IDEAS home Printed from https://ideas.repec.org/a/wsi/nmncxx/v08y2012i01ns1793005712400017.html
   My bibliography  Save this article

Taming The Incomputable, Reconstructing The Nonconstructive And Deciding The Undecidable In Mathematical Economics

Author

Listed:
  • K. VELA VELUPILLAI

    (Department of Economics, University of Trento, Via Inama, 5, 381 00 Trento, Italy;
    Girton College, Cambridge CB3 0JG, UK)

Abstract

The emergence of non-constructivities in economics is entirely due to the unnecessary and inappropriate formalization of economics by means of 'classical' mathematics. I have made similar claims for the emergence of uncomputabilities and undecidabilities in economics in earlier writings. Here, on the other hand, I want to suggest a way of confronting uncomputabilities, and remedying non-constructivities, in economics, and turning them into a positive force for modeling, for example, endogenous growth, as suggested by Stefano Zambelli.107,108In between, a case is made for economics to take seriously the kind ofmathematical methodologyfostered by Feynman and Dirac, in particular the way they developed thepath integraland theδ-function, respectively. A sketch of a "research program" in mathematical economics, analogous to the way Gödel thoughtincompletenessand its perplexities should be interpreted and resolved, is also outlined, albeit briefly, in the concluding section.

Suggested Citation

  • K. Vela Velupillai, 2012. "Taming The Incomputable, Reconstructing The Nonconstructive And Deciding The Undecidable In Mathematical Economics," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 5-51.
    • Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:01:n:s1793005712400017
    DOI: 10.1142/S1793005712400017
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S1793005712400017
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S1793005712400017?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. Mount,Kenneth R. & Reiter,Stanley, 2007. "Computation and Complexity in Economic Behavior and Organization," Cambridge Books, Cambridge University Press, number 9780521037891, January.
    2. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521319867, November.
    3. K. Vela Velupillai, 2008. "Sraffa's mathematical economics: a constructive interpretation," Journal of Economic Methodology, Taylor & Francis Journals, vol. 15(4), pages 325-342.
    4. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    5. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    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. Sundar Sarukkai, 2012. "Mathematics In Economics: Reducibility And/Or Applicability?," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 81-93.

    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, 2007. "Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics," Department of Economics Working Papers 0722, Department of Economics, University of Trento, Italia.
    2. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    3. K. Vela Velupillai, 2010. "The Algorithmic Revolution in the Social Sciences: Mathematical Economics, Game Theory and Statistical Inference," ASSRU Discussion Papers 1005, ASSRU - Algorithmic Social Science Research Unit.
    4. K. Vela Velupillai, 2010. "To the Beat of Different Drumer....Freedom, Anarchy and Conformism in Research," ASSRU Discussion Papers 1003, ASSRU - Algorithmic Social Science Research Unit.
    5. Giat, Yahel & Subramanian, Ajay, 2013. "Dynamic contracting under imperfect public information and asymmetric beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2833-2861.
    6. Haider A. Khan, 2007. "Social Accounting Matrix: A Very Short Introduction for Economic Modeling," CIRJE F-Series CIRJE-F-477, CIRJE, Faculty of Economics, University of Tokyo.
    7. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    8. Feigenbaum, James, 2008. "Can mortality risk explain the consumption hump?," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 844-872, September.
    9. Grochulski, Borys & Zhang, Yuzhe, 2011. "Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2356-2388.
    10. Espino, Emilio & González Rozada, Martín, 2013. "Normative Fiscal Policy and Growth: Some Quantitative Implications for the Chilean Economy," IDB Publications (Working Papers) 4648, Inter-American Development Bank.
    11. Marvin Goodfriend, 2004. "Monetary policy in the new neoclassical synthesis : a primer," Economic Quarterly, Federal Reserve Bank of Richmond, vol. 90(Sum), pages 21-45.
    12. Bjarne S. Jensen, 2004. "Pareto Efficiency, Relative Prices, and Solutions to CGE Models," DEGIT Conference Papers c009_006, DEGIT, Dynamics, Economic Growth, and International Trade.
    13. Shouqiang Wang & Peng Sun & Francis de Véricourt, 2016. "Inducing Environmental Disclosures: A Dynamic Mechanism Design Approach," Operations Research, INFORMS, vol. 64(2), pages 371-389, April.
    14. Miao, Jianjun & Zhang, Yuzhe, 2015. "A duality approach to continuous-time contracting problems with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 929-988.
    15. Karim, Mohamed, 2013. "Taxation of agricultural sector in Morocco. An Analysis using a Dynamic Computable General Equilibrium Model," MPRA Paper 45622, University Library of Munich, Germany.
    16. Govinda R. Timilsina & Ram M. Shrestha, 2002. "General equilibrium analysis of economic and environmental effects of carbon tax in a developing country: case of Thailand," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 5(3), pages 179-211, September.
    17. Govinda R. Timilsina & Ram M. Shrestha, 2003. "General equilibrium analysis of economic and environmental effects of carbon tax in a developing country: case of Thailand," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 5(3), pages 179-211, April.
    18. Yashiv, Eran, 2007. "Labor search and matching in macroeconomics," European Economic Review, Elsevier, vol. 51(8), pages 1859-1895, November.
    19. Konstantinos Angelopoulos & Jim Malley & Apostolis Philippopoulos, 2011. "Time-consistent Fiscal Policy under Heterogeneity: Conflicting or Common Interests?," CESifo Working Paper Series 3444, CESifo.
    20. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2005. "Incomplete-market dynamics in a neoclassical production economy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 407-438, August.

    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:wsi:nmncxx:v:08:y:2012:i:01:n:s1793005712400017. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/nmnc/nmnc.shtml .

    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.