Walras' law and nonoptimal equilibria in overlapping generations models (Q1199741)

This paper demonstrates the connection between failure of Walras' law and the nonoptimality of the competitive equilibrium allocation corresponding to a weakly Pareto optimal (WPO) endowment allocation in a finite commodity overlapping generations model (OLG). In finite economies, Walras' Law implies that for any strictly positive price vector there cannot be excess supply (in value terms) for a subset of goods without excess demand (in value terms) in some other subset of goods. It is shown here that this implication fails if and only if there exists a competitive equilibrium that is not Pareto optimal. The main result is proven here: An interior WPO endowment allocation that is bounded and bounded away from zero is nonoptimal if and only if for each positive and sufficiently small \(\varepsilon\), there exist positive prices that that; (i) the resulting demand allocation is uniformly within \(\varepsilon\) of the endowment and (ii) there is positive excess supply (in value terms) for some date \(t\) set of goods and no excess demand (in value terms) of any date \(t\) set of goods. The same result is also proven without using a WPO endowment allocation for a one good OLG model.