Cross-diffusion Modeling in Macroeconomics

TL;DR

This paper investigates the stability of a macroeconomic model with capital and labor as predator-prey populations, incorporating spatial movement through cross-diffusion, and explores conditions leading to market stability or Turing instability.

Contribution

It introduces a novel macroeconomic model with cross-diffusion effects for multi-country markets and analyzes stability conditions including Turing instability criteria.

Findings

Cross-diffusion can destabilize the market leading to Turing patterns.

Stability conditions depend on the nature of cross-diffusion effects.

Hectic capital movement can cause market instability.

Abstract

This paper deals with the stability properties of a closed market, where capital and labour force are acting like a predator-prey system in population-dynamics. The spatial movement of the capital and labour force are taken into account by cross-diffusion effect. First, we are showing two possible ways for modeling this system in only one country's market (applying a simple functional response and a Holling-type ratio-dependent response as well), examining the conditions of their stability properties. We extend the ratio-dependent model into two countries common market where two kind of cross-diffusion effects are present, and find those additional conditions, whose are necessary for the stability of the global common market besides the stability of each countries local markets. Our four-dimensional model highlights that a hectic movement of the capital toward labour force can cause a Turing instability.