Violation of the Law of Demand

Yakar Kannai, Larry Selden

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Following the classic work of Mitjuschin, Polterovich and Milleron, necessary and sufficient as well as sufficient conditions have been developed for when the multicommodity Law of Demand holds. We show when the widely cited Mitjuschin and Polterovich sufficient condition also becomes necessary. Using this result, violation regions for the very popular Modified Bergson (or hyperbolic absolute risk aversion) class of utility functions are fully characterized in terms of preference parameters. For a natural extension of the constant elasticity of substitution member of the Modified Bergson family that is neither homothetic nor quasihomothetic, we create the first simple, explicit example of which we are aware that (i) fully characterizes violation regions in both the preference parameter and commodity spaces and (ii) analyzes the range of relative income and price changes within which violations occur.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalEconomic Theory
Issue number1
StatePublished - Jan 2014
Externally publishedYes


  • Law of Demand
  • Minimum concavity point
  • Monotonicity
  • Violation region


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