Cross-Diffusion Modeling in Macroeconomics
This paper deals with the stability properties of a closed market, where capital and labour force are acting like a predatorprey 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 countrys 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 market. Our four-dimensional model highlights that a hectic movement of the capital toward labour force can cause a Turing instability.
cross-diffusion functional response ratio-dependence turing instability capitallabour system