Economic Theory

, Volume 14, Issue 1, pp 1–27

Non-computability of competitive equilibrium

  • Marcel K. Richter
  • Kam-Chau Wong
Research Articles

DOI: 10.1007/s001990050281

Cite this article as:
Richter, M. & Wong, KC. Economic Theory (1999) 14: 1. doi:10.1007/s001990050281

Summary.

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]).

Key words and Phrases: Bounded rationality, Computability, General equilibrium, Recursive analysis.
JEL Classification Numbers: D51, C68.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Marcel K. Richter
    • 1
  • Kam-Chau Wong
    • 2
  1. 1.Department of Economics, University of Minnesota, Minneapolis, MN 55455, USA US
  2. 2.Department of Economics, Chinese University of Hong Kong, Shatin, HONG KONG HK