Hotelling's Lemma

$$\begin{array}{rlr}\frac{\partial \pi (w,r,p)}{\partial p}& =x(w,r,p)& \text{output supply}\\ \frac{\partial \pi (w,r,p)}{\partial w}& =-l(w,r,p)& \text{labor demand}\\ \frac{\partial \pi (w,r,p)}{\partial r}& =-k(w,r,p)& \text{capital demand}\end{array}$$