Acta Oeconomica Pragensia 2005, 13(1):18-25 | DOI: 10.18267/j.aop.124
Choice between the Discrete and Continuous Models in Economic Applications and Its Implications
When building a dynamic model we express an impact of past on future state variables. We usually know if the change should be positive or negative and have an idea about a magnitude of the change. But if we express the change with either a difference or a derivative often depends on such factors, as is ease of evaluation of discrete models. We show that this choice may have important stability implications. We choose a more general approach and consider the choice not only between discrete and continuous models but among discrete models with various lengths of the step (considering a continuous model be a discrete model with infinitely small step). We derive a closed form formula that says if the equilibrium point in a system with a particular step length is stable or not and some implications about the stability of the same system with different step lengths. As a special case we get a relationship between stability of a discrete model and the corresponding continuous model where a difference was substituted by a derivative.
Keywords: continuous models, discrete models, stability
JEL classification: C62
Published: March 1, 2005 Show citation
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