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...

We prove that the Strong Axiom of Revealed Preference tests the existence of a strictly quasiconcave (in fact, continuous, generically C(infinity), strictly concave, and strictly monotone) utility function generating finitely many demand observations. This sharpens earlier results of Afriat,...

We present a theoretical view of computation, delineating what types of approximations are possible and what types are impossible. A practical consequence is an approximation algorithm with numerous applications. For several classical problems (finding maximizers, fixed points, equilibrium...