Ordients: Optimization and comparative statics without utility functions

• 成果类型: Article
• 署名作者: Renou, Ludovic; Schlag, Karl H.
• 署名单位: University of Essex; University of Vienna
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2014.09.013
• 发表日期: 2014
• 页码: 612-632
• 关键词: Binary relation; Ordient; maxima; Envelope theorem; Implicit function theorem

摘要

This paper introduces the concept of ordient for binary relations (preferences), a relative of the concept of gradient for functions (utilities). Ordients have a natural economic interpretation as marginal rates of substitution. Some examples of ordientable binary relations include the lexicographic order, binary relations resulting from the sequential applications of multiple rationales or binary relations with differentiable representations. We characterize the constrained maxima of binary relations through ordients and provide an implicit function theorem and an envelope theorem. (c) 2014 Elsevier Inc. All rights reserved.