Computational Techniques for Stability Analysis of a Class of Dynamic Economic Models

Abstract

Modern microeconomics and macroeconomics study dynamic phenomena. Dynamics could predict future states of an economy based on its structural characteristics. Dynamic models in discrete time discrete state economic systems may take the form of one single linear difference equation or a system of linear difference equations. In this study we use Xcas and Mathematica as software tools in order to generate results concerning the dynamic properties of the solutions of the difference equation(s) and, determine whether an economic equilibrium exists. Our computational approach does not require solving the difference equation(s) and makes no assumptions for initial conditions. The results provide quantitative information based on the qualitative properties of the mathematical solutions rather than on their quantifiable ones. The relevant output of CAS software is created in a way as to be interpreted without the knowledge of advanced mathematics. The computer codes are fully presented and can be reproduced as they are in computational-based research practice and education.