城市规模—产出关系的分形性质与分维特征——对城市规模—产出幂指数模型的验证与发展  

A STUDY OF FRACTIONAL DIMENSION ON THE RELATIONSHIP BETWEEN POPULATION SIZES AND ECONOMIC OUTPUTS OF CITIES

作　　者：陈彦光[1] 周一星[1] 

机构地区：[1]北京大学城市与环境学系,中国北京100871

出　　处：《经济地理》2003年第4期476-481,共6页Economic Geography

基　　金：国家自然科学基金(40071035);河南省自然科学基金(004071200)资助项目的部分内容。

摘　　要：在分形性质非退化的前提下,城市规模(S)与产出(Y)之间具有双对数关系Y=a+bS,式中b为具有广义分维性质,且一般b>1。这暗示,在正常情况下,城市规模越大,城市的人均产出一般也就越高;城市的产出效率决定城市规模,城市规模反作用于城市的产出能力。城市规模与产出的相关性强弱可以反映出城市与城市体系性状的好坏。The component parts of a city as a system are related to the economic output of the city, if a function, Y=f(x1,x2,...,xn), is given, a generalised Cobb-Douglas function, Y=μni=1xiσi can be derived from it as a priori model, where xi is a certain measurement of the ith element of the city, Y is the output, μ, σi are parameters and σi=dlnY/dlnxi (i=1,2,...,n; n is the number of the urban component parts, or elements). All of these indicate that a city may be self-affine and has fractal nature. Considering the allometric relationship between xi and xj, namely, xi∝xjαij, the C-D function can be reduced to a two-variable model, e.g., Y∝xidi where αij, di are paremeters, and the former is usually called the allometric coefficient. Amongst the component parts of a city, population is the most important one, and the relationships between the population sizes and the economic outputs of cities draw much attention in China these years. In this paper, a fractal model on urban size-output relationship is advanced as Y=aSb,based on some of the studies made by Prof. Zhou Yixing, where S is the city population size, Y is the urban economic output, a is a proportionality coefficient, and b is called scaling factor which is regarded as generalized fractal dimension because b=D1/D2, here D1 is the dimension of city size and D2 is the dimension of urban output. It is discovered that, ①The larger the city size is, the more the corresponding urban economic output is, for b>1.②The population size of a city is determined by its capability of economic output and in turn reacts on it.③The fractal relationship of urban size output is a kind of good relationship for a city as a system or a system of cities, which indicates that urban systems can be optimized by means of fractal idea related.

关 键 词：城市规模 产出效率 分形性质 双对数关系 人均产出 产出能力 相关性 城市体系 河南 城市经济 

分 类 号：F299.2[经济管理—国民经济] F290