城市的大小分佈、最適規模與效率

Abstract

Many things in the natural world consist of an ever larger number of ever smaller pieces. It is called a fractal, which can be an object in space or a process in time. This fractal system has been observed in various fields, such as in the physical, biomedical, and social sciences. In economics the size distribution of cities and the distribution of the number of AOL users empirically fit the fractal. The purpose of this paper is to investigate the possible underlying mechanisms of the distribution of cities, which can generate not only the general power law rather than the specific Zipf`s law but also contain economic intuition. In the present paper we will introduce and simulate the proposed stochastic model to examine the feature that could generate power law which explains the regularity of the distribution of cities; furthermore, the extended features regarding the optimal scale and the efficiency prospect of the cities` distribution is also investigated. We find that the growth process with a diminishing returns` agglomeration economy or bounded an increasing returns` agglomeration economy converges to a stable limiting distribution with a constant expected proportion. On the contrary, the growth process with an unbounded increasing returns` agglomeration economy generates a fractal kind of limiting distribution with a time variant expected value. Given the assumption of agglomeration economies and robust evidence of Zipf`s in city distribution, our result suggests the presence of unbounded agglomeration economies in residents` location benefit.