On the stability of equilibrium for a reformulated foreign trade model of three countries

Subject Areas : Mathematical Optimization

Ioannis K. Dassios ¹ , Grigoris Kalogeropoulos ²

1 - School of Mathematics and Maxwell Institute, The University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, UK
2 - Department of Mathematics, University of Athens, Athens, Greece

Received: 2020-10-02 Accepted : 2020-10-02 Published : 2014-09-01

Keywords: Mathematical modelling  Foreign trade, model  Difference equations  Jury criterion,

Abstract :

In this paper, we study the stability of equilibrium for a foreign trade model consisting of three countries. As the gravity equation has been proven an excellent tool of analysis and adequately stable over time and space all over the world, we further enhance the problem to three masses. We use the basic Structure of Heckscher–Ohlin–Samuelson model. The national income equals consumption outlays plus investment plus exports minus imports. The proposed reformulation of the problem focus on two basic concepts: (1) the delay inherited in our economic variables and (2) the interaction effect along the three economies involved. Stability and stabilizability conditions are investigated while numerical examples provide further insight and better understanding. Finally, a generalization of the gravity equation is somehow obtained for the model.