Further, by Hotelling's Lemma Ym = ∂ R/∂ Pm is the supply equation for Ym (where Y denotes output and m the specific product), so R is convex in P (own-price supply responses are non- negative; ∂2 R/∂ Pm2 = ∂Ym/∂ Pm ≥ 0). There is, however, no condition ...