theorem perCapitaSurplusDeriv_neg {J ρ : ℝ} (hJ : 2 < J) (hρ : ρ < 1) :
perCapitaSurplusDeriv J ρ < 0 := by
simp only [perCapitaSurplusDeriv]
apply div_neg_of_neg_of_pos
· exact mul_neg_of_pos_of_neg (by linarith) (by linarith)
· exact pow_pos (by linarith) 3Paper 1c: Formal Calculus on K(J) and V(J)