HOPF CYCLES IN ONE-SECTOR OPTIMAL GROWTH MODELS WITH TIME DELAY

Abstract

This paper analyzes the existence of Hopf bifurcation and establishes the conditions under which the equilibrium path converges toward periodic solutions in a one-sector optimal growth model with delay. We establish the limits and the possibilities of nonlinear dynamics (i.e., cycles) vis-a-vis delays. In particular, we formulate a new method to further comprehend the root distribution of the characteristic equation of a standard optimal growth model with delayed investment structure. We show that non-monotonic dynamics (limit cycles, persistent oscillations) occurs when the delayed investment causes permanent adjustment failures among the economic variables in the economy.