Abraham Wald's Equilibrium Existence Proof Reconsidered

For his proof of the existence of a general competitive equilibrium Abraham Wald assumed a strictly pseudomonotone inverse market demand function or, equivalently, that market demand satisfies the Weak Axiom of Revealed Preference. It is well known that more recent existence theorems do not need this assumption. In order to clarify its role in Wald's proof, the question of existence of an equilibrium for a modified version of the Walras-Cassel model is reduced to the solvability of a related variational inequality problem. In general, the existence of a solution to such a problem can only be proved by advanced mathematical methods. We provide an elementary induction proof which demonstrates the essence of Abraham Wald's famous contribution