The discrete separation theorem and price adjustment directions in markets with heterogeneous commodities

研究成果: Article査読

1 被引用数 (Scopus)

抄録

The separation theorem in discrete convex analysis states that two disjoint discrete convex sets can be separated by a hyperplane with a 0–1 normal vector. We apply this theorem to markets with heterogeneous commodities and uncover the mathematical structure behind price adjustment processes. When p is not an equilibrium price vector, i.e., when aggregate demand and aggregate supply are disjoint, the separation theorem indicates the existence of overdemanded/underdemanded items. This observation yields a generalization of Hall's (1935) theorem and a characterization of equilibrium price vectors by Gul and Stacchetti (2000). Building on this characterization, we show that adjusting the prices of overdemanded/underdemanded items corresponds to Ausbel's (2006) auction. We further extend our approach to markets with continuous commodities and uncover a striking connection between auctions and classical taˆtonnement processes.

本文言語English
ページ(範囲)134-143
ページ数10
ジャーナルDiscrete Applied Mathematics
275
DOI
出版ステータスPublished - 2020 3 31
外部発表はい

ASJC Scopus subject areas

  • 離散数学と組合せ数学
  • 応用数学

フィンガープリント

「The discrete separation theorem and price adjustment directions in markets with heterogeneous commodities」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル