A Unifying Framework for Economic Equilibrium and Optimal Transport in Infinite-Dimensional Hilbert Spaces

26 Pages Posted: 26 Apr 2024

See all articles by Ian Helfrich

Ian Helfrich

Georgia Institute of Technology - School of Economics

Date Written: March 25, 2024

Abstract

In this paper, I introduce a novel framework that unifies the concepts of economic equilibrium and optimal transport in infinite-dimensional Hilbert spaces, providing a rigorous and flexible foundation for analyzing complex economic systems. My framework builds upon recent developments in the theory of tensor-valued measures and nonlinear operator theory, allowing me to extend the notions of economic equilibrium and optimal transport to infinite-dimensional settings. I establish the existence and uniqueness of economic equilibrium under mild assumptions on preferences and endowments, characterize the equilibrium allocations as optimal transport plans, and represent the equilibrium prices as gradients of convex potential functions. My unifying framework has far-reaching implications for economic theory and practice, enabling the analysis of efficiency, stability, and distributional properties of economic systems in a wide range of contexts.

Keywords: Economic equilibrium, optimal transport, Hilbert spaces

JEL Classification: C02, C6, C62, C68, D5

Suggested Citation

Helfrich, Ian, A Unifying Framework for Economic Equilibrium and Optimal Transport in Infinite-Dimensional Hilbert Spaces (March 25, 2024). Available at SSRN: https://ssrn.com/abstract=4772016 or http://dx.doi.org/10.2139/ssrn.4772016

Ian Helfrich (Contact Author)

Georgia Institute of Technology - School of Economics ( email )

217 Habersham
Atlanta, GA 30332
United States

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