Abrupt positive feedback and the social cost of carbon

Optimal climate policy should act in a precautionary fashion to deal with tipping points that occur at some future random moment. The optimal carbon tax should include an additional component on top of the conventional present discounted value of marginal global warming damages. This component increases with the sensitivity of the hazard to temperature or the stock of atmospheric carbon. If the hazard of a catastrophe is constant, no correction is needed of the usual Pigouvian tax. The results are applied to a tipping point resulting from an abrupt and irreversible release of greenhouse gases from the ocean floors and surface of the earth, which set in motion a positive feedback loop. Convex enough hazard functions cause overshooting of the carbon tax, but a linear hazard function gives rise to undershooting. A more convex hazard function and a high discount rate speed up adjustment.