Chapter 10
A Complete Characterization of Optimal
Growth Paths in an Aggregated Model with a
Non-Concave Production Function
W. Davis Dechert and Kazuo Nishimura
10.1 Introduction
The convexity of technology has played a crucial role in economic analyses of
optimal one-sector growth problems. For example, two of the key results on the
traditional model of Ramsey (1928) that have relied on the convexity of the
technology are that optimal intertemporal growth involves moving monotonically
towards a unique steady state (as in Cass 1965; Koopmans 1965), and that the
value function is a concave differentiable function of the initial capital stock (as in
Benveniste and Scheinkman 1979). Moreover, convexity is a convenient assumption
in that it guarantees that the sequence of optimal stocks is uniquely determined
and that the first-order conditions (i.e., the Euler equation and the transversality
condition) are sufficient as well as necessary for optimality (as in Weitzman 1973).
Clark (1971) initiated an analysis, subsequently completed by Majumdar and
Mitra (1980), for a problem that was the equivalent of an optimal growth model
Journal of Economic Theory 31, 332–354, 1983
We wish to thank Professor W. A. Brock for calling our attention to the topic discussed in
this paper. We thank Professors W. A. Brock, David Cass and especially Tapan Mitra for many
helpful conversations and comments about the problem. We have also benefitted greatly from the
comments of the referee and the assistance of Mr. Kenji Yamamoto in preparing this draft. An
earlier version of the paper was presented at seminars at the University of Southern California and
the California Institute of Technology. Thanks are due to the participants of those seminars, too.
D. Dechert ()
Department of Economics, University of Houston, USA
e-mail: wdechert@gmail.com
K. Nishimura
Institute of Economic Research, Kyoto University, Japan
e-mail: nishimura@kier.kyoto-u.ac.jp
237 J. Stachurski et al. (eds.), Nonlinear Dynamics in Equilibrium Models,
https://doi.org/10.1007/978-3-642-22397-6_10
© The Author(s) 2021