The von Neumann Facet and Optimal Cycles with with Small Discounting

This paper presents a standard two-sector optimal growth model with general neoclassical production functions: strictly quasi-concave, twice continuously differentiable homogeneous of degree one functions. The following two results will be established when the discount factor is sufficiently close to 1: a) under either capital intensity condition defined at an optimal steady state (OSS), a dynamical system displays simple dynamics: any optimal path converges either to OSS or to a cycle of period two. b) given the capital intensity condition such that the consumption sector is more capital intensive, and the discount factor is sufficiently close to one, then under some combination of parameters of technologies, a depreciation rate and a discount factor, any optimal path converges to a cycle of period two. In a subsidiary argument, it will also be established that if the discount factor is sufficiently close to one and some other conditions of parameter values hold for such a discount factor, the Turnpike Property holds.