Non-computability of competitive equilibrium

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]). Received: September 9, 1997; revised version: December 17, 1997