The Extended Moving-Equilibrium Method: A Presentation

Abstract

The moving-equilibrium method represents an approximation procedure for systems of differential equations that include variables which exhibit big differences in their speed of adjustment. In economic models one usually distinguishes three typs of variables: “constants”, “slow variables” and “fast variables”. The first are exogenous quantities in the model, their speed of adjustment is zero by assumption. The second and third are endogenous quantities of the model. It is assumed that slow variables react with a positive finite speed, whereas fast variables react “instantaneously”. Mathematically, this assumption is expressed by formulating explicit differential equations (DEs) for slow variables and replacing the ones for the fast variables by equilibrium conditions. The advantage of this procedure consists in the reduction of the dimensions of the system of DEs that is to be analyzed from the initial number of DEs to the number of DEs that describe the evolution of slow variables. Without this simplification many models could actually not be analyzed. The procedure is called “Moving-Eqilibrium Method” (MEM) because it studies the movement of short-run equilibria in the course of long-run adjustments.