Bifurcations and Chaotic Attractors in an Overlapping Generations Model with Negative Environmental Externalities

We analyze an overlapping generations model with the following features. There exists a continuum of identical individuals whose welfare depends on leisure, on the stock E of a free access environmental good and on the consumption C of a private good. The private good is produced by a continuum of identical perfectly competitive firms via a constant returns technology (represented by a Cobb–Douglas production function); the representative firm uses physical capitalK and labour L of the representative individual as productive inputs. Each economic agent considers as negligible the negative impact of his choices on the environmental good; this implies that the choices of each agent generate negative externalities on the others. Following Zhang (1999), Antoci et al. (2007) and Itaya (2008) (among the others), we assume that individuals’ utility function is non separable in E and C; that is, the marginal utility of C depends on the value of E; in particular, we consider both the cases in which marginal utility increases (i.e. C and E are substitutes) and decreases (i.e. C and E are complements) when the value of E decreases.