Abstract

This paper shows that the Romer (1990)Journal of Political Economy, 98, 71–102 model of endogenous growth, its version for the social planning problem, has a unique steady state and is saddle path stable. The steady state can be monotonically reached by an appropriate choice of the initial values of the control variables if the initial values of the state variables lie in the vicinity of the steady state. For the original version, as well as for generalizations of it, we demonstrate that Hopf bifurcation can be excluded. We also demonstrate that the market variant of the Romer model as, for example, presented in Benhabib, Perli and Xie (1994)Ricerche Economiche, 48, 279–298, does admit Hopf bifurcation and stable periodic solutions. The technique employed here may be useful in studying other variants of endogenous growth models.

Author Keywords: Endogenous growth, Hopf bifurcation, cycles.

*1 The work on this paper was begun while Toichiro Asada was visiting the New School for Social Research and Willi Semmler was visiting Stanford University. The paper has benefited from discussions at seminars at the University of Augsburg, Germany; University of Bielefeld, Germany; Asia University, Tokyo; and the New School for Social Research, New York. We are grateful for communications and discussions with Jess Benhabib, Geoffrey Heal and Roberto Perli. We want also to thank Gang Gong for research assistance.

^f2 Author for correspondence.