Application of Delay Differential Equations in the Model of the Relationship Between Unemployment and Inflation

Abstract

Purpose of the article: The article deals with a formulation of the dynamic model which expresses the relationship between the rate of inflation and the rate of unemployment more accurately and which has become to be known as the Phillips curve. Methodology/methods: The economic theory in question, which is an essential basis of all economic models (Phillips curve, hysteresis of unemployment,...) is sufficiently explained in the introductory chapters and serves as the basis for formulating relationships of the economic quantities which are being explored. Here, there are applied methods of analysis, synthesis, dynamic modelling and differential equations. Scientific aim: The classic model is limited to relations and mutual connections in time t only and eliminates the influence of factors from periods preceding time t. Mathematically, the model leads to a system of common differential equations. The aim of submitted the article is elimination of the simplifications by constructing a more realistic model, which takes into consideration the data from previous periods, and create a new model expressed by a system of two delay differential equations. Findings: The new model can be solved (under various circumstances) and constructed even on the above mentioned more complex conditions and the impact of particular parameters of the model on its solution can be observed. Conclusions: The original classic model of the relationship between the rate of inflation and the rate of unemployment which led to the Phillips curve has been replaced in this article by a new model expressing the real economic situation more precisely while respecting the influence of the history of the factors taken into account using so-called delay differential equations.