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 the ecosystem ("stored carbon"). The desired mix of extracted versus stored carbon by each country is determined by its stochastically evolving factor elasticities. We characterize Business-as-usual (BAU) equilibria as smooth, Markov Perfect equilibrium profiles of carbon usage across countries. A BAU equilibrium is shown to generate lower aggregate output and higher carbon use each period than the socially efficient path, although some countries might actually use less carbon under BAU. We characterize properties of {\em tipping points}, threshold levels of stored carbon stocks below which the global commons collapses, spiraling downward toward a steady state of marginal sustainability. We show that if the profile of carbon factor elasticities reaches a high enough threshold, a tipping point will be breached. Even in this case, there remains a time span (a "negotiation window") in which a collapse may be averted if the countries agree to implement the efficient profile of carbon usage.