• 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).

First thing I tried was this: First-Order = (a-2bQ) - (at-2bQt+c)
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).

First thing I tried was this: First-Order = (a-2bQ) - (at-2bQt+c)
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, $\displaystyle \frac{\partial TT}{\partial Q}$ and $\displaystyle \frac{\partial TT}{\partial t}$, and four (though two of them will be the same) second order derivatives, $\displaystyle \frac{\partial^2 TT}{\partial Q^2}$, $\displaystyle \frac{\partial^2 TT}{\partial t^2}$, and $\displaystyle \frac{\partial^2 TT}{\partial Q\partial t}= \frac{\partial^2 TT}{\partial t\partial Q}$.

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)