Thanks for the gentle intro. Your explanation is clear, and I wish I could have watched it when I first learned the concept several years ago. That said, I argue that you explained only the primer to understand the Envelope Theorem, not yet touching the core of the theorem yet. In this video we solved for x*, writing it in terms of a, and substituting it for x so that we can find Y* in terms of a (i.e., the value function). This is faster than trying different values of a and conjecturing the effect of the change of a on the change of Y*. But this approach only quickens the process for objective functions with one endogenous variable x. Scholars usually call this approach "direct computation" of the the value function (before taking its derivative wst the parameter on hand). When there are multiple endogenous variables (e.g., x_1, x_2, ..., x_n), to find the relationship between Y* and a, you will have to take a partial derivative of Y with respect to each variable, amounting to n first-order-condition equations, which enable you to write x*_1, x*_2, ..., x*_n in terms of a. Ultimately, you have to substitute all these optimal variables (in the form of the parameter) back into the objective function to, FINALLY, take total derivative of Y* wrt a to find the relationship between Y* and the parameter. As you can see, this method starts to get messy very soon. A better way, and this is where the Envelope Theorem shines, is to simply ignore the indirect effect through which a affects the Y via those multiple endogenous variables, accounting for only the direct effect of a on Y*. This can be proved by using the chain rule when taking the total derivative of an objective function with multiple endogenous variables. And you can see that ∂Y/∂x*_1, ∂Y/∂x*_2, ∂Y/∂x*_3, ..., and ∂Y/∂x*_n will all be zeros, leaving the ∂Y/∂a the surviving term in the equation, hence quickening the process of finding the relationship between our ∂Y* and ∂a.
Cheers man your teaching style is so much clearer than my prof's!
Not all heroes wear capes. thanks a ton for these videos
Glad you like them!
Super-clear explanation with a really easy-to-understand example. Thank you.
You are welcome!
Thanks for a clear and lucid explanation. Much appreciated.
Glad it was helpful!
Thanks for the gentle intro. Your explanation is clear, and I wish I could have watched it when I first learned the concept several years ago.
That said, I argue that you explained only the primer to understand the Envelope Theorem, not yet touching the core of the theorem yet.
In this video we solved for x*, writing it in terms of a, and substituting it for x so that we can find Y* in terms of a (i.e., the value function). This is faster than trying different values of a and conjecturing the effect of the change of a on the change of Y*. But this approach only quickens the process for objective functions with one endogenous variable x. Scholars usually call this approach "direct computation" of the the value function (before taking its derivative wst the parameter on hand).
When there are multiple endogenous variables (e.g., x_1, x_2, ..., x_n), to find the relationship between Y* and a, you will have to take a partial derivative of Y with respect to each variable, amounting to n first-order-condition equations, which enable you to write x*_1, x*_2, ..., x*_n in terms of a. Ultimately, you have to substitute all these optimal variables (in the form of the parameter) back into the objective function to, FINALLY, take total derivative of Y* wrt a to find the relationship between Y* and the parameter.
As you can see, this method starts to get messy very soon.
A better way, and this is where the Envelope Theorem shines, is to simply ignore the indirect effect through which a affects the Y via those multiple endogenous variables, accounting for only the direct effect of a on Y*. This can be proved by using the chain rule when taking the total derivative of an objective function with multiple endogenous variables. And you can see that ∂Y/∂x*_1, ∂Y/∂x*_2, ∂Y/∂x*_3, ..., and ∂Y/∂x*_n will all be zeros, leaving the ∂Y/∂a the surviving term in the equation, hence quickening the process of finding the relationship between our ∂Y* and ∂a.
This is the best video. THANK YOU!
I appreciate that! Thank you for the comment and watching.
Thanks for the video, quite helpful for my analysis and optimization class.
That's great! Thanks for watching!
Very very very very interesting. Outstanding. Gorgeous. Superb. The best one. Thanks
just great im self studying all these mme topic and vedios like yours are helpful
Thank you so very much!! Really appreciate this video. Bless you!!!
This is extremely helpful. Thank you.
Thank you!
Very helpful! Thank you!
Awesome video..thank you
0:55 How did you get 20?
Adding 4x to both sides and then solving for X
very clear, thanks alot
You are welcome!
how do we apply this on the real world
169 approximates 161, not the other way around, no?
Y Starrrrrrrrrrrr, nice accent
Thank you for making me understand this theorem. So it gives you the wrong answer? WTF