theorem sigma_rho_inverse {ρ : ℝ} (hρ : ρ ≠ 1) :
ρ = 1 - 1 / elasticityOfSubstitution ρ := by
simp only [elasticityOfSubstitution]
have h : (1 : ℝ) - ρ ≠ 0 := by intro h; apply hρ; linarith
field_simp
linarithEconomics extensions for CES formalization: