Tipping Points and Business-as-Usual in a Global Carbon Commons

This paper formulates a dynamic model of global carbon consumption in the absence of an effective international agreement. Each period, countries extract carbon from the global ecosystem. A country’s output depends both on its carbon usage and on“stored carbon” in the ecosystem. We characterize Business-as-usual (BAU) equilibria as smooth, Markov Perfect equilibrium profiles of carbon usage across countries. In any BAU equilibrium, the desired mix of extracted versus stored carbon by each country is determined by its stochastically evolving output elasticities with respect carbon input. A non-concavity in the carbon dynamic creates the possibility that global system reaches a tipping point, a threshold level of stored carbon stock below which the global commons collapses, spiraling downward toward a steady state of marginal sustainability. We show that if, in any BAU equilibrium, the profile of carbon factor elasticities reaches a high enough threshold, a tipping point will be breached. Ironically, the countries actually accelerate their rates of carbon usage the closer the carbon commons comes to tipping. Even so, there remains a time span (a “negotiation window”) in which a collapse may be averted if the countries agree to implement the socially efficient profile of carbon usage. JEL Codes: C73, D82, F53, Q54, Q58