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Sraffa: some alternative proofs

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  • Saccal, Alessandro

Abstract

Relative to the germane academic literature in this work I offer alternative and more direct proofs for (i) the existence and unicity of Sraffa’s ‘Standard System’, (ii) the (existence and) unicity of R=r_i (for w=0) across the ‘Real System’ and the ‘Standard System’ and (iii) the existence (and unicity) of Sraffa’s Fundamental Equation r=R(1−w) across both kinds of system. While the proof for (iii) be outrightly unprecedented and that for (ii) certainly shorter, the proof for (i) is not necessarily superior to those of the germane academic literature, which judgement is left open for debate.

Suggested Citation

  • Saccal, Alessandro, 2024. "Sraffa: some alternative proofs," MPRA Paper 120418, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:120418
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    File URL: https://mpra.ub.uni-muenchen.de/120418/1/MPRA_paper_120418.pdf
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    References listed on IDEAS

    as
    1. Marco Lippi, 2008. "Some Observations on Sraffa and Mathematical Proofs With an Appendix on Sraffa’s Convergence Algorithm," Palgrave Macmillan Books, in: Guglielmo Chiodi & Leonardo Ditta (ed.), Sraffa or An Alternative Economics, chapter 12, pages 243-259, Palgrave Macmillan.
    2. Michel‐Stéphane Dupertuis & Ajit Sinha, 2009. "Existence Of The Standard System In The Multiple‐Production Case: A Solution To The Manara Problem," Metroeconomica, Wiley Blackwell, vol. 60(3), pages 432-454, July.
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    More about this item

    Keywords

    Abel Ruffini Theorem; mathematical induction; multiple and single production; Perron Frobenius Theorem; Real and Standard System; Schur decomposition; Sraffa’s Fundamental Equation.;
    All these keywords.

    JEL classification:

    • B24 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Socialist; Marxist; Scraffian

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