Losing Equilibrium: On the Existence of Abraham Wald's Fixed-Point Proof of 1935

Abstract

In fall 1935, Abraham Wald presented a fixed-point proof of a general equilibrium model to Karl Menger's Mathematical Colloquium in Vienna. Due to limited space, the paper could not be printed in the eighth proceedings of the colloquium (the Ergebnisse) published in spring 1937 but was scheduled for the ninth issue of the series. After the annexation of Austria to Nazi Germany in March 1938, however, Menger's colloquium ended and the proof never appeared in print. Nor did Wald, after he fled to the United States and launched a career in statistics, attempt to circulate his proof. After his sudden death in 1950, only Wald's preliminary proof of 1934 was translated into English for Econometrica. When thus Kenneth J. Arrow, Gérard Debreu, and Lionel McKenzie in 1954 referred in their own fixed-point proofs only to Wald's preliminary published version, his 1935 fixed-point proof was forgotten. This did not change when economists and historians of economics, the authors included, reconstructed Wald's contribution. New evidence, however, proves its existence. This article tells the story of Wald's lost equilibrium proof.