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Law of Conservation of the Capital-Output Ratio*

Authors
  • Paul A. Samuelson
Publication Date
Nov 01, 1970
Source
PMC
Keywords
License
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Abstract

Just as simple harmonic motion, definable by a variational condition, δ [unk] (½ ẋ2 - ½ x2) dt = 0, has motions which must conserve the sum of kinetic and potential energies, ½ ẋ2 + ½x2 ≅ 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 ΣPtjKtj/ΣPtjKt j. This is derived as an „energy” integral of a time-free integrand1 in an optimal-control problem of variational type.

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