## A General and Intuitive Envelope Theorem (2017, with A. Clausen)

Previous envelope theorems establish differentiability of value functions. Our techniques apply to all functions whose derivatives appear in first-order conditions. We derive first-order conditions involving the derivatives of (i) the Stackelberg follower’s policy in a Stackelberg leader’s problem, and (ii) a borrower’s value function and default cut-off policy function in an unsecured credit economy. Our techniques also accommodate optimization problems involving discrete choices, infinite horizon stochastic dynamic programming, and Inada conditions.