On the demand generated by a smooth and concavifiable preference ordering

Leonid Hurwicz, James Jordan, Yakar Kannai

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

It is shown that if a consumer's preference ordering is strictly convex and is representable by means of a concave, twice continuously differentiable utility function, then the partial derivative of a demanded commodity with respect to its price is bounded from above in a neighborhood of a price vector at which the demand fails to be differentiable. In the case of two commodities, if the demand does not possess finite derivatives with respect to prices at a certain point, then the partial 'derivative' of a commodity with respect to its price is equal to minus infinity. The same result holds for n commodities under 'almost every' choice of coordinates in the commodity space. If preferences are weakly convex but the same representation assumption holds, demand may not be single-valued but own-price difference quotients are still bounded from above.

Original languageEnglish (US)
Pages (from-to)169-189
Number of pages21
JournalJournal of Mathematical Economics
Volume16
Issue number2
DOIs
StatePublished - 1987

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'On the demand generated by a smooth and concavifiable preference ordering'. Together they form a unique fingerprint.

Cite this