped to improve the present version for publication at the Pavia University Press.
The so-called Cambridge controversy in the theory of capital took place between the beginning of the 1950s and the mid-1970s, though arguably it got its heyday after the publication of Sraffa’s 1960 book. That there existed a controversy between Cambridge (UK) and Cambridge, Massachusetts (US), could hardly be ignored by any practitioner of the discipline. Yet the recognition of its most relevant results is still lacking even though they touch upon the core of the basic economic principles underlying the core of mainstream neoclassical economics.
Certainly, after more than fifty years since the first exchanges in these debates many articles and books have been written about this theoretical conflict in the economic theory, and in fact the present book has dealt with most if not all of them in our reconstruction. But, unlike many of the reviews available, our reconstruction attempted to present an account which, first, does not follow a chronological survey of the contributions to the Cambridge controversy but rather focuses on the analytical arguments necessary to understand the implications of the phenomena of ‘reswitching’ and ‘reverse capital deepening’. In order to understand why these phenomena affect the very core of neoclassical economics, we have thoroughly examined the ultimate reason of their theoretical existence: the specification of capital in value terms among the data of the theory in order to determine equilibrium variables through supply and demand forces which ultimately rely on the factor substitution principle. These arguments, from a chronological viewpoint, were visibly recognised in the last contributions of a first phase of the debates. Secondly, we present and discuss some contributions of a later phase of the controversy in which the treatment of capital among the data of the theory had already been shifted to its Walrasian specification, but which have not been thoroughly dealt with by previous surveys and which deserve due attention to better understand the present state of the controversy between the neoclassical authors and the critical side.
Another issue examined in the present study, and which also deserves due attention for understanding the evolution of the controversy, is the different – and sometimes we may say radically different – positions not only between the two camps of the debate but also within the critical side of the controversy, in particular during its later phase. Despite the fact that the critically oriented (Cambridge, UK) side agreed that the main results of the controversy had put the foundations of neoclassical economics at serious risks – and hence the latter had to be replaced with an alternative economic theory – differences in the method among the critical side (and also the silence on the part of the marginalist authors in the second phase as to accepting the controversy’s results) helped to prevent that alternative from surfacing at that time.