Economics seminar: An Envelope Theorem for Endogenous Functions

Event Date: 19 February 2014

Andrew Clausen,
University of Edinburgh

Time: 16.15-17.30

Dept. of Economics

Rm 2.11 Architecture Bldg

Abstract:

Optimisation problems often include endogenous functions such as value functions or non-linear prices.  Previous envelope theorems only establish first-order conditions for problems containing value functions.  Our envelope theorem applies to all endogenous functions and our novel proof technique allows us to drop concavity, equidifferentiability, and bounded derivative requirements.  The theory is widely applicable.  In unsecured credit models, neither interest rates nor continuation values are globally differentiable.  Nevertheless, we establish an Euler equation involving marginal prices and values.  In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s).  Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.

Published: 29 January 2014