  So as to simplify the notation let \(g(C(t))\) denote the percentage rate of growth in \(C(t)\) (i.e. \(g(C(t)) = [dC(t)/dt]/C(t)\), which can be negative), and let \(\sigma(C)\) denote the elasticity of marginal well-being (i.e., \(\sigma(C) = -CU_{CC}/U_C \gt 0)\). Equation (7) then simplifies to