The Wong-Viner Envelope Theorem for subdifferentiable functions

Anthony Horsley and Andrew Wrobel

STICERD - Theoretical Economics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

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.

Keywords: Wong-Viner Envelope Theorem; nondifferentiable joint costs; profit-imputedvaluation of fixed inputs; general equilibrium; public utility pricing. (search for similar items in EconPapers)
JEL-codes: C61 D21 D41 (search for similar items in EconPapers)
Date: 2005-04
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Related works:
Working Paper: The Wong-Viner envelope theorem for subdifferentiable functions (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stitep:489

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