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A practical statistical analysis on the regional populations and GDPs ofChina is conducted. The result shows that the distribution of the populationsand that of the GDPs obeys the shifted power law, respectively. To understandthese characteristics, a generalized Langevin equation describing variation ofpopulation is proposed based on the correlation between population and GDP aswell as the random fluctuations of the related factors. The equation istransformed into the Fokker-Plank equation, and the solution demonstrates atransform of population distribution from the normal Gaussian distribution to ashifted power law. It also suggests a critical point of time at which thetransform occurs. The shifted power law distribution in the supercriticalsituation is qualitatively in accordance with the practical result. Thedistribution of the GDPs is derived based on the Cobb-Douglas productionfunction, and presents a change from a shifted power law to the Gaussiandistribution. This result indicates that the regional GDP distribution of oursociety will be the Gaussian distribution in the future. The analysis on thegrowth trend of economy suggests it will become a reality. These theoreticalattempts may draw a historical picture of our world in the aspects ofpopulation and economy.

Statistical Dynamics of Regional Populations and Economies