### 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 language | English (US) |
---|---|

Pages (from-to) | 169-189 |

Number of pages | 21 |

Journal | Journal of Mathematical Economics |

Volume | 16 |

Issue number | 2 |

DOIs | |

State | Published - 1987 |

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### All Science Journal Classification (ASJC) codes

- Economics and Econometrics
- Applied Mathematics

### Cite this

*Journal of Mathematical Economics*,

*16*(2), 169-189. https://doi.org/10.1016/0304-4068(87)90006-1

}

*Journal of Mathematical Economics*, vol. 16, no. 2, pp. 169-189. https://doi.org/10.1016/0304-4068(87)90006-1

**On the demand generated by a smooth and concavifiable preference ordering.** / Hurwicz, Leonid; Jordan, James; Kannai, Yakar.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the demand generated by a smooth and concavifiable preference ordering

AU - Hurwicz, Leonid

AU - Jordan, James

AU - Kannai, Yakar

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38249036110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249036110&partnerID=8YFLogxK

U2 - 10.1016/0304-4068(87)90006-1

DO - 10.1016/0304-4068(87)90006-1

M3 - Article

AN - SCOPUS:38249036110

VL - 16

SP - 169

EP - 189

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 2

ER -