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

Harutaka Takahashi

The Japanese Economic Review, 2001, vol. 52, issue 3, 328-338

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.

Date: 2001
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