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SUBSTITUTION AND COMPLEMENTARITY OF GOODS IN TERMS OF UTILITY FUNCTION
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SUBSTITUTION AND COMPLEMENTARITY OF GOODS IN TERMS OF UTILITY FUNCTION
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Authors
Vladimir Danilov 
Edition
Volume 51 Issue 4
Pages
25-36
Abstract

In The Paper We Consider A Problem Of Characterization Of Utility Functions Which Generates Gross Substitute Demand. Let F Be A Concave Function; We Consider It As A Utility Function Of Some Comsumer Expressed In Terms Of Money. This Means That Demand (At A Price P) Is Formed As Solunion Of The Problem F(X)–P(X) → Max. Such A Function Is A GS-Function If An Increasing Of Price Of Any Good Yields Increasing Of Demand Of Other Goods. We Prove That F Is A GS-Function If And Only If The Conjugate Function F * Is Supermodular. As A Corollary We Prove That Any GS-Function Is Submodular. We Provide Also A Rule For Calculation Of The Derivative Of The Convolution Of Several Concave Functions.

Keywords
concave functions, supermodularity, submodularity, Fenchel duality
Date of publication
01.10.2015
Number of purchasers
1
Views
751
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Additional sources and materials

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Danilov V.I., Koshevoj G.A., Lang K. (2013). Ravnovesiya na rynke nedelimykh tovarov // Zhurnal Novoj ehkonomicheskoj assotsiatsii. T. 2(18). S. 10–34.


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Danilov V.I., Koshevoy G.A., Lang C. (2003). Gross Substitution, Discrete Convexity, and Submodularity // Discrete Applied Mathematics. Vol. 131. P. 283–298.


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Murota K. (2003). Discrete Convex Analysis. Philadelphia: SIAM.


Topkis D.M. (1998). Supermodularity and Complementarity. Princeton: Princeton Univ. Press.

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