Optimal economic growth with a random environmental shock

The government in a small open economy uses both an old 'dirty," or "polluting," technology and a new "clean" technology simultaneously. However, because of climate change, it should take into account that at some stage in the future it will be penalized for production based on the old technology. In this paper, pollution is alleviated through international agreements that restrict polluting activities. The government's incentives to invest in cleaner technologies are based on productivity of the technology and randomly increasing abatement costs for pollution in future. In contrast to the Schumpeterian model of creative destruction, both technologies can be used simultaneously. The technologies are subject to AK production functions. Assuming that the exogenous environmental shock follows a Poisson process, we use Pontryagin's maximum principle to find the optimal investment policy. We find conditions under which a rational government should invest all its resources in one technology, while the other is moderately run down, as well as conditions under which it should divide the investments between the technologies in a certain ratio