theorem herfindahl_merger_increase {a_i a_j : ℝ} (hi : 0 < a_i) (hj : 0 < a_j) : 0 < (a_i + a_j) ^ 2 - a_i ^ 2 - a_j ^ 2 := by rw [herfindahl_merger_formula] positivity
thesis/CESProofs/Hierarchy/HerfindahlDynamics.lean:94
Herfindahl Dynamics: Entry, Exit, and Merger Effects on Concentration