Hotelling's lemma is a result in microeconomics that relates the supply of a good to the profit of the good's producer. It was first shown by Harold Hotelling, and is widely used in the theory of the firm. The lemma is very simple, and can be stated:
Let
for
The proof of the theorem stems from the fact that for a profit-maximizing firm, the maximum of the firm's profit at some output
The proof is also a corollary of the envelope theorem.