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An alternative derivation of Sraffa’s fundamental equation with applications

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  • Saccal, Alessandro

Abstract

I derive Sraffa’s fundamental equation r = R(1 − w) by means of differential equations and optimisation, on which I work three remarks: (i) I analytically provide an alternative formulation of Sraffa’s fundamental equation; (ii) it is analogous to the optimisation problem of a particle moving along a straight line; (iii) the optimisation problem’s objective function is that of the minimisation of R. I additionally ask whether such an optimisation problem may also apply to any corresponding ‘Real System’ of the ‘Standard System’, to which it is already found to apply, and I answer positively. I ulteriorly assess the application of Heisenberg’s Uncertainty Principle to the same equation and derive an equation for the momentum of the particle in terms of its momentum uncertainty and in terms of its position, in which the particle is the ‘Standard Net Product’ and its momentum is R. I finally appraise the brachistochrone problem from a Sraffian perspective and find that in the presence of distributional gravity, for a meaningful mass function for the ‘Standard Net Product’, the optimal path for the distribution of the ‘Standard Net Product’ between profits and wages is no longer r = R(1 − w), but a Sraffian cycloid with specific position coordinates w and r.

Suggested Citation

  • Saccal, Alessandro, 2024. "An alternative derivation of Sraffa’s fundamental equation with applications," MPRA Paper 120282, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:120282
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    References listed on IDEAS

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    1. Michel-Stéphane Dupertuis & Ajit Sinha, 2009. "A Sraffian critique of the classical notion of centre of gravitation," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 33(6), pages 1065-1087, November.
    2. Ajit Sinha, 2016. "A Revolution in Economic Theory," Springer Books, Springer, number 978-3-319-30616-2, December.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    brachistochrone problem; cost function; cycloid; distribution; fundamental equation; Heisenberg Uncertainty Principle; income; output; path; profits; wages.;
    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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