On the demand generated by a smooth and concavifiable preference ordering |
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Institution: | 1. Department of Finance, College of Business Administration, King Saud University, Riyadh, Saudi Arabia;2. Faculty of Economic sciences and Management of Sousse, University of Sousse, Sousse, Tunisia;3. IPAG Lab, IPAG Business School, Paris, France;4. International Finance Group – Tunisia |
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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. |
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