Do Natural Disasters Make Sustainable Growth Impossible?

We consider the prospects for sustainable growth using expected utility models of optimal investment under threat from a natural disaster. Extension of a discrete, two-period model, to continuous time over an infinite time horizon permits the analysis of sustainability under uncertainty regarding adverse events, including both one-time and recurrent disasters. Natural disasters, with destruction of productive capital, disrupt the optimal consumption and utility paths, but the Arrow et al. (2004) sustainability criterion is still satisfied even without adding strong or weak sustainability constraints. We also consider a separate natural resource sector and show that, except for extreme cases, the optimal steady state level of the renewable resource is not affected by the possibility of natural disasters. In the case of catastrophic events, however, damage to the resource system may be severe enough to push the system below a critical value tipping point, undermining the prospects of long-run sustainability.