theorem pigouvian_subsidy_decreasing {J₁ J₂ ρ : ℝ}
(hJ₁ : 0 < J₁) (hρ : ρ < 1) (hJ : J₁ < J₂) :
marginalK J₂ ρ < marginalK J₁ ρ := by
simp only [marginalK]
apply div_lt_div_of_pos_left (by linarith) (sq_pos_of_pos hJ₁)
exact sq_lt_sq' (by linarith) hJCore definitions for the Lean formalization of Paper 1c: