The Construction of a Mathematical Economic Model using the Complex System for an Economic Analysis Concerning the Decreasing Number of Labors with the Declining Birthrates

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This study has the following academic significances:(1) We have constructed a mathematical economic model of the complex system that was the most important problem in building an economic-geographic model, and which had not significantly studied.(2) We have constructed an economic-geographic model by modifying agent-based model, a cutting edge technique in numerical analysis that had not used because of its mathematical difficulties regardless of its known usefulness in mathematical economics. We could also offer economists a useful computer program package for employing agent-based models.This study has not only above-mentioned academic significances but also great significance in terms of demographical analysis. The demographical model developed by Weidlich-Haag was originally a mathematical model that emphasizes empirical significance that could contribute to forecasting demographic movement in the European Union. In Japan, it was once believed that the demographic movement would slow down due to its declining birthrate and because of its aging society. However, there are the regions where population has been declining, and all the people move out of some villages in those regions. On the other hand, it is forecasted that there will be a large increase in population in the big cities like Tokyo. Such demographic movements as population increase in big cities and population decrease in some remote regions become one of the most urgent political agenda in Japan as well as in China and the Southeast Asian countries. Therefore, this study is planned to solve these problems by applying a mathematical economic approach. It is needless to say that this study presents helpful and critical suggestions to the policy makers, and thus we hoped that this study would contribute to demographical analysis and policy making.