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Cross-Diffusion Modeling in Macroeconomics

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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 market. Our four-dimensional model highlights that a hectic movement of the capital toward labour force can cause a Turing instability.

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Authors and Affiliations

  1. Institute of Mathematics, Budapest University of Technology and Economics, Budapest, 1111, Hungary

    László Balázsi & Krisztina Kiss

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  1. László Balázsi
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  2. Krisztina Kiss
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Correspondence to Krisztina Kiss.

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Balázsi, L., Kiss, K. Cross-Diffusion Modeling in Macroeconomics. Differ Equ Dyn Syst 23, 147–166 (2015). https://doi.org/10.1007/s12591-014-0224-8

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  • DOI: https://doi.org/10.1007/s12591-014-0224-8

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