🤖 AI Summary
This study addresses the continuity of the equilibrium correspondence in infinite-dimensional commodity spaces, circumventing the traditional reliance on differentiability assumptions. Within a Banach lattice framework, economies are modeled as Borel probability measures over a space of characteristics, with aggregate endowments defined via Bochner or Gel'fand integration. The analysis of equilibrium behavior is carried out in an appropriately chosen Polish topology. By providing a unified treatment of locally convex space models, the approach encompasses complex economic settings such as infinite-horizon planning, monopolistic competition, and asymmetric information. The paper establishes that the equilibrium correspondence is continuous on a dense subset of the set of economies that admit equilibria, thereby substantially extending the scope of both classical and recent continuity theorems.
📝 Abstract
We examine the continuity of equilibrium correspondences in infinite-dimensional settings where the commodity spaces are Banach lattices. Economies are modeled as Borel probability measures on a space of characteristics, with aggregate endowments defined via Bochner or Gel'fand integrals. Within this framework, we prove that the equilibrium correspondence is continuous on a dense subset of the domain of economies admitting equilibria, endowed with a suitable Polish topology. These results extend both classical and recent continuity theorems by providing a unified analytical treatment applicable to a substantially broader class of locally convex spaces and encompass models with infinite planning horizons, monopolistic competition, neoclassical economies, financial equilibria, and asymmetric information. Importantly, this study demonstrates that there is no necessity to impose differentiability assumptions that are typically required in regular economies to study equilibrium continuity.