Consistency of the doctor-optimal equilibrium price vector in job-matching markets

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Abstract

In a many-to-many variation of Kelso and Crawford's (1982) and Kojima et al.'s (2019) job-matching model, we prove that the doctor-optimal equilibrium price vector satisfies a striking property termed consistency. It states that the price vector remains an equilibrium price vector in the market where an arbitrary doctor reduces her capacity by one. Combining consistency with Kojima et al.'s (2019) result, we delineate how the set of equilibrium price vectors moves when a doctor reduces her capacity by one: the set moves up but still contains the original doctor-optimal equilibrium price vector. We apply this result to establish comparative statics of welfare at equilibrium. As a byproduct, we also provide a simple and short proof of the claim that the doctor-optimal stable mechanism is a pivotal mechanism under quasi-linear preferences.

Original languageEnglish
Article number105346
JournalJournal of Economic Theory
Volume197
DOIs
Publication statusPublished - 2021 Oct
Externally publishedYes

Keywords

  • Comparative statics
  • Competitive equilibria
  • Discrete convex analysis
  • Job matching
  • Strategy-proofness

ASJC Scopus subject areas

  • Economics and Econometrics

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