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A simplified energy balance climate model is considered with the global mean temperature as the state variable, and an endogenous ice line. The movements of the ice line towards the Poles are associated with damage reservoirs where initial damages are high and then eventually vanish as the ice caps vanish and the damage reservoir is exhausted. We couple this climate model with a simple economic growth model and we show that the endogenous ice line induces a nonlinearity. This nonlinearity when combined with two sources of damages - the conventional damages due to temperature increase and the reservoir damages - generates multiple steady states and Skiba points. It is shown that the policy ramp implied by this model calls for high mitigation now. Simulation results suggest that the policy ramp could be U-shaped instead of the monotonically increasing with low starting mitigation gradualist policy ramp.
Brock, William; Engstrom, Gustav; and Xepapadeas, Anastasios, "Energy Balance Climate Models, Damage Reservoirs and the Time Profile of Climate Change Policy" (May 09, 2012). Fondazione Eni Enrico Mattei Working Papers. Paper 671.