Accelerator and Multiplier for Macroeconomic Processes with Memory

Abstract

The paper proposes an approach to the description of macroeconomic phenomena, which takes into account the effects of fading memory. The standard notions of the accelerator and the multiplier are very limited, since the memory of economic agents is neglected. We consider the methods to describe the economic processes with memory, which is characterized by the fading of a power-law type. Using the mathematical tools of derivatives and integrals of non-integer orders, we suggest a generalization of the concept of the accelerator and multiplier. We derive the equations of the accelerator with memory and the multiplier with memory, which take into account the changes of endogenous and exogenous variables on a finite time interval. We prove the duality of the concepts of the multiplier with memory and the accelerator with memory. The proposed generalization includes the standard concepts of the accelerator and the multiplier as special cases. In addition these generalizations provide a range of intermediate characteristics to take into account the memory effects in macroeconomic models.