Abstract
Semi-algebraic economies are economic models, the equilibria of which could be characterized by semi-algebraic systems. Semi-algebraic economies are usually divided into two classes:static equilibrium models and dynamic equilibrium models. In this paper, we propose general methods to transfer the problems of detecting multiple equilibria in static models and analyzing the stability of equilibria in dynamic models into counting real solutions of semi-algebraic systems. Furthermore, we describe systematic algorithms for computing the number of distinct real solutions of semi-algebraic systems with or without parameters. Compared to the methods by Kubler and Schmedders, ours can better handle models with inequality constraints and can give the precise number of equilibria. The effectiveness of our algorithms is illustrated by the computational results of analyzing a number of specific economic models.
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