Studies of Cost-Income Modelof the optimum spatial scale of cities
城市适度空间规模的成本-收益分析模型探讨

Optimum scale of cities is inexistent in historical view. But the optimum scale of cities in a concrete region exists in aperiod of time. Firstly, this paper proposes the hypothesis that the oper ating objective of cities is maximization of their economic profits.Then it an alyzes the transformation trend of incomes and costs of the cities when the scales of cities heighten. Next, the necessary and sufficient condition when optimu mscale of cities exists is resulted. The optimum scale of cities is in a stabl estate of the cities. Cities regulate their scales to reach the optimum scale basing on raising economic level or enlarging scale, when their scales are not optimum.The scales of cities are the urban ranges of cities. This paper chooses GDP sas incomes and budget expenditures as cost of cities. The dynamical models of incomes and costs of cities are established using territorial area and populati on, GDP per capita as independent variables based on statistical data of Jiangsu province. The model to calculate the optimum scale of cities in Jiangsu Province is drawn. The evolutionary trend of the optimum scale of cities with different population sizes is simulated using GDP percapita as independent variable.Some important results are concluded. The more the population is, the more the optimum scale, when the GDP per capita of cities keeps invariant. The last opti mum scale of cities covers an area of 2030 km~2 in Jiangsu Province when th e GDP percapita is high enough, whatever the population of cities. The speed to reach 2030 km~2 is faster when the population of cities reaches 2.8 million.Finally, this paper evaluates the adjustment of the administrative divisions of cities in Jiangsu Province in the last two years.The adjustments of Suzhou , Wuxi and Nanjing are appropriate and the adjustment extents of Huaiyin and Yan gzhou are too great. It is necessary for Changzhou, Zhenjiang and Nantong to enlarge their urban ranges. The existing scales are greater than the optimum scale of Xuzhou, Lianyungang, Yancheng, Taizhou and Suqian because of their low GDP percapita.