Non-computability of competitive equilibrium
AbstractWe provide a "computable counterexample" to the Arrow-Debreu competitive equilibrium existence theorem . 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 , Richter and Wong ) and computational economics (cf. Scarf ). To prove the theorem, we establish a "computable counterexample" to Brouwer's Fixed Point Theorem (similar to Orevkov ) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell , Geanakoplos , Wong ).
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Bibliographic InfoArticle provided by Springer in its journal Economic Theory.
Volume (Year): 14 (1999)
Issue (Month): 1 ()
Note: Received: September 9, 1997; revised version: December 17, 1997
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Find related papers by JEL classification:
- D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
- C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
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PIER Working Paper Archive
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