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WHY IS OPTIMAL GROWTH THEORY MUTE? RESTORING ITS RIGHTFUL VOICE

Published online by Cambridge University Press:  30 January 2018

Olivier de La Grandville
Olivier de La Grandville*
Affiliation:
Stanford University and Goethe University, Frankfurt am Main
*
Address correspondence to: Olivier de La Grandville, Department of Management Science and Engineering, Stanford University, Huang Engineering Center, Via Ortega 475, Stanford, CA 94305, USA; e-mail: odelagrandville@gmail.com.
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Abstract

Optimal growth theory as it stands today does not work. Using strictly concave utility functions systematically inflicts on the economy distortions that are either historically unobserved or unacceptable by society. Moreover, we show that the traditional approach is incompatible with competitive equilibrium: Any economy initially in such equilibrium will always veer away into unwanted trajectories if its investment is planned using a concave utility function. We then propose a rule for the optimal savings-investment rate based on competitive equilibrium that simultaneously generates three intertemporal optima for society. The rule always leads to reasonable time paths for all central economic variables, even under very different hypotheses about the future evolution of population and technical progress.

Keywords

Optimal Savings RateCalculus of VariationsOptimal Control
Type
Articles
Information
Macroeconomic Dynamics , Volume 22 , Special Issue 1: Current Macroeconomic Challenges , January 2018 , pp. 77 - 100
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

A preliminary preprint of this article appeared in our book Economic Growth: a Unified Approach [La Grandville (2017)]. I want to acknowledge the invaluable help extended to me by my colleague Ernst Hairer without which I would not have been able to put the utility functions to the test of competitive equilibrium. The numerical solutions of the resulting differential equations and the spectacular diagrams are due to him. I am also very grateful to Kenneth Arrow, Michael Binder, Giuseppe De Arcangelis, Giovanni Di Bartolomeo, Robert Chirinko, Daniela Federici, Robert Feicht, Giancarlo Gandolfo, Jean-Marie Grether, Erich Gundlach, Andreas Irmen, Bjarne Jensen, Anastasia Litina, Miguel Leon-Ledesma, Rainer Klump, Peter McAdam, Bernardo Maggi, Enrico Saltari, Wolfgang Stummer, Robert Solow, Juerg Weber, and Milad Zarin-Nejadan, as well as to participants in seminars at Stanford, Frankfurt, Luxembourg, and Rome (La Sapienza) for their highly helpful remarks. The very constructive comments and suggestions of two referees are also gratefully acknowledged.

References

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