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NEW INSIGHTS FROM THE CANONICAL RAMSEY–CASS–KOOPMANS GROWTH MODEL

Published online by Cambridge University Press:  05 February 2020

Eric Nævdal*
Affiliation:
Ragnar Frisch Centre for Economic Research
*
Address correspondence to: Eric Nævdal, Frisch Centre, University of Oslo, Gaustadalléen 21, N-0349 Oslo, Norway. e-mail: eric.navdal@frisch.uio.no. Phone: +47 906 28 707.

Abstract

The present article presents novel results on the Ramsey–Cass–Koopmans growth model. It is shown that the shadow price of capital goes to infinity as the capital stock goes to zero even if all functions are bounded with finite derivatives and that imposing the Inada condition of infinite derivative of the per capita production function at zero stock is irrelevant. It is also shown that unless marginal utility at zero consumption is infinity, there will be a non-empty interval where the Keynes–Ramsey rule does not hold. The paper also shows that the stable saddle path in a phase diagram with the state variable and the shadow price has an unrecognized economic interpretation that enables us to illustrate the value function as the integral of the stable saddle path.

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Articles
Copyright
© Cambridge University Press 2020

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Footnotes

I have benefited from comments by Alexander Sigurdsson and an anonymous associate editor. I am grateful for funding from Norwegian Research Council’s program Environment 2015, project 196199.

References

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