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Minimal entropy and uniqueness of price equilibria in a pure exchange economy

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  • Loi, Andrea
  • Matta, Stefano

Abstract

We introduce uncertainty into a pure exchange economy and establish a connection between Shannon’s differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability distribution: entropy is minimal if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and, under certain conditions, for an arbitrary number of consumers and two goods.

Suggested Citation

  • Loi, Andrea & Matta, Stefano, 2021. "Minimal entropy and uniqueness of price equilibria in a pure exchange economy," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    • Handle: RePEc:eee:mateco:v:97:y:2021:i:c:s030440682100118x
    DOI: 10.1016/j.jmateco.2021.102555
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    References listed on IDEAS

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    1. Andrea Loi & Stefano Matta, 2012. "Measures of economies with an arbitrarily large number of equilibria," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(4), pages 337-343, December.
    2. Aaberge, Rolf & Mogstad, Magne & Peragine, Vito, 2011. "Measuring long-term inequality of opportunity," Journal of Public Economics, Elsevier, vol. 95(3), pages 193-204.
    3. DeMichelis, Stefano & Germano, Fabrizio, 2000. "Some consequences of the unknottedness of the Walras correspondence," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 537-545, December.
    4. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047.
    5. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
    6. Loi, Andrea & Matta, Stefano, 2008. "Geodesics on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1379-1384, December.
    7. Safra, Zvi, 1983. "Manipulation by reallocating initial endowments," Journal of Mathematical Economics, Elsevier, vol. 12(1), pages 1-17, September.
    8. Aditya Goenka & Stefano Matta, 2008. "Manipulation of endowments and sunspot equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 267-282, August.
    9. Loi, Andrea & Matta, Stefano, 2018. "Curvature and uniqueness of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 62-67.
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    Cited by:

    1. Loi, Andrea & Matta, Stefano & Uccheddu, Daria, 2023. "Equilibrium selection under changes in endowments: A geometric approach," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    2. Andrea Loi & Stefano Matta & Daria Uccheddu, 2023. "Uniqueness of equilibrium and redistributive policies: a geometric approach to efficiency," Papers 2308.03706, arXiv.org.
    3. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    4. Andrea Loi & Stefano Matta & Daria Uccheddu, 2022. "Equilibrium selection: a geometric approach," Papers 2208.10860, arXiv.org.
    5. Andrea Loi & Stefano Matta, 2021. "Risk aversion and uniqueness of equilibrium: a polynomial approach," Papers 2107.01947, arXiv.org, revised Oct 2021.

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