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Modelling in public economics due differential equations with delay This paper focuses on describing the basics of modelling in economics. The results of this field of science often lead to the solution of ordinary differential equations (ODE). However, models constructed in this way are not always close enough to reality. In order to be able to better model real situations, in addition to the current states of variables, we also consider their behaviour in the past, which then leads to change of the model to a system of functional differential equations. We often include dependence on the past in the models with shifted arguments, in that case we are talking about the so-called differential equations with a delay (DDE), which cannot be solved using standard methods for solving ODE. This article also introduces DDE, along with a basic method for finding a solution and illustrative mod.