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Non-computability of competitive equilibrium

  • Kam-Chau Wong

    (Department of Economics, Chinese University of Hong Kong, Shatin, HONG KONG)

  • Marcel K. Richter

    (Department of Economics, University of Minnesota, Minneapolis, MN 55455, USA)

We provide a "computable counterexample" to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a "computable counterexample" to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]).

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 14 (1999)
Issue (Month): 1 ()
Pages: 1-27

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Handle: RePEc:spr:joecth:v:14:y:1999:i:1:p:1-27
Note: Received: September 9, 1997; revised version: December 17, 1997
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