Business Cycles explained by Instability

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 differ-ential equations. However, the solution is marginal stable. Therefore we find a nat-ural sinusoidal oscillation of inflation and unemployment just as observed in busi-ness cycles. When speculation is present, the instability becomes more severe. So we present for the first time a mathematical explanation for business cycles. The steering of central banks by setting interest rates to keep inflation stable and low needs an overhaul. One has to distinguish between real monetary instability and the one caused naturally by business cycles.