In my math courses, I have never come across the idea of being "too convex", but this is from an economics course. Essentially, you have some function $P(Q)$, where $Q>0$.
The model tells us to assume that $P(Q)$ is downward sloping, i.e. $P'(Q)<0$. Secondly, we are to assume that $P(Q)$ is not "too convex", i.e. $P'(Q)+QP''(Q) <0$.
I am probably forgetting something really basic from calculus, but why does $P'(Q)+QP''(Q) <0$ tell us that $P(Q)$ is not "too convex"?
Thank you.....
(Just to be clear, I recognize that this is not an Economics StackExchange. However, there is no theoretical/academic economic SE. Secondly, since the core of my question concerns math, I believe that it is still in the spirit of this SE.)
This may not be the correct answer, just my guess. I suggest you discuss with your professor or classmates.
If $f$ is twice differentiable, the $f^{''}\geq 0$ if and only if it is convex. And the larger $f^{''}$, the more convex it is. We can transform the condition to $P{''}(Q)< -\frac{P^{'}(Q)}{Q}$, where the RHS is positive. This gives an upper bound to $f^{''}$. So $f$ can't be too convex.