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.

A working draft is available at https://ssrn.com/abstract=4772016

Co-author: Elizaveta Gonchar

Abstract:
The distribution of population across and within countries naturally relates to the distribution of economic production. In this paper, we explore differences in gravity model estimates of trade that take into account spatial factors of population distributions, introducing a novel measure of geodesic distance between countries using population-weighted centroids as endpoints for bilateral distance measures. Canonical gravity models of international trade have relied on time-invariant measures of bilateral distance between nations, including distance between national capitals, geographic centroids, and weighted centroids based on the N largest population centers. By using annual global population density rasters to identify the spatial tendency of the population, the location of any country’s weighted centroid changes each year. This allows the weighted distance between two countries to change over time and introduces a source of variation into the standard gravity model framework.