Optimal Timing of Carbon Capture Policies Under Alternative CCS Cost Functions

We determine the optimal exploitation time-paths of three types of perfect substitute energy resources: The first one is depletable and carbon-emitting (dirty coal), the second one is also depletable but carbon-free thanks to a carbon capture and storage (CCS) process (clean coal) and the last one is renewable and clean (solar energy). We assume that the atmospheric carbon stock cannot exceed some given ceiling. These optimal paths are considered along with alternative structures of the CCS cost function depending on whether the marginal sequestration cost depends on the flow of clean coal consumption or on its cumulated stock. In the later case, the marginal cost function can be either increasing in the stock thus revealing a scarcity effect on the storage capacity of carbon emissions, or decreasing in order to take into account some learning process. We show among others the following results: Under a stockdependent CCS cost function, the clean coal exploitation must begin at the earliest when the carbon cap is reached while it must begin before under a flow-dependent cost function. Under stock-dependent cost function with a dominant learning effect, the energy price path can evolve non-monotonically over time. When the solar cost is low enough, this last case can give rise to an unusual sequence of energy consumption along which the solar energy consumption is interrupted for some time and replaced by the clean coal exploitation. Last, the scarcity effect implies a carbon tax trajectory which is also unusual in this kind of ceiling models, its increasing part been extended for some time during the period at the ceiling.