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The Wong-Viner Envelope Theorem for subdifferentiable functions

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Author Info
Anthony Horsley
Andrew J Wrobel

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Abstract

The Wong-Viner Envelope Theorem on the equality of long-run and short-run marginalcosts (LRMC and SRMC) is reformulated for convex but generally nondifferentiable costfunctions. 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., toidentify suitable SRMCs as LRMCs. This goal is achieved by equating the profit-imputedvalues of the fixed inputs to their prices. Thus reformulated, the theorem is proved froma lemma on the sections of the joint subdifferential of a bivariate convex function. Thenew technique is linked to the Partial Inversion Rule of convex calculus.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Theoretical Economics Paper Series with number /2005/489.

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Date of creation: Apr 2005
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Handle: RePEc:cep:stitep:/2005/489

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Related research
Keywords: Wong-Viner Envelope Theorem; nondifferentiable joint costs; profit-imputedvaluation of fixed inputs; general equilibrium; public utility pricing.;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
D21 - Microeconomics - - Production and Organizations - - - Firm Behavior
D41 - Microeconomics - - Market Structure and Pricing - - - Perfect Competition

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Horsley, Anthony & Wrobel, Andrew J., 2002. "Efficiency rents of pumped-storage plants and their uses for operation and investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 109-142, November. [Downloadable!] (restricted)
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  2. Anthony Horsley & Andrew Wrobel, 2005. "Continuity of the equilibrium price density and its uses in peak-load pricing," Economic Theory, Springer, vol. 26(4), pages 839-866, November. [Downloadable!] (restricted)
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  1. Anthony Horsley & Andrew J Wrobel, 2005. "A Practical Short-run Approach to Market Equilibrium," STICERD - Theoretical Economics Paper Series /2005/488, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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