Single and Attractive: Uniqueness and Stability of Economic Equilibria under Monotonicity Assumptions

TL;DR

This paper introduces a new theorem that provides sufficient conditions for the uniqueness and stability of equilibria in complex economic models with multiple agents and markets, with applications to trade models.

Contribution

It offers a novel theorem that guarantees equilibrium uniqueness and stability in diverse economic models, including multi-sector and heterogeneous country trade models.

Findings

Proves equilibrium uniqueness in multi-sector trade models.

Establishes stability of equilibria with heterogeneous country features.

Provides a practical toolkit for applying the theorem to various models.

Abstract

This paper characterizes equilibrium properties of a broad class of economic models that allow multiple heterogeneous agents to interact in heterogeneous manners across several markets. Our key contribution is a new theorem providing sufficient conditions for uniqueness and stability of equilibria in this class of models. To illustrate the applicability of our theorem, we characterize the general equilibrium properties of two commonly used quantitative trade models. Specifically, our analysis provides a first proof of uniqueness and stability of the equilibrium in multi-country trade models featuring (i) multiple sectors, or (ii) heterogeneity across countries in terms of their labor cost shares. These examples also provide a practical toolkit for future research on how our theorem can be applied to establish uniqueness and stability of equilibria in a broad set of economic models.