A macroeconomic mathematical model for the national income of a union of countries with interaction and trade

In this article, we assume a union of countries where each national economy interacts with the others. We propose a new model where (a) delayed variables are incorporated into the system of equations and (b) the interaction element is restricted into the annual governmental expenditure that is determined according to the experience of the total system and the trade relations of these countries (exports-imports). In addition, we consider the equilibrium(s) of the model (a discrete-time system) and study properties for stability, the appropriate control actions as well as the total system design in order to obtain a stable situation. Finally, a practical application is also investigated that provides further insight and better understanding as regards the system design and produced business cycles.