@techreport{ef28e85b00824659ae8ceba4984f7941,
title = "A General and Intuitive Envelope Theorem",
abstract = "Previous envelope theorems establish differentiability of value functions inconvex settings. Our envelope theorem applies to all functions whose derivatives appear in first-order conditions, and in non-convex settings. For example, in Stackelberg games, the leader{\textquoteright}s first-order condition involves the derivative of the follower{\textquoteright}s policy. Similarly, we differentiate (i) the borrower{\textquoteright}s value function and default cut-off policy function in an unsecured credit economy, (ii) the firm{\textquoteright}s value function in a capital adjustment problem with fixed costs, and (iii) the households{\textquoteright} value functions in insurance arrangements with indivisible goods. Our theorem accommodates optimization problems involving discrete choices, infinite horizon stochastic dynamic programming, and Inada conditions.",
author = "Andrew Clausen and Carlo Strub",
note = "Update of version number 248",
year = "2016",
month = apr,
day = "8",
language = "English",
series = "ESE Discussion Papers",
publisher = "Edinburgh School of Economics Discussion Paper Series",
number = "274",
type = "WorkingPaper",
institution = "Edinburgh School of Economics Discussion Paper Series",
}