Resource Depletion and Capital Accumulation under Catastrophic Risk: The Role of Stochastic Thresholds and Stock Pollution

An intertemporal optimal strategy for accumulation of reversible capital and management of an exhaustible resource is analyzed for a global economy when resource depletion generates discharges that add to a stock pollutant that affects the likelihood for hitting a tipping point or threshold of unknown location, causing a random“disembodied technical regress”. We characterize the optimal strategy by imposing the notion “precautionary tax” on current extraction. Such a tax will internalize future expected damages or expected welfare loss should a threshold be hit. With reversible capital the presence of a stochastic threshold should speed up accumulation as long as no threshold is hit so as to build up a buffer or stock for future consumption should a threshold be hit.