Dynamic intersectoral models with power-law memory

TL;DR

This paper introduces intersectoral dynamic models incorporating power-law memory via Caputo derivatives, providing solutions with Mittag-Leffler functions, and explores how fading memory influences economic growth and sector dominance.

Contribution

It develops novel intersectoral models with power-law memory using fractional calculus and analyzes their impact on economic sector dynamics.

Findings

Memory effects can alter economic growth rates.

Fading memory influences sector dominance.

Models use Mittag-Leffler functions for solutions.

Abstract

Intersectoral dynamic models with power-law memory are proposed. The equations of open and closed intersectoral models, in which the memory effects are described by the Caputo derivatives of non-integer orders, are derived. We suggest solutions of these equations, which have the form of linear combinations of the Mittag-Leffler functions and which are characterized by different effective growth rates. Examples of intersectoral dynamics with power-law memory are suggested for two sectoral cases. We formulate two principles of intersectoral dynamics with memory: the principle of changing of technological growth rates and the principle of domination change. It has been shown that in the input-output economic dynamics the effects of fading memory can change the economic growth rate and dominant behavior of economic sectors.