ABSTRACT
The proof of existence of a general competitive equilibrium is generally considered one of the most important and robust results of economic theory. The proofs of existence, which appeared in the 1950s, relied on results of topology, using a fixed-point theorem to demonstrate the existence of an equilibrium point. These proofs employ a suitable mapping, transforming points of a convenient set of prices and quantities onto itself. Our argument, in brief, is that the mappings used in these proofs are mathematically convenient but economically meaningless: they do not correspond to any plausible process of price variation.
