MODELLING OF THE CYCLES OCCURRENCE IN ECONOMY

Abstract

Objective: to prove the existence and conditions of appearance of a plane wave during the investing into the renewable factors of production.Methods: abstraction, economic-mathematical modeling.Results: the cyclical nature of the economy is studied and proved in many studies, but most of them are based on the empirical data without analytical proof. The author of the article proves the existence of plane waves, which occur as a result of updates of the renewable factors of production. The identified factors include physical capital, the amount of labor resources and human capital.Basing on the vector analysis, it is proved that the plane wave arises in case of potential investments and fulfillment of the following condition: the speed of investment in renewable factors of production must be proportional to the velocities of the factors of production. It was determined that in case of changes in the rate of funding of any of the factors, the development of other factors of production will change, i.e., a vortex will appear. The formulated system of equations of the changing velocity of production factors in a vector form was solved by a plane wave under the condition of parallelism of any two vectors. On the basis of the proven allegations, it was concluded that the cyclic character is a natural way of the economy development.Scientific novelty: on the basis of vector analysis, the existence of a plane wave in the production factors development is proved.Practical significance: knowing the dynamics of the plane wave, its length and amplitude, we can determine the moments of time tightening and loosening of taxation and fiscal policy to regulate investment in the factors of production.

Keywords

• mathematical and instrumental methods in economics
• dynamic rotor
• factors of production
• plane wave
• investments