Reaction-Diffusion Equations with Applications to Economic Systems

Abstract

In this article, we discuss reaction-diffusion equations and some potential applications to economic phenomena. Such equations are useful for capturing nonlinear coupled evolution of multiple quantities and they show endogenous oscillatory behavior as well as non-convergence to a constant equilibrium state. We model technological competition and spill-over of productivity shocks across countries using simple variants of reaction equations of the Lotka-Volterra type. Coupled with standard real business cycle models for individual countries, this gives rise to non-trivial lag-lead structure in the time-series properties of the macroeconomic variables across countries. We show that this simple model captures a number of properties of the real data.