Sustainable growth and environmental catastrophes

In the standard AK growth model we introduce the threat of an ecological catastrophe and study the consequences for the economic variables in the long-run. We extend the basic framework by considering two environmental externalities: the first one is local and gives account of the marginal damage from emissions flow; the second one is aggregate, or global, and relates to the extreme damage which may happen if the accumulated stock of pollutants is on the threshold of a worldwide catastrophe. In this context dominated by market failures, we focus on the socially optimal solution and the search of conditions for sustainability. We identify the efficient balanced growth path, which may even show a singularity with trajectories truncating and changing course. In short, with respect to the economy's long-run performance, we study how environment matters in different ways and at different stages, giving conditions to prevent the catastrophe and preserve (a lower) sustained growth. This paper may also be read as a clear and rigorous example of an optimal control problem involving a pure state-space constrain