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
    ---><---

    Other versions of this item:

    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. Aaberge, Rolf & Mogstad, Magne & Peragine, Vito, 2011. "Measuring long-term inequality of opportunity," Journal of Public Economics, Elsevier, vol. 95(3), pages 193-204.
    5. 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.
    6. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047.
    7. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
    8. Loi, Andrea & Matta, Stefano, 2008. "Geodesics on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1379-1384, December.
    9. 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. 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.

    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. Shweta Bahl & Ajay Sharma, 2021. "Education–Occupation Mismatch and Dispersion in Returns to Education: Evidence from India," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(1), pages 251-298, January.
    2. Andrea Loi & Stefano Matta & Daria Uccheddu, 2022. "Equilibrium selection: a geometric approach," Papers 2208.10860, arXiv.org.
    3. Alvaredo, Facundo & Cogneau, Denis & Piketty, Thomas, 2021. "Income inequality under colonial rule. Evidence from French Algeria, Cameroon, Tunisia, and Vietnam and comparisons with British colonies 1920–1960," Journal of Development Economics, Elsevier, vol. 152(C).
    4. Yonatan Berman, 2022. "The Long-Run Evolution of Absolute Intergenerational Mobility," American Economic Journal: Applied Economics, American Economic Association, vol. 14(3), pages 61-83, July.
    5. Tatjana Miljkovic & Ying-Ju Chen, 2021. "A new computational approach for estimation of the Gini index based on grouped data," Computational Statistics, Springer, vol. 36(3), pages 2289-2311, September.
    6. Bhuller, Manudeep & Mogstad, Magne & Salvanes, Kjell G., 2011. "Life-Cycle Bias and the Returns to Schooling in Current and Lifetime Earnings," IZA Discussion Papers 5788, Institute of Labor Economics (IZA).
    7. Kaltenberg, Mary & Foster-McGregor, Neil, 2020. "The impact of automation on inequality across Europe," MERIT Working Papers 2020-009, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    8. Andrea Loi & Stefano Matta & Daria Uccheddu, 2023. "Uniqueness of equilibrium and redistributive policies: a geometric approach to efficiency," Papers 2308.03706, arXiv.org.
    9. Miia Bask & Mikael Bask, 2015. "Cumulative (Dis)Advantage and the Matthew Effect in Life-Course Analysis," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-14, November.
    10. Ausloos, Marcel, 2020. "Rank–size law, financial inequality indices and gain concentrations by cyclist teams. The case of a multiple stage bicycle race, like Tour de France," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    11. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Economics Working Paper Archive (University of Rennes & University of Caen) 2019-09, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    12. Kotschy, Rainer, 2022. "Health improvements impact income inequality," The Journal of the Economics of Ageing, Elsevier, vol. 22(C).
    13. Loi, Andrea & Matta, Stefano & Uccheddu, Daria, 2023. "Equilibrium selection under changes in endowments: A geometric approach," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    14. Bach, Stefan & Thiemann, Andreas & Zucco, Aline, 2019. "Looking for the missing rich: tracing the top tail of the wealth distribution," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 26(6), pages 1234-1258.
    15. Eliazar, Iddo, 2021. "Five degrees of randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    16. Mariko I Ito & Hisashi Ohtsuki & Akira Sasaki, 2018. "Emergence of opinion leaders in reference networks," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-21, March.
    17. Michael Albertus & Thomas Brambor & Ricardo Ceneviva, 2018. "Land Inequality and Rural Unrest," Journal of Conflict Resolution, Peace Science Society (International), vol. 62(3), pages 557-596, March.
    18. Pablo A. Mitnik & Anne-Line Helsø & Victoria L. Bryant, 2020. "Inequality of Opportunity for Income in Denmark and the United States: A Comparison Based on Administrative Data," NBER Chapters, in: Measuring Distribution and Mobility of Income and Wealth, pages 317-382, National Bureau of Economic Research, Inc.
    19. Rolando I. Valdez & Francisco García-Fernández, 2022. "The distribution of wage inequality across municipalities in Mexico: a spatial quantile regression approach," Equilibrium. Quarterly Journal of Economics and Economic Policy, Institute of Economic Research, vol. 17(3), pages 669-697, September.
    20. Hodler, Roland & Srisuma, Sorawoot & Vesperoni, Alberto & Zurlinden, Noémie, 2020. "Measuring ethnic stratification and its effect on trust in Africa," Journal of Development Economics, Elsevier, vol. 146(C).

    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.