On the stability properties of a delay differential neoclassical model of economic growth

Abstract

The main aim of this paper is to establish sharp global stability conditions for the positive equilibrium of a well-known model of economic growth when a delay is considered in the production function. In order to deal with a broad scenario, we establish some results of global attraction for a general family of differential equations with variable delay; for it, we use the notion of strong attractor, which allows us to simplify the proofs, as well as to generalize previous results. Our study reveals that sometimes production delays are not able to destabilize the positive equilibrium, even if they are large. In other cases, the stability properties of the equilibrium depend on the interaction between the delay and other relevant model parameters, leading sometimes to stability windows in the bifurcation diagram.

Keywords

• delay differential equation
• neoclassical growth model
• global stability
• stability switches
• lasota equation
• gamma-ricker map