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.
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U2 - 10.1016/0304-4068(87)90006-1
DO - 10.1016/0304-4068(87)90006-1
M3 - Article
AN - SCOPUS:38249036110
SN - 0304-4068
VL - 16
SP - 169
EP - 189
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
IS - 2
ER -