ABSTRACT
In the Preface of Production of Commodities by Means of Commodities Sraffa thanks three mathematicians: “My greatest debt is toA. S. Besicovitch for invaluable mathematical help over many years. I am also indepted for similar help at different periods to the late Mr Frank Ramsey and to Mr Alister Watson” (Sraffa 1960: vi-vii). In the various drafts of the Preface Sraffa composed, he consistently singled out Besicovitch as the mathematician to whom he owed the greatest intellectual debt. This is not surprising since Besicovitch can be said to have taken a crucial part in the development of Sraffa’s thought in the second and third phase of his work on the 1960 book. As is well known, Sraffa’s work fell broadly in three periods: the first comprised the years from 1927 to 1931, the second the years from 1940-41 to 1948, and the third from 1954 to 1958. In the first period he was helped on a few occasions by Ramsey, whereas Besicovitch andWatson appeared on the stage only in the second period and continued to be of help to him in the third period. In an earlier contribution we dealt with the collaboration between Ramsey and Watson and Sraffa (Kurz-Salvadori 2001). At the time we set aside Besicovitch for the following reason: “Sraffa consulted Besicovitch on virtually all problems of amathematical nature he was confronted with. There are numerous documents in his unpublished papers reflecting their close collaboration. A proper treatment of it is beyond the scope of this chapter: the material is too huge and complex and ought to be dealt with separately . . .This is a serious limitation of the chapter, which we hope to be able to make good in another work” (ibid.: 255). In this contribution we attempt to accomplish at least partly the task. We select
two fields with regard to which Sraffa sought and received Besicovitch’s mathematical assistance: the analysis of fixed capital and the distinction between basic and non-basic commodities in the case of joint production. It can be said that with regard to both fields and some other fields we cannot deal with here Besicovitch provided invaluable help to Sraffa. Indeed, it is hardly an exaggeration to maintain that without Besicovitch’s assistance and support Sraffa’s treatise might never
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have been completed and published. In addition to dealing in some detail with the two issues specified we give various hints as to the rest of the material that witnesses to the close collaboration between the two Cantabrigians. The interested reader is invited to consult also our earlier paper on Sraffa and the mathematicians (Kurz-Salvadori 2001) which contains some useful information on the general themes which will not be repeated here. The composition of the paper is the following. Section 2 contains a portrait of
AbramS. Besicovitch. Section 3 provides a summary account of Sraffa’smeetings, discussions and exchange of letters with Besicovitch, our main sources being Sraffa’s diaries and his unpublished papers; unfortunately, we could not trace any remaining papers of Besicovitch: they appear to have been destroyed. The main part of the paper consists of Sections 4 and 5. Section 4 deals with the problem of fixed capital. After several unsuccessful attempts to cope with durable instruments of production from a purely ‘objectivist’ point of view, Sraffa, around the turn of the year 1942-43, eventually adopted the joint-products approach and, assisted by Besicovitch, quickly solved the problem at hand. Section 5 points out that the completion of Sraffa’s book was considerably delayed by his discovery in the second half of the 1950s that the distinction between basic and non-basic products needed to be fundamentally revised in joint production. It was Besicovitch who, around the turn of 1957, helped Sraffa out of the impasse. Section 6 contains some concluding remarks.
