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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
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: [email protected]. Phone: +47 906 28 707.
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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.

Keywords

Economic GrowthRamsey–Cass–Koopmans ModelOptimal ControlStable Saddle Path
Type
Articles
Information
Macroeconomic Dynamics , Volume 25 , Issue 6 , September 2021 , pp. 1569 - 1577
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

REFERENCES

Acemoglu, D. (2009) Introduction to Modern Economic Growth. Princeton: Princeton University Press.Google Scholar
Becker, R. A. and Mitra, T. (2012) Efficient ramsey equilibria. Macroeconomic Dynamics 16(S1), 18–32.10.1017/S1365100511000538CrossRefGoogle Scholar
Bénassy, J.-P. (2011) Macroeconomic Theory. New York: Oxford University Press.10.1093/acprof:osobl/9780195387711.001.0001CrossRefGoogle Scholar
Biljanovska, N. (2019) Optimal policy in collateral constrained economies. Macroeconomic Dynamics 23(2), 798–836.10.1017/S1365100517000049CrossRefGoogle Scholar
Blanchard, O. J. and Fischer, S. (1989). Lectures on Macroeconomics. Cambridge: MIT Press.Google Scholar
Guo, S. and Jiang, Z. (2017) Optimal fiscal policy with land financing in China. Macroeconomic Dynamics 21(8), 1–26.Google Scholar
Judd, K. L. (1998) Numerical Methods in Economics. Cambridge MA: MIT Press.Google Scholar
Romer, D. (2006) Advanced Macroeconomics (Third edition). New York: McGrawHill/Irwin.Google Scholar
Spear, S. E. and Young, W. (2014) Optimum savings and optimal growth: The Cass–Malinvaud–Koopmans nexus. Macroeconomic Dynamics 18(1), 215–243.10.1017/S1365100513000291CrossRefGoogle Scholar
Wikipedia contributors (2019). Ramsey–Cass–Koopmans model. Wikipedia, The Free Encyclopedia, 17 June 2019. Web. 14 August 2019.Google Scholar