IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2102.09827.html
   My bibliography  Save this paper

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

Author

Listed:
  • Andrea Loi
  • Stefano Matta

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

  • Andrea Loi & Stefano Matta, 2021. "Minimal entropy and uniqueness of price equilibria in a pure exchange economy," Papers 2102.09827, arXiv.org.
    • Handle: RePEc:arx:papers:2102.09827
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2102.09827
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Safra, Zvi, 1983. "Manipulation by reallocating initial endowments," Journal of Mathematical Economics, Elsevier, vol. 12(1), pages 1-17, September.
    2. 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.
    3. 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.
    4. 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.
    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. Loi, Andrea & Matta, Stefano, 2018. "Curvature and uniqueness of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 62-67.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrea Loi & Stefano Matta & Daria Uccheddu, 2023. "Uniqueness of equilibrium and redistributive policies: a geometric approach to efficiency," Papers 2308.03706, arXiv.org.
    2. Andrea Loi & Stefano Matta, 2021. "Risk aversion and uniqueness of equilibrium: a polynomial approach," Papers 2107.01947, arXiv.org, revised Oct 2021.
    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. Loi, Andrea & Matta, Stefano & Uccheddu, Daria, 2023. "Equilibrium selection under changes in endowments: A geometric approach," Journal of Mathematical Economics, Elsevier, vol. 108(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Andrea Loi & Stefano Matta & Daria Uccheddu, 2022. "Equilibrium selection: a geometric approach," Papers 2208.10860, arXiv.org.
    3. Andrea Loi & Stefano Matta & Daria Uccheddu, 2023. "Uniqueness of equilibrium and redistributive policies: a geometric approach to efficiency," Papers 2308.03706, arXiv.org.
    4. Loi, Andrea & Matta, Stefano & Uccheddu, Daria, 2023. "Equilibrium selection under changes in endowments: A geometric approach," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    5. Loi, Andrea & Matta, Stefano, 2019. "Minimality and uniqueness of equilibrium," MPRA Paper 98055, University Library of Munich, Germany.
    6. Alonso-Villar, Olga & del Río, Coral, 2010. "Local versus overall segregation measures," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 30-38, July.
    7. Cowell, Frank & Flachaire, Emmanuel & Bandyopadhyay, Sanghamitra, 2009. "Goodness-of-fit: an economic approach," LSE Research Online Documents on Economics 25433, London School of Economics and Political Science, LSE Library.
    8. Golan, Amos & Perloff, Jeffrey M. & Wu, Ximing, 2001. "Welfare Effects of Minimum Wage and Other Government Policies," Institute for Research on Labor and Employment, Working Paper Series qt36r7v1cr, Institute of Industrial Relations, UC Berkeley.
    9. Frank A Cowell & Maria-Pia Victoria-Feser, 1993. "Robustness Properties of Inequality Measures: The Influence Function and the Principle of Transfers (Revised version in Economica, 64 (1996), pp.77-101)," STICERD - Distributional Analysis Research Programme Papers 01, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Ji-Won Park & Chae Un Kim, 2021. "Getting to a feasible income equality," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-16, March.
    11. Stéphane Mussard & Pi Alperin María Noel & Françoise Seyte & Michel Terraza, 2005. "Extensions Of Dagum’S Gini Decomposition," Cahiers de recherche 05-07, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    12. Ram Sewak Dubey & Minwook Kang, 2019. "Transfer paradox in a stable equilibrium," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 259-269, December.
    13. Vargas, Carmen, 1996. "A social welfare model for the evaluation of the spanish income tax system," UC3M Working papers. Economics 4100, Universidad Carlos III de Madrid. Departamento de Economía.
    14. Frank Cowell & Emmanuel Flachaire, 2021. "Inequality Measurement: Methods and Data," Post-Print hal-03589066, HAL.
    15. Frank A Cowell & Christian Schluter, 1998. "Income Mobility: A Robust Approach (published in Income Inequality Measurement: From Theory to Practice, J Silber (ed, Dewenter: Kluver , 1999)," STICERD - Distributional Analysis Research Programme Papers 37, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    16. S. T. Buckland & Y. Yuan & E. Marcon, 2017. "Measuring temporal trends in biodiversity," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 461-474, October.
    17. Bich, Philippe & Fixary, Julien, 2022. "Network formation and pairwise stability: A new oddness theorem," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    18. Erik Figueiredo, 2011. "A Note on the Measurement of Unfair Inequality in Brazil," Economics Bulletin, AccessEcon, vol. 31(4), pages 2944-2951.
    19. Somdeb Lahiri, 2005. "Manipulation via Endowments in a Market with Profit Maximizing Agents," Game Theory and Information 0511008, University Library of Munich, Germany.
    20. Stéphane Mussard, 2007. "Between-Group Pigou Dalton Transfers," Cahiers de recherche 07-06, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2102.09827. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.