Eventual periodicity in the two-sector RSL model: equilibrium vis-à-vis optimum growth

This paper investigates the well-known phenomenon of eventual periodicity of Li–Yorke chaos in the context of the two-sector Robinson–Shinkai–Leontief model of economic growth. It locates its (i) presence under specific parameter restrictions that include the extreme classical saving specification, and its (ii) absence in savings generated by the optimization of an infinitely-lived representative agent with perfect foresight. These results in which rare events, chaos and stability are all brought together under the rubric of upward and downward inertia, while of substantive economic interest of their own, also highlight phenomena in economic dynamics that may go towards a clearer definitional understanding of chaotic systems.