Environmental sustainability, nonlinear dynamics and chaos reloaded: 0 matters!

In this paper, we reconsider the overlapping generations (OLG) environmental model introduced in John and Pecchenino (1994) and Zhang (1999) by adopting the specification of the environmental dynamics proposed by Naimzada and Sodini (2010). The model is characterized by two different regimes that may alternate: one in which environmental evolution and economic growth co-evolve in the same direction; the other in which the environmental problem is not internalized by the agents, that is, the agents do not devolve any private resource to the environmental quality, leading to a possible trade-off between environment and economic growth. The analysis of the equilibrium dynamics, described by a two dimensional piecewise smooth map, shows that starting from a parametric configuration in which the dynamics are eventually driven by a unique regime, the increase of the negative effect of the agents’ consumption activity ends up in scenarios where the two regimes alternate, determining the rise of stable cycles or the occurrence of chaotic regimes. It is interesting to notice that because of the nonsmoothness of the map, the rise in environmental harm produced by economic activity may induce a sudden transition to chaotic regime.