I have a function with first-order derivatives and second-order derivatives .
Additionally I know that the degree of homogeneity of the function is larger than but smaller than .
In an economics paper I found the statement that given these assumptions the derivative of with regard to is negative if the first-order derivative with regard to is held constant:
Why is this so?
I understand that I can decompose into
Now, I would have to show that but I don't know how to do that using and the information about the degree of homogeneity.