TITLE:
Business Cycles Explained by Instability
AUTHORS:
Galiya Klinkova, Michael Grabinski
KEYWORDS:
Business Cycles, Instability, Differential Equations, System Dynamics
JOURNAL NAME:
Theoretical Economics Letters,
Vol.15 No.6,
December
3,
2025
ABSTRACT: Business cycles (a periodic change of e.g. GDP over five to ten years) exist, but a proper explanation for it is still lacking. Here we extend the well-known NAIRU (non-accelerating inflation rate of unemployment) model, resulting in a set of differential equations. However, the solution is marginal stable. Therefore, we find a natural sinusoidal oscillation of inflation and unemployment just as observed in business cycles. When speculation is present, the instability becomes more severe. So we present for the first time a mathematical explanation for business cycles rather than a description. The steering of central banks by setting interest rates to keep inflation stable and low needs some overhaul. One has to distinguish between real monetary instability and the one caused naturally by business cycles.