Uniqueness of equilibrium and redistributive policies: a geometric approach to efficiency

TL;DR

This paper uses a geometric approach to analyze how redistributive policies affect the uniqueness and efficiency of economic equilibria, linking geometric properties like geodesics to stability and policy implications.

Contribution

It introduces the finite geodesic property as a condition for global uniqueness of equilibrium in economies with two consumers and multiple goods.

Findings

Geodesic coordinate functions imply equilibrium optimization.

Presence of geodesic variables indicates economic efficiency.

Link established between curvature, entropy, geodesics, and equilibrium uniqueness.

Abstract

This paper examines the relationship between resource reallocation, uniqueness of equilibrium and efficiency in economics. We explore the implications of reallocation policies for stability, conflict, and decision-making by analysing the existence of geodesic coordinate functions in the equilibrium manifold. Our main result shows that in an economy with M = 2 consumers and L goods, if L coordinate functions, representing policies, are geodesics on the equilibrium manifold (a property that we call the finite geodesic property), then the equilibrium is globally unique. The presence of geodesic variables indicates optimization and efficiency in the economy, while non-geodesic variables add complexity. Finally, we establish a link between the existing results on curvature, minimal entropy, geodesics and uniqueness in smooth exchange economies. This study contributes to the understanding of the geometric and economic properties of equilibria and offers potential applications in policy considerations. Keywords: Uniqueness of equilibrium, redistributive policies, geodesics, equilibrium manifold, equilibrium selection, curvature, geodesics.