On the demand generated by a smooth and concavifiable preference ordering

Leonid Hurwicz, James Jordan, Yakar Kannai

Research output: Contribution to journalArticle

5 Citations (Scopus)

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

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Derivatives
Partial derivative
Single valued
Continuously differentiable
Strictly Convex
Utility Function
Differentiable
Quotient
Infinity
Demand
Commodities
Derivative

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics
  • Applied Mathematics

Cite this

Hurwicz, Leonid ; Jordan, James ; Kannai, Yakar. / On the demand generated by a smooth and concavifiable preference ordering. In: Journal of Mathematical Economics. 1987 ; Vol. 16, No. 2. pp. 169-189.
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On the demand generated by a smooth and concavifiable preference ordering. / Hurwicz, Leonid; Jordan, James; Kannai, Yakar.

In: Journal of Mathematical Economics, Vol. 16, No. 2, 1987, p. 169-189.

Research output: Contribution to journalArticle

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