Environmental externality and capital accumulation in an overlapping generations model with heterogeneous preference

We study an overlapping generations model á la Diamond in which two types of agents are alive at the same time. One type of agents cares about its own level of consumption and an idex of environmental quality, while the other type of agents carse only about its own consumption. At any period, the environmental quality is negatively affected by the saving decision of the previous generation, and this creates an intergenerational externality over time. Young agents that care about environmental quality can invest in productive capital and/or in environmental preservation, while the other agents can invest only in productive capital. We show that in such a framework, capital and environmental quality accumulation over time depend crucially on the characteristics of the technology. Furthermore, we derive a general condition for the local stability of a steady state implying an high level of capital and a high level of environmental quality. This stability condition depends on the relative effects of the capital and environmental quality on the saving functions of the individuals. Finally, we show that saddle-node bifurcations may arise in our model.