Finding and Verifying All Solutions of a System of Nonlinear Equations Using Public Domain
Wendy A. Campione, Max E. Jerrell · RePEc: Research Papers in Economics · 2003
Economic models are often stated as systems of nonlinear equations, for example general equilibrium models, game theory models, and macroeconomic models. A critical issue is wether the model has a solution and is the solution unique. Interval arithmetic is an arithmetic that operates on intervals rather than point values. It can be used to find all solutions of a system of nonlinear equations over a specified region. We present arguments demonstrating that this arithmetic is capable of determining existence and uniqueness. We then use a public domain software package on several simple economic examples.