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...

Many economics problems are maximization or minimization problems, and can be formalized as problems of solving “linear difference systems” of the form <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$r_i-r_j \geqq c_{ij}$</EquationSource> </InlineEquation> and r <Subscript> k </Subscript>-r <Subscript> l </Subscript> c <Subscript> kl </Subscript>, for r-unknowns, with given c-constants. They typically involve strict as well as weak...</subscript></subscript></subscript></equationsource></inlineequation>

We integrate and sharpen two characterizations of aggregate excess demand functions: we obtain Mas-Colell's (1977) equilibrium invariance, and strengthen Geanakoplos' (1984) weakly concave utility functions to strictly concave ones. Our proofs modify and extend Geanakoplos' utility-construction....

For continuous aggregate excess demand functions of economies, the existing literature (e.g. Sonnenschein (1972, 1973), Mantel (1974), Debreu (1974), Mas-Colell (1977), etc.) achieves a complete characterization only when the functions are defined on special subsets of positive prices. In this...

We prove that, for finitely many demand observations, the Strong Axiom of Revealed Preference tests not only the existence of a strictly concave, strictly monotone and continuous utility generator, but also one that generates an infinitely differentiable demand function. Our results extend those...