Choice between the Discrete and Continuous Models in Economic Applications and Its Implications
|Type:||Articles in refereed journals|
|ISSN / ISBN:|
|Published in:||Acta Oeconomica Pragensia 1/2005|
|Grants:||402/03/H057 Nonlinear Dynamical Economic Systems:Theory and Applications|
|Abstract:||During the process of building a model we formalize our ideas about the pressure on future increase or decrease of state variables, depending on the present value of the state variables. If we choose to express this change with either a difference or a derivative and thus get a discrete or continuous model depends mainly on our taste.
We’ll show that our choice between the discrete and continuous model may have an impact on stability of the model. Some values of parameters can result in a stable system in one case and an unstable system in the other so we have to take care about their interpretation.
We choose a more general approach and choose 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.