Besicovitch, Sraffa, and the existence of the Standard commodity

Salvadori, Neri (2010): Besicovitch, Sraffa, and the existence of the Standard commodity.

Abstract

The proof of the existence of the Standard commodity contained in Sraffa's book (section 37) has been debated recently. Lippi (2008) has argued that the algorithm in section 37 of Sraffa’s book is not precisely stated and does not need to converge to the desired eigenvalue and eigenvector. In this paper I will show that also the proof provided by Besicovitch to Sraffa on 21 September 1944 is incomplete, but it can easily be completed.

• Item Type: MPRA Paper
• Language: English
• Keywords: Sraffa; Besecovitch; Standard Commodity; Perron-Frobenius Theorem
• Subjects: B - History of Economic Thought, Methodology, and Heterodox Approaches > B3 - History of Economic Thought: Individuals > B31 - Individuals; B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B23 - Econometrics ; Quantitative and Mathematical Studies; B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B29 - Other

References

Kurz, H. D. and Salvadori, N. (1993) The 'Standard Commodity' and Ricardo's Search for an 'invariable measure of value', in M. Baranzini e G. C. Harcourt (eds), The Dynamics of the Wealth of Nations. Growth, Distribution and Structural Change, London: Macmillan. Kurz, H. D. and Salvadori, N. (1995) Theory of Production, Cambridge: Cambridge UP. Kurz, H. D. and Salvadori, N. (2001) Sraffa and the Mathematicians: Frank Ramsey and Alister Watson, in T. Cozzi and R. Marchionatti (eds), Piero Sraffa's Political Economy. A Centenary Estimate, London and New York: Routledge, 254-84. Lippi, M. (2008) Some observations on Sraffa and mathematical proofs, in G. Chiodi and L. Ditta (eds) Sraffa or an Alternative Economics, Houndmills: Palgrave Macmillan, pp. 243-52. Salvadori, N. (2008) On a proof of Sraffa's, in G. Chiodi and L. Ditta (eds) Sraffa or an Alternative Economics, Houndmills: Palgrave Macmillan, pp. 253-9. Sraffa, P. (1960) Production of Commodities by Means of Commodities, Cambridge: Cambridge UP.