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The Wong-Viner envelope theorem for subdifferentiable functions

Horsley, Anthony and Wrobel, Andrew J. (2005) The Wong-Viner envelope theorem for subdifferentiable functions. TE, 489. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.

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Abstract

The Wong-Viner Envelope Theorem on the equality of long-run and short-run marginal costs (LRMC and SRMC) is reformulated for convex but generally nondifferentiable cost functions. The marginal cost can be formalized as the multi-valued subdifferential a.k.a. the subgradient set but, in itself, this is insufficient to extend the result effectively, i.e., to identify suitable SRMCs as LRMCs. This goal is achieved by equating the profit-imputed values of the fixed inputs to their prices. Thus reformulated, the theorem is proved from a lemma on the sections of the joint subdifferential of a bivariate convex function. The new technique is linked to the Partial Inversion Rule of convex calculus.

Item Type: Monograph (Discussion Paper)
Official URL: http://sticerd.lse.ac.uk
Additional Information: © 2005 the authors
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Journal of Economic Literature Classification System: D - Microeconomics > D4 - Market Structure and Pricing > D41 - Perfect Competition
D - Microeconomics > D2 - Production and Organizations > D21 - Firm Behavior
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Sets: Collections > Economists Online
Departments > Economics
Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: 489
Date Deposited: 11 Jul 2008 11:52
URL: http://eprints.lse.ac.uk/19309/

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