基于扩展杜能模型的个体城市空间发展的经济学分析

杜能模型解决了均质区域内以城市为中心由内向外的空间变化过程，但是没有论述城市发展过程中的非均衡扩展问题。事实上，距离城市中心率同区位各种生产要素的组合状态、相互替代状态以及意愿的布局数量等都会因为总收益的水平而有很大的不同，进而影响着城市特别是影响域内的不同区位以不同状态向外扩展。为此，传统的杜能模型需要进行扩展，在原始模型的基础上加入偶然成本以压影响城市扩展的摩擦因子以对其进行完善，以便解释摩擦因子的不同强度对城市扩展的不同影响。新模型系统地论述了差异影响下个体城市自中心向外缘扩展的微观经济学机理。计算分析表明，扩展杜能模型中收益对距离的二阶导数为正数，这说明以经济核为中心向外延伸的经济行为存在收益最小点，这个最小点就是个体城市扩展的最远边界，在数值上等于净价格与运费的商。

Economic Analysis of Individual Urban Spatial Development Based on Supplemental Thunen Model

Thunen Model explains in a spatial economic manner the expansion procession of a city from centre to the margin areas, but the question of uneven development procession for a city remains unresolved. Actually, as the total revenue produces decisive influence on the combination, substitution and quantity of different factors at certain location, which can further exert crucial impaction on urban expansion, the characteristics of urban expansion to the margin areas are not the same at different locations. In order to interpret the impact from different intensity of friction factors on urban development, a new model is developed by adding incidental cost and friction factors to the traditional Thunen Model. The new model systematically studies the microeconomie dynamics of individual urban expansion to the margin areas under different impactions. Analysis indicates that the second differential coefficient for rent to distance in supplemental Thunen Model is a positive number, which in turn shows that income minimum, being equal to the quotient of net price to freightage, exists for economic extension to margin areas, and becomes the farthest borderline for a city.