Augmented IS–LM model based on particular functions

In this paper, we create our own static and dynamic augmented IS–LM model based on concrete particular functions. These functions represent a mathematical and analytical description of economical quantities on which the IS–LM model is based and whose properties follow from the corresponding economical theories.We prove several theorems about parameters of this model, we describe dynamical behaviour of this system and prove (un)stability of the singular points including their classification. Then, we demonstrate this model on some illustrative examples and we suggest our own econometric non-linear regression models of the particular functions courses.