The Construction of a Mathematical Economic and GeographicalModel using the Complex System for an Economic Analysis of theUrban Formation Process and Its Computer Simulation

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Based on a population movement model of the socio-dynamics, we built a mathematical economic and geographical model. In this study, I. Takagi, a mathematical economist, and M. Tabata, a mathematician whose specialty is numerical analysis have satisfactorily analyzed the model of the socio-dynamics from the viewpoints of an endogenous economic growth model and numerical analysis.In a mathematical model of population movement, it is difficult to calculate a population density function directly due to specificity of the distance and time lag effects. Therefore, traditional methods in numerical analysis could not be applied to the study and the research on this topic has been delayed for a long time. On the other hand, by the advancement of the mathematical statistics theory of computation, by using mathematical statistical pan-function of the population density function (capacity and entropy), the algorithm to evaluate latromathematical school agent based model has been developed. In calc … More ulating population density and regional real wage in the mathematical economic and geographical model, a program package for numerical analysis incorporated the highest calculation technique was used. Therefore, we could grasp the spatial and temporal change of population density real wages easily and precisely, and a population movement model came to be able to in this way chase the behavior of the model quickly even if we let an endogenous economic growth model be alliance in various form.We inspected whether the prototype model that we built is consistent with such models as von Thunen model，Dixit-Stiglitz model，and Simon model by a numerical value experiment. Then, we examined whether a big city was located in the core by a self-organization process pointed out by Krugman and whether we could explain in the prototype model that a formationprocess of Edge City where plural satellite cities were born in the outskirts built.We repeated a correction of the prototype model that we built and decided the final mathematics model. By a final mathematical model, we were able to explain the birth of the city, self-organization of the many hierarchical structure of the city, and a formation process of Edge City where satellite cities were born around metropolis. Less