The atmospheric carbon resilience problem: A theoretical analysis

We study a dynamic carbon pollution model where carbon accumulates both inside a nonrenewable and a renewable reservoir with a constant regeneration rate. Two primary energy sources are available: a cheap exhaustible fossil fuel (coal) and an expensive clean energy alternative (solar). To avoid catastrophic climate events, the global carbon concentration has to remain below some critical mandated ceiling. We show that there exists an upper bound on the coal endowment that can be consumed, which distinguishes two main cases: coal is initially abundant or scarce. If the energy sector has to provide a constant aggregate energy flow to the final users, cost-effectiveness requires that the global ceiling should be attained only when solar energy is introduced. Then the economy stays forever at the ceiling and coal use is progressively replaced by solar energy use. In the abundant coal case, this energy sources substitution process lasts for an infinite duration while in the scarce coal case, coal exploitation ends in finite time. Under a welfare maximization criterion, if coal is abundant, we show that the economy may follow a sequence of phases at the ceiling and below the ceiling before the final transition towards clean energy.