Energy substitutions, climate change and carbon sinks

We determine the optimal exploitation time-paths of two energy resources, one being depletable and polluting, namely a fossil fuel, the other being renewable and clean. These optimal paths are considered along with the two following features. First, the cumulative atmospheric pollution stock is set not to exceed some critical threshold and second, the polluting emissions produced by the use of fossil fuel can be reduced at the source and stockpiled in several carbon sinks of limited capacity. We show that, if the renewable resource flow is abundant, the optimal path requires that sequestration is implemented only once the ceiling is reached. Moreover, the reservoirs should be completely filled by increasing order of their respective sequestration costs.