Special Issue: Constructive and Computable Analysis in Mathematical Finance — The Festschrift Issue for Prof Kumaraswamy (Vela) VelupillaiNo Access

A NOTE ON THE CONCEPT OF APPROXIMATE EQUILIBRIUM IN ECONOMIC THEORY

DUNCAN K. FOLEY

DUNCAN K. FOLEY

Department of Economics, New School for Social Research, 6 East 16th Street, New York, NY 10003, USA

Santa Fe Institute, USA

I am delighted to contribute to this special issue of New Mathematics and Natural Computation in honor of Kumaraswamy Velupillai, whose passionate critique of received economic doctrine has been an inspiration and source of instruction for me.

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https://doi.org/10.1142/S1793005712400054Cited by:0 (Source: Crossref)

Abstract

The problem of the computability of Walrasian competitive equilibrium is considered from the point of view of concepts of approximate equilibrium. Neither the market-clearing nor Negishi approaches to the proof of existence of Walrasian competitive equilibrium give rise to adequately robust notions of approximate equilibrium. This explains the non-computability of Walrasian competitive equilibrium. The problem lies in the economic conception of markets, in particular the inconsistent treatment of information underlying the Walrasian definition. When trade takes place at disequilibrium prices decentralized market exchange redistributes income and economic welfare, and its equilibrium is path-dependent. The set of such equilibrium outcomes, however, in contrast to the Walrasian competitive equilibrium, is constructive and computable.

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References

K. Marx , Grundrisse: Foundations of the Critique of Political Economy (Rough Draft), Introduction ( Penguin , Harmondsworth , 1973 ) . Google Scholar
D. K. Foley, Journal of Economic Behavior and Organization 75, 115 (2010), DOI: 10.1016/j.jebo.2010.03.023. Crossref, Web of Science, Google Scholar
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K. Vela Velupillai, Constructivity, computability and computers in economic theory: Some cautionary notes, in Metroeconomica Special Issue: Computability, Constructivity, and Complexity in Economic Theory, ed. K. Vela Velupillai, Metroeconomica 44 (2–3) (2004) 121–140 . Google Scholar

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A NOTE ON THE CONCEPT OF APPROXIMATE EQUILIBRIUM IN ECONOMIC THEORY

Abstract

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