- #1
Bman12345
- 2
- 0
Hi there,
I have what I suspect is a straightforward question.
I wish to take the total derivative of the following function:
[itex]W(q,x) = q \cdot u(x) + c(q,x)[/itex]
Subject to the constraint: [itex]\frac{q}{x}[/itex]=[itex]\bar{m}[/itex], where [itex]\bar{m}[/itex] is some constant > 0, and c(q,x) is additively separable.
Without the constraint the total derivative is simply:
[itex] dW(q,x) = u(x) dq + q \cdot u_{x} dx + c_{q}(q,x) dq + c_{x}(q,x) dx [/itex]
My question is: How do I incorporate the constraint?
Thanks for any help!
Brent.
I have what I suspect is a straightforward question.
I wish to take the total derivative of the following function:
[itex]W(q,x) = q \cdot u(x) + c(q,x)[/itex]
Subject to the constraint: [itex]\frac{q}{x}[/itex]=[itex]\bar{m}[/itex], where [itex]\bar{m}[/itex] is some constant > 0, and c(q,x) is additively separable.
Without the constraint the total derivative is simply:
[itex] dW(q,x) = u(x) dq + q \cdot u_{x} dx + c_{q}(q,x) dq + c_{x}(q,x) dx [/itex]
My question is: How do I incorporate the constraint?
Thanks for any help!
Brent.