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We characterise the optimal exploitation paths of two primary energies (coal and solar) that supply the energy needs of two sectors. Sector 1 can reduce its carbon emissions at a reasonable cost thanks to a CCS device. Sector 2 has access only to air capture technology, but at a significantly higher cost. We assume that the atmospheric carbon stock cannot exceed a given ceiling. We show that the optimal approach consists in, first, fully capturing sector-1 emissions before the ceiling is reached and, second, deploying air capture to partially abate sector-2 emissions. The optimal carbon tax should increase in the pre-ceiling phase then decline in stages to zero.