Resource extraction and uncertain tipping points

A global planning problem is analyzed for extracting an exhaustible resource like oil when resource extraction - the only source for current consumption - also generates additions to the stock of GHGs that influence the likelihood of hitting a threshold representing climate change. We derive conditions for optimal extraction when we take into account joint emissions that accumulate to a stock that is governing the planner's beliefs of facing a climate change that will involve a loss in the production capacity of the global economy. Except for "annuity of the continuation payoff", which is the stationary rate of welfare after a climate change, the optimality conditions are very similar to the results found in Loury (1978) - where optimal extraction of a non-renewable resource of unknown size was analyzed. Not surprisingly we find that extraction has a cost ("environmental cost") beyond the standard opportunity cost ("resource rent"), implying a lower rate of extraction as long as no threshold has been hit, compared to the risk-free case. Such saving has an expected rate of return along an optimal strategy should be balanced against the standard required rate of return - the Keynes- Ramsey-Cass-Koopmans-condition.