theorem marginal_externality_pos {J ρ c : ℝ}
(hJ : 1 < J) (hρ0 : 0 < ρ) (hρ1 : ρ < 1) (hc : 0 < c) :
0 < J * valueFunctionDeriv J ρ c :=
mul_pos (by linarith) (valueFunctionDeriv_pos hJ hρ0 hρ1 hc)Paper 1c: Formal Calculus on K(J) and V(J)