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Stable and related matrices in economic theory

Giorgi G.

Control and Cybernetics

2003

Vol. 32, no 2

397-410

It is well known that local stability analysis of a Walrasian multiple markets model is performed by approximating, according to Taylor's expansion, a system of first-order differential equations. So, one has to study the stability of a linear system (with constant coefficients). Since the earlier studies of Walrasian economic equilibrium, economists have suggested numerous conditions ensuring local stability of the same. The aim of this note is to give a survey of various conditions, used in economic analysis, ensuring that a (real) square matrix is stable. We show, in a unified manner, their inter-relations and make some new remarks on quasi-dominant matrices and on D-stable matrices.