Mathematical Economic Model of the Complex System in International Economics

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In a field of mathematical social science that belongs to a science of the complex system to be called economics of complex system and economic physics, many mathematical models are built by using technique of statistical mechanics for analysis of a social economic phenomenon. However, in a new field of a science of the complex system, a mathematical foundation equal to that for the theory of statistical mechanics does not almost exist yet. Therefore, we analyzed a mathematical economic model with a method of functional analysis. We built a mathematical model that expresses a self-organization phenomenon that caused by interaction of labor movement and economic growth like that happened in the EU market unification. In statistical mechanics a solution of a master equation in a population movement theory proved to be very close to a solution of the Fokker-Planck equation by using the Kramers-Moyal expansion in closeness of degree permitted in physics when the moving cost that is necessa … More ry for international labor mobility is large enough. In addition, we were able to prove mathematically and precisely the consistency of the theory of population movement of Hotelling's with that of Weidlich-Haag's.In an article, "A geometrical similarity between migration of human population and diffusion of biological particles", we built an Agent-based Model that describes a population movement phenomenon when a utility function expressing a certain local economic advantage is a linear function or a quadratic function of agent density. Furthermore, in conventional studies, mathematically precise proofs for the convergence of the Kramers-Moyal expansion and an expansion of high degree terms were extremely difficult, so an almost meaningful result was not provided. However, we proved that a solution for a master equation in a theory of population movement by using the limited Kramers-Moyal expansion that modified by us was very close to a solution for the Fokker-Planck equation when the cost of population movement was large enough. Less