theorem curvature_decreasing_in_H {ρ H₁ H₂ : ℝ}
(hρ : ρ < 1) (hH12 : H₁ < H₂) :
(1 - ρ) * (1 - H₂) < (1 - ρ) * (1 - H₁) := by
apply mul_lt_mul_of_pos_left _ (by linarith)
linarithHerfindahl Dynamics: Entry, Exit, and Merger Effects on Concentration