theorem policyResponse_pos_crossing {J : ℕ} (hJ : 2 ≤ J) {ρ : ℝ} (hρ : ρ < 1)
{T_new T_old Tstar : ℝ} (hTs : 0 < Tstar)
(hNew_nn : 0 ≤ T_new) (hNew : T_new < Tstar) (hOld : Tstar ≤ T_old) :
0 < policyResponse J ρ T_new T_old Tstar := by
simp only [policyResponse]
rw [effectiveCurvatureKeff_above_critical J ρ T_old Tstar hTs hOld]
simp only [sub_zero]
exact effectiveCurvatureKeff_pos hJ hρ hNew_nn hTs hNewMonetary Policy and the Liquidity Trap