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

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.

The Samuelson's model as a singular discrete time system

“…Many authors have studied generalised discrete & continuous time systems, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], and their applications especially in cases where the memory effect is needed including generalised discrete & continuous time systems with delays, see [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Many of these results have already been extended to systems of differential & difference equations with fractional operators, see [43][44][45][46][47][48][49].…”

“…Although primitive and using only the demand point of view, the Samuelson's prospect still provides an excellent insight into the problem and justification of business cycles appearing in national economies. In the past decades, many more sophisticated models have been proposed by other researchers [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. All these models use superior and more delicate mechanisms involving monetary aspects, inventory issues, business expectation, borrowing constraints, welfare gains and multi-country consumption correlations.…”

Causality of singular linear discrete time systems

“…Many authors have studied generalized discrete & continouus time systems, see , and their applications, see [29][30][31][32][33][34][35]. Many of these results have already been extended to systems of differential & difference equations with fractional operators, see [36][37][38][39][40][41][42][43][44][45].…”

Homogeneous linear matrix difference equations of higher order: Singular case

“…Many authors have studied generalized discrete & continouus time systems, see , and their applications, see [29][30][31][32][33][34][35]. Many of these results have already been extended to systems of differential & difference equations with fractional operators, see [36][37][38][39][40][41][42][43][44][45].…”