IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v54y2014icp36-39.html
   My bibliography  Save this article

Constructive and computable Hahn–Banach theorems for the (second) fundamental theorem of welfare economics

Author

Listed:
  • Vela Velupillai, K.

Abstract

The Hahn–Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using non-constructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn–Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented economics intrinsically computational.

Suggested Citation

  • Vela Velupillai, K., 2014. "Constructive and computable Hahn–Banach theorems for the (second) fundamental theorem of welfare economics," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 36-39.
    • Handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:36-39
    DOI: 10.1016/j.jmateco.2014.08.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406814001062
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2014.08.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Debreu, Gerard, 1984. "Economic Theory in the Mathematical Mode," American Economic Review, American Economic Association, vol. 74(3), pages 267-278, June.
    2. Starr,Ross M., 2011. "General Equilibrium Theory," Cambridge Books, Cambridge University Press, number 9780521533867.
    3. Debreu, Gerard, 1984. "Economic Theory in the Mathematical Mode," American Economic Review, American Economic Association, vol. 74(3), pages 267-278, June.
    4. Starr,Ross M., 2011. "General Equilibrium Theory," Cambridge Books, Cambridge University Press, number 9780521826457.
    5. Mark Blaug, 2007. "The Fundamental Theorems of Modern Welfare Economics, Historically Contemplated," History of Political Economy, Duke University Press, vol. 39(2), pages 185-207, Summer.
    6. Kumaraswamy Vela Velupillai, 2013. "Turing's Economics. A Birth Centennial Homage," Economia politica, Società editrice il Mulino, issue 1, pages 13-32.
    Full references (including those not matched with items on IDEAS)

    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. K.Vela Velupillai, 2014. "Constructive and Computable Hahn-Banach Theorems for the (Second) Fundamental Theorem of Welfare Economics," ASSRU Discussion Papers 1403, ASSRU - Algorithmic Social Science Research Unit.
    2. Kilenthong, Weerachart T. & Qin, Cheng-Zhong, 2014. "Trade through endogenous intermediaries," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 262-268.
    3. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, December.
    4. Annie-Lou Cot & Jérôme Lallement, 2006. "1859-1959 : de Walras à Debreu, un siècle d'équilibre général," Revue économique, Presses de Sciences-Po, vol. 57(3), pages 377-388.
    5. Fernando Cardoso Cotelo & Bruno Martins Hermann & Sergio Goldbaum, 2016. "A Controvérsia Neg X Peg: Uma Disputa Metodológica No Campo Da Geografia Econômica," Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting] 009, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    6. Olkhov, Victor, 2018. "Economic Transactions Govern Business Cycles," MPRA Paper 87207, University Library of Munich, Germany.
    7. Victor Olkhov, 2018. "How Macro Transactions Describe the Evolution and Fluctuation of Financial Variables," IJFS, MDPI, vol. 6(2), pages 1-19, March.
    8. Olkhov, Victor, 2019. "Methods of Economic Theory: Variables, Transactions and Expectations as Functions of Risks," MPRA Paper 95628, University Library of Munich, Germany.
    9. Trockel, Walter & Haake, Claus-Jochen, 2017. "Thoughts on social design," Center for Mathematical Economics Working Papers 577, Center for Mathematical Economics, Bielefeld University.
    10. Kanjamapornkul, K. & Pinčák, Richard & Bartoš, Erik, 2016. "The study of Thai stock market across the 2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 117-133.
    11. Nieto-Barthaburu, Augusto, 2021. "Competitive General Equilibrium with network externalities," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    12. Victor Olkhov, 2018. "Econophysics Beyond General Equilibrium: the Business Cycle Model," Papers 1804.04721, arXiv.org.
    13. K. Vela Velupillai, 2016. "Seven Kinds of Computable and Constructive Infelicities in Economics," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 219-239, November.
    14. Schmidt, Lawrence D.W., 2012. "On the dimensionality of bounds generated by the Shapley–Folkman theorem," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 59-63.
    15. Michael S. Harr'e & Adam Harris & Scott McCallum, 2019. "Singularities and Catastrophes in Economics: Historical Perspectives and Future Directions," Papers 1907.05582, arXiv.org.
    16. Paula C. Pereda & Andrea Lucchesi, 2022. "Alternative frameworks for cost-effectiveness analysis of environmental policies in maritime transport," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 24(3), pages 630-650, September.
    17. Victor Olkhov, 2017. "Econophysics Macroeconomic Model," Papers 1701.06625, arXiv.org.
    18. Starr, Ross & Spini, Pietro Emilio, 2022. "Thick Market Externality and Concentration of `Money'," University of California at San Diego, Economics Working Paper Series qt8qr0r0n7, Department of Economics, UC San Diego.
    19. Alain Béraud, 2014. "Le développement de la théorie de l'équilibre général. Les apports d'Allais et de Hicks," Revue économique, Presses de Sciences-Po, vol. 65(1), pages 125-158.
    20. K. Velupillai, 2015. "Negishi’s Theorem and Method: Computable and Constructive Considerations," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 183-193, February.

    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:eee:mateco:v:54:y:2014:i:c:p:36-39. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.