Optimal capture and sequestration from the carbon emission flow and from the atmospheric carbon stock with heterogeneous energy consuming sectors

We characterize the optimal exploitation paths of two primary energy resources. The first one is a non-renewable polluting resource, the second one a pollution-free renewable resource. Both resources can supply the energy needs of two sectors. Sector 1 is able to reduce the potential carbon emissions generated by its non-renewable energy consumption at a reasonable cost while sector 2 cannot. Another possibility is to capture the carbon spread in the atmosphere but at a significantly higher cost. We assume that the atmospheric carbon stock cannot exceed some given ceiling and that this constraint is effective. We show that there may exist paths along which it is optimal to begin by fully capturing the sector 1's potential emission flow before the ceiling constraint begins to be effective. Also there may exist optimal paths along which both capture devices have to be activated, in which case the potential emission flow of sector 1 is firrst fully abated and next the society must resort to the atmospheric carbon reducing device.