Lecture 38(A): The Envelope Theorem: How the Optimal Value Changes

The Envelope Theorem tells us how the optimal value changes when parameter values change.
The video begins with a simple example of a profit-maximizing firm, and an exercise.
Then we generalize the example to present and prove the Envelope Theorem.
We first prove the theorem for one variable and one parameter, and then for multiple variables and multiple parameters.

The Lectures 36(A & B) provide an important foundation for the theorem, and for optimization problems more generally:
https://www.youtube.com/watch?v=0RUamFRX-s4&t=65s
https://www.youtube.com/watch?v=aLSxRjAM5Is

Видео Lecture 38(A): The Envelope Theorem: How the Optimal Value Changes канала Arizona Math Camp