The local bifurcation of Ramsey equilibrium

Summary The elasticity of substitution has been proposed as one factor in the generation of aggregate fluctuations in dynamic models with incomplete markets. We study the existence of periodic solutions in a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous agents. A dynamical system representing an equilibrium profile with only the most patient agent holding capital is analyzed when capital income is not an increasing function of total capital. Conditions for the linear approximation system at a steady state to have an eigenvalue of — 1 are found. A one-parameter family of maps based on a perturbation of the production function is introduced and the dynamical system is reduced to 1 dimension via an application of a center manifold theorem. Conditions for a stable flip bifurcation are shown to hold at the steady state.This paper is dedicated to Professor Nicolas Spulber, one of the great pioneers in the study of growth theory. He brought us together and encouraged our joint work on Ramsey equilibrium theory.We thank Nicolas Spulber for his usual insightful comments and we thank Michele Boldrin for a useful discussion. We also thank a referee for suggesting improvements in the paper as well as the seminar participants at the University of Rochester and Cornell University for their comments on the paper.