本稿の目的は, 一般均衡理論において, 均衡価格の安定性を論じる際に前提となる, 微分方程式の解の滞留性に関する主要な結果を厳密に述べること, およびその結果を応用して三つの古典的な経済モデルの解の滞留性が統一的に記述できることを示すことである。具体的には, Crandall(1972)に基づいて, Nagumo-Crandallの定理の証明を厳密に記述し, それを用いて, Nikaidô and Uzawa(1960), Nikaidô(1959), および, Arrow, Block, and Hurwicz(1959)の定式化した価格の模索過程における解の滞留性について論じる。
This study strictly discusses the main results relating to the viability of solutions to differential equations, which are premises when debating the stability of equilibrium prices in general equilibrium theory, while also indicating that, with an application of the results obtained, three solutions for classical economic models can be described in a unified form.
In practice, based on Crandall (1972), we strictly describe a proof of the Nagumo–Crandall theorem and, based on this, discuss the viability of solutions in tâtonnement processes for formularized prices in Nikaidô and Uzawa (1960), Nikaidô (1959), and Arrow, Block, and Hurwicz (1959).
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