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Foley's Thesis, Negishi's Method, Existence Proofs and Computation

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  • K. Vela Velupillai
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    Abstract

    Duncan Foleyís many-faceted and outstanding contributions to macroeconomics, microeconomics, general equilibrium theory, the theory of taxation, history of economic thought, the magnificent dynamics of classical economics, classical value theory, Bayesian statistics, formal dynamics and, most recently, fascinating forays into an interpretation of economic evolution from a variety of complexity theoretic viewpoints have all left -and continue to leave - significant marks in the development and structure of economic theory. He belongs to the grand tradition of visionaries who theorise with imaginative audacity on the dynamics, evolution and contradictions of capitalist economies - a tradition that, perhaps, begins with Marx and Mill, continues with Keynes and Schumpeter, reaching new heights with the iconoclastic brilliancies of a Tsuru and a Goodwin, a Chakravarty and a Nelson, and to which Duncan Foley adds a lustre of much value. In this contribution I return to mathematical themes broached in Foleyís brilliant and pioneering Yale doctoral dissertation (Foley, 1967) and attempt to view them as a Computable Economist would.The intention is to suggest that algorithmic indeterminacies are intrinsic to the foundations of economic theory in the mathematical mode

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    Paper provided by ASSRU - Algorithmic Social Science Research Unit in its series ASSRU Discussion Papers with number 1124.

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    Date of creation: 2011
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    Handle: RePEc:trn:utwpas:1124

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    Keywords: Equilibrium existence theorems; Welfare theorems; Constructive proofs; Computability;

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    1. K. Vela Velupillai, 2011. "Towards An Algorithmic Revolution In Economic Theory," Journal of Economic Surveys, Wiley Blackwell, vol. 25(3), pages 401-430, 07.
    2. Itzhak Gilboa, 2010. "Rational Choice," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262014009, December.
    3. K. Vela Velupillai, 2005. "The Foundations of Computable General EquilibriumTheory," Working Papers 0093, National University of Ireland Galway, Department of Economics, revised 2005.
    4. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521266550, October.
    5. K. Vela Velupillai, 2008. "Uncomputability and Undecidability in Economic Theory," Department of Economics Working Papers 0806, Department of Economics, University of Trento, Italia.
    6. Takashi Negishi, 2008. "Unnoticed predecessors of the early Negishi theorems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(2), pages 167-173.
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