Law of Conservation of the Capital-Output Ratio

Just as simple harmonic motion, definable by a variational condition, delta [unk] ((1/2) x(2) - (1/2) x(2)) dt = 0, has motions which must conserve the sum of kinetic and potential energies, (1/2) x(2) + (1/2)x(2) congruent with constant, so in a neoclassical von Neumann economy, where all output is saved to provide capital formation for the system's growth, it will be true that there exists a conservation law-namely the constancy along any intertemporally-efficient motion of the capital-output ratio SigmaP(t) (j)K(t) (j)/SigmaP(t) (j)K(t) (j). This is derived as an "energy" integral of a time-free integrand(1) in an optimal-control problem of variational type.