A Nonsmooth Approach to Envelope Theorems

25 Pages Posted: 26 May 2015

See all articles by Olivier F. Morand

Olivier F. Morand

University of Connecticut - Department of Economics

Kevin Reffett

Arizona State University - Department of Economics

Suchismita Tarafdar

Shiv Nadar University, Department of Economics

Date Written: January 1, 2015

Abstract

We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian-Fromowitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems.

Keywords: Constrained Optimization with Nonconvexities, Envelope Theorems, Nonsmooth Analysis, stochastic growth, Lattice Programming

JEL Classification: D1, E1, E2

Suggested Citation

Morand, Olivier F. and Reffett, Kevin L. and Tarafdar, Suchismita, A Nonsmooth Approach to Envelope Theorems (January 1, 2015). Available at SSRN: https://ssrn.com/abstract=2609292 or http://dx.doi.org/10.2139/ssrn.2609292

Olivier F. Morand

University of Connecticut - Department of Economics ( email )

Unit 1063
Storrs, CT 06269-1063
United States

Kevin L. Reffett

Arizona State University - Department of Economics ( email )

Tempe, AZ 85287-3806
United States

Suchismita Tarafdar (Contact Author)

Shiv Nadar University, Department of Economics ( email )

NH-91, Village- Chithera, Tehsil-Dadri,
Dist. Gautam Buddha Nagar, UP
Gautam Buddha Nagar, Uttar Pradesh
India

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