Saccal, Alessandro (2024): Sraffa: some alternative proofs.
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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.
Item Type: | MPRA Paper |
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Original Title: | Sraffa: some alternative proofs |
English Title: | Sraffa: some alternative proofs |
Language: | English |
Keywords: | Abel Ruffini Theorem; mathematical induction; multiple and single production; Perron Frobenius Theorem; Real and Standard System; Schur decomposition; Sraffa’s Fundamental Equation. |
Subjects: | B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B24 - Socialist ; Marxist ; Sraffian |
Item ID: | 120418 |
Depositing User: | Dr. Alessandro Saccal |
Date Deposited: | 13 Apr 2024 18:03 |
Last Modified: | 13 Apr 2024 18:03 |
References: | [1] Bapat R. B., Olesky D.D. and Van Den Driessche P. (1995) “Perron-Frobenius Theory for a Generalized Eigenproblem”, Linear and Multilinear Algebra 40, 2:141-152. [2] Dupertuis M.-S. and Sinha A. (2009) “Existence of the Standard System in the Multiple-Production Case: a Solution to the Manara Problem”, Metroeconomica 60, 3:432-454. [3] Lippi M. (2008) “Some Observations on Sraffa and Mathematical Proofs with an Appendix on Sraffa’s Convergence Algorithm”, in Chiodi G. and Ditta L. (2008) “Sraffa or an Alternative Economics”, Palgrave Macmillan. [4] Manara C. F. (1968) “Il Modello di Piero Sraffa per la Produzione Congiunta di Merci a Mezzo di Merci”, L’Industria 1, 1:3-18. [5] Mangasarian O. L. (1971) “Perron-Frobenius Properties of Ax − λBx”, Journal of Mathematical Analysis and Applications 36, 1:86-102. [6] Miyamoto J. (2008) “Correction of Sraffa’s Imaginary Experiment”, Kwansei Gakuin University Repository. [7] Saccal A. (2023) “An Alternative Derivation of Sraffa’s Fundamental Equation with Applications”, Paper. [8] Saccal A. (2023) “From Sraffa’s Fundamental Equation to the Sraffian Cycloid: a Note”, Paper. [9] Saccal A. (2023) “An Explanation of Distributional Gravity for the Sraffian Brachistochrone”, Paper. [10] Salvadori N. (2008) “Commentary by Neri Salvadori: on a Proof of Sraffa’s”, in Chiodi G. and Ditta L. (2008) “Sraffa or an Alternative Economics”, Palgrave Macmillan. [11] Schefold B. (1989) “Mr. Sraffa on Joint Production and Other Essays”, Unwin Hyman. [12] Schefold B. (2021) “Why Sraffa was Right not to Publish his Last Article: a Rectification of Yoann Verger”, in Sinha A. (2021) “A Reflection on Sraffa’s Revolution in Economic Theory”, Palgrave Macmillan. [13] Sinha A. (2022) “A Response to Pignalosa and Trabucchi and Perri and Oro”, History of Economic Ideas 30, 3:107-131. [14] Sinha A. and Verger Y. (2021) “A Response to Schefold’s ‘Why Sraffa was Right not to Publish his Last Article”’, in Sinha A. (2021) “A Reflection on Sraffa’s Revolution in Economic Theory”, Palgrave Macmillan. [15] Sraffa P. (1960) “Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory”, Cambridge University Press. [16] Verger Y. (2021) “Sraffa and Manara: The Mystery of the Last Article of Piero Sraffa”, in Sinha A. (2021) “A Reflection on Sraffa’s Revolution in Economic Theory”, Palgrave Macmillan. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/120418 |