Equilibrium Proofmaking

Abstract

Each year, new economics Ph.D. students learn the proof of the existence of a competitive equilibrium as if it were a rite of passage. From the utility-maximizing behavior of consumers and the profit-maximizing behavior of firms, neophyte economists soon can demonstrate that under certain conditions there exists a competitive market-clearing general equilibrium price vector. While there are a number of proofs that establish the existence of such an equilibrium, the validity of these proofs is indubitable. Indeed, economists with even scant knowledge of the history of economics can identify Kenneth J. Arrow and Gerard Debreu's Econometrica paper as having provided the proof that settled the issue.