A new approach to the envelope theorem

We study the di¤erentiability of the value function of a constrained optimization problem. We consider the envelope-theorem framework of Milgrom and Segal (2002), and we accomplish two goals. We show how one can relax Milgrom and Segal’s assumption that the choice set does not vary with parameters. More importantly, we develop a new approach to proving the di¤erentiability of the value function. The key idea and main mathematical tool we employ in our approach are a novel feature in the literature dealing with the di¤erentiability of the value function.