Non-Linear Model of the Dynamics of the Macroeconomic System: Multiplier-Accelerator.

Abstract

The paper proposes a new approach to the development of a mathematical model of the dynamics of the mutual multiplier, which indicates the marginal propensity to save as a result of GDP growth, and the accelerator, which reflects the growth of national income capital. The model is based on the hypothesis of a non-linear dependence of consumption on the amount of profit. At the same time, it is assumed that the growth of consumption will be limited, that is, the effect of saturation. In addition, the model takes into account the delayed reaction of the accelerator to the influence of the multiplier. When building the model, processes are considered in continuous time. The application of this model to the analysis of the dynamic properties of the macroeconomic system makes it possible to estimate the parameters under which the "multiplier-accelerator" system enters a critical state. The presence of a double limit cycle with corresponding "soft" and "hard" modes of birth (death) of the limit cycle was also substantiated.