In the presence of rising carbon concentrations more attention should be given to the role of the oceans as a sink for atmospheric carbon. We do so by setting up a simple dynamic global carbon cycle model with two reservoirs containing atmosphere and two ocean layers. The net flux between these reservoirs is determined by the relative reservoir size and therefore constitutes a more appropriate description of the carbon cycle than a proportional decay assumption. We exploit the specific feature of our model, the mixing of the carbon reservoirs, by allowing for a special form of carbon capture and storage: The capture of CO2 from the air and the sequestration of CO2 into the deep ocean reservoir. We study the socially optimal anthropogenic intervention of the global carbon cycle using a non-renewable resource stock. We find that this kind of carbon capture and storage facilitates achieving strict stabilization targets for the atmospheric carbon content. It accelerates the slow natural flux within the carbon cycle, and because of its temporary abatement character it dampens the overshooting of the atmospheric reservoir. Furthermore, we analyze the optimal paths of the carbon tax. The carbon tax shows to be inverted u-shaped but depending on the initial sizes of the reservoirs and the speed of carbon fluxes between the reservoirs we also find the optimal tax to be increasing, decreasing or u-shaped. Finally, we suggest to link the level of the carbon tax to the declining ability of the deep ocean to absorb atmospheric carbon.