• Sep 1st 2009, 03:50 AM
econmajor
Hey Guys, I'm having some serious trouble with a profit function, and hoping someone can help soon!

TT= (aQ-bQ^2)-(t(aQ-bQ^2) + cQ).

which could then be this:(I think)

TT= (aQ-bQ^2)-(taQ-tbQ^2) + cQ): But, can I skip this part and just find the First-Order?

I need to find the First and Second Order derivitives, but the extra variable (t) is the one I'm having problems with. In this function (t) represents taxes, (just FYI).

Do I also need to take the partial derivative of (t)?
Second-Order = is also trippin me up.

If anyone can help I would be very thankful. (Wondering)
• Sep 1st 2009, 06:17 AM
HallsofIvy
Quote:

Originally Posted by econmajor
Hey Guys, I'm having some serious trouble with a profit function, and hoping someone can help soon!

TT= (aQ-bQ^2)-(t(aQ-bQ^2) + cQ).

which could then be this:(I think)

TT= (aQ-bQ^2)-(taQ-tbQ^2) + cQ): But, can I skip this part and just find the First-Order?

I need to find the First and Second Order derivitives, but the extra variable (t) is the one I'm having problems with. In this function (t) represents taxes, (just FYI).

Do I also need to take the partial derivative of (t)?
Second-Order = is also trippin me up.

If anyone can help I would be very thankful. (Wondering)

Find the first and second derivatives with respect to what variable?

If you want to find the derivatives with respect to Q (what you appear to be doing), then t is just treated as a constant.

If you are asked to find all first and second partial derivatives, then there are two first order derivatives, $\frac{\partial TT}{\partial Q}$ and $\frac{\partial TT}{\partial t}$, and four (though two of them will be the same) second order derivatives, $\frac{\partial^2 TT}{\partial Q^2}$, $\frac{\partial^2 TT}{\partial t^2}$, and $\frac{\partial^2 TT}{\partial Q\partial t}= \frac{\partial^2 TT}{\partial t\partial Q}$.

Each partial derivative with respect to the given variable, is taken exactly like an ordinary derivative, treating the other variable as if it were a constant.
• Sep 1st 2009, 10:37 AM
econmajor
Quote:

Find the first and second derivatives with respect to what variable?

If you want to find the derivatives with respect to Q (what you appear to be doing), then t is just treated as a constant.

If you are asked to find all first and second partial derivatives, then there are two first order derivatives, http://www.mathhelpforum.com/math-he...25e01699-1.gif and http://www.mathhelpforum.com/math-he...79501c38-1.gif, and four (though two of them will be the same) second order derivatives, http://www.mathhelpforum.com/math-he...5e326b11-1.gif, http://www.mathhelpforum.com/math-he...075ea30c-1.gif, and http://www.mathhelpforum.com/math-he...2b5a654a-1.gif.

Each partial derivative with respect to the given variable, is taken exactly like an ordinary derivative, treating the other variable as if it were a constant.
Ok, I do need to take the derivative to all variables, but I'm not familiar with that. Normally I would be fine if asked to take the First and Second derivatives of just Q. The extra variable is confusing me.

Thanks, I can find this in the text book, but can you actually show me what it would look like??????????????

I know I've just gotten confused somewhere, and need the extra help to understand it, especially after looking at it for the past two days. I can go to my professor for hints, but I was hoping someone on this forum would be a little more helpful than he would be.

This is not a test question or even a HW question that holds value. But I need to understand this before I can move on to the next material in class. We move on to Matrix Algebra this afternoon and I'd like to feel comfortable with this Function, before doing so.

(Crying)