Concept of dynamic memory in economics

TL;DR

This paper introduces a fractional calculus-based concept of dynamic memory in economics, exploring its properties and restrictions, and applies it to generalize the Harrod-Domar growth model with power-law memory effects.

Contribution

It presents a novel fractional calculus framework for modeling dynamic memory in economic systems, including principles and applications to growth models.

Findings

Memory functions can be modeled using fractional calculus.

The generalized Harrod-Domar model incorporates power-law memory effects.

Restrictions like fading and reversibility shape the memory structure.

Abstract

In this paper we discuss a concept of dynamic memory and an application of fractional calculus to describe the dynamic memory. The concept of memory is considered from the standpoint of economic models in the framework of continuous time approach based on fractional calculus. We also describe some general restrictions that can be imposed on the structure and properties of dynamic memory. These restrictions include the following three principles: (a) the principle of fading memory; (b) the principle of memory homogeneity on time (the principle of non-aging memory); (c) the principle of memory reversibility (the principle of memory recovery). Examples of different memory functions are suggested by using the fractional calculus. To illustrate an application of the concept of dynamic memory in economics we consider a generalization of the Harrod-Domar model, where the power-law memory is taken into account.