On the Collaboration between Sraffa and Besicovitch: The ‘Proof of Gradient’

Abstract

As is well known, Chapters III-VI of Production of Commodities by Means of Commodities explore the results arrived at as regards the model defined in the second part of Chapter II. Whereas the main aim of Chapter III is to provide a ‘preliminary survey’ (p. 15) of price movements consequent upon changes in distribution without the help of any specific tool, the complete analysis of these movements is presented in Chapter VI, where Sraffa has recourse to the tool elaborated in Chapters IV and V, the Standard Commodity. In analyzing price movements, Sraffa maintains in section 49, i.e. the very last section of Chapter VI, that ‘there is … a restriction to the movement of the price of any product: if as a result of a rise in the rate of profits the price falls, its rate of fall cannot exceed the rate of fall of the wage/This property is important because if the wage as a function of the rate of profits is decreasing in any numeraire, then it is decreasing in all numeraires. And since the Standard Commodity is a numeraire in which the wage as a function of the rate of profits is a decreasing straight line, then ‘if the the wage is cut in terms of any commodity (no matter whether it is one that will consequently rise or fall relatively to the Standard) the rate of profits will rise; and vice versa for an increase of the wage/(Sraffa, 1960, pp. 38 and 40; Sraffa’s italics)

We should like to thank Pierangelo Garegnani, literary executor of Sraffa’s papers and correspondence, for granting us permission to quote from them. Citations beginning with the letter D followed by a series of numbers refer to Sraffa’s papers at Trinity College Library, Cambridge; the format of the citations follows the catalogue prepared by Jonathan Smith, archivist. Unless otherwise stated, all emphases are in the original; we shall use italics when Sraffa used underlinings. He frequently abbreviated and by +; we shall use the word instead of the symbol. With one obvious exception, all additions in wavy brackets, , in quotations are ours. We are grateful to Jonathan Smith and the staff of Trinity College Library for continuous assistance while working on the Sraffa papers. The views contained in this article have not been discussed with all the participants in the project of preparing an edition of Sraffa’s papers and correspondence and therefore do not implicate them.