Stable Optimal Cycles With Small Discounting in a Two-sector Discrete-time Model: A Non-bifurcation Approach

Abstract

This paper presents a standard two-sector optimal growth model with general neoclassical production functions: strictly quasi-concave, twice continuously differentiable homogeneous of degree 1 functions. Instead of applying the standard local bifurcation theory, I exploit two well established properties in Turnpike Theory—“simple dynamics” and the Neighbourhood Turnpike— and, combining both results, I demonstrate that there exists an interval of the discount factor near 1 such that a corresponding optimal steady state is totally unstable and an optimal path converges asymptotically to a two-period cycle for a chosen discount factor in it. JEL Classification Numbers: O21, O41.