住宅立地論へのプログラミングアプローチ
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概要
- 論文の詳細を見る
The purpose of this study is to clearify the theoretical relations between two streams of studies on urban residential theory. One is the market equilibrium models which are typically represented by the works by Alonso and Muth. The other is the programming models originated by Herbert and Stevens. It is first proved that the optimum solution of Herbert and Stevens model coincides with the market equilbirium solution of Alonso-Muth model under certain conditions. The necessary and sufficient conditions are obtainded for this coincidence. Then, by using this result, the Pareto optimality of the equilibrium solution in Alonso-Muth model is proved. A theoritical property of the market clearing submodel in the recent NBER urban simulation model is also clearified. It is further shown that these results enable us to transform market equilibrium models of urban activities into equivalent programming models. Thus the computational difficulty in obtaining the equilibrium solution can be overcomed by using this method.In the second part of this paper, these results in static models are extended into dynamic cases. For this purpose, dynamic extensions of Alonso-Muth model and Herbert-Stevens model are first obtained. Then, each result in the above static case is generalized into the dynamic case by using these two models. It is shown these correspondence relations are quite useful, for example, in the analysis of the stability property of the equilibrium path in the original problem.
- 日本地域学会の論文