Wald and Existence Proofs

Abstract

Only in the early Thirties of the 20th century was it possible to prove, in a mathematically rigorous way, the existence of a solution to a Walrasian-like general equilibrium system. There are some good reasons to explain why. First of all, the founders, Walras and Pareto, were not so well trained in mathematics as to be able to really present a mathematical proof while, at the same time, they felt sure they had supplied a proof, simply by counting the number of independent equations and unknowns to show they are equal.’ Secondly, at the start of 20th century, when Pareto wrote his last contributions to economic theory, there was no fixed point theorem to be used to formulate existence proofs. At the same time, no economist had seriously posed the problem of the existence of a general equilibrium solution.