The author establishes a property of supply for a competitive firm: Assuming differentiability of the production frontier, linearly independent price vectors have disjoint image sets under the supply mapping. This property supports the main results. First, the author drew a simple proof of McFadden's proposition that differentiability of the production frontier is necessary and sufficient for strict quasi-convexity of the profit function. This proposition rules out linearity of the profit function on any subset of price domain, in turn ruling out supply and input-demand functions that are constant and have zero values for all price effects. Second, for discrete price changes, own-price effects in supply are strictly positive, assuming a differentiable technology. In this context, strict convexity of the production set is irrelevant. The author indicates implications for cost and demand theory. (Contains 8 notes and 1 figure.)