Non-computability of competitive equilibrium

Kam-Chau Wong and Marcel Richter
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Kam-Chau Wong: Department of Economics, Chinese University of Hong Kong, Shatin, HONG KONG

Economic Theory, 1999, vol. 14, issue 1, 27 pages

Abstract: 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]).

Keywords: Bounded rationality; Computability; General equilibrium; Recursive analysis. (search for similar items in EconPapers)
JEL-codes: C68 D51 (search for similar items in EconPapers)
Date: 1999-07-08
Note: Received: September 9, 1997; revised version: December 17, 1997
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Citations: View citations in EconPapers (27)

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