Global carbon cycle and the optimal time path of a carbon tax

The existing models of fossil fuel consumption with carbon accumulation imply that the optimal time path of carbon tax is either hump-shaped or monotonically decreasing. These models specify the decay of atmospheric carbon as a constant rate of total concentration. We extend this specification to more accurately reflect the global carbon cycle models of climatologists and show that this extension changes the basic economic properties of the optimal carbon tax. Our analysis reveals that the optimal carbon tax may as well be constant through time, increase monotonically, or have a U-shape. In addition, optimal resource extraction may have an open-close-open cycle.