Growth, renewables and the optimal carbon tax

Optimal climate policy is investigated in a Ramsey growth model of the global economy with exhaustible oil reserves, an infinitely elastic supply of renewables, stock-dependent oil extraction costs and convex climate damages. Four regimes can occur. If the initial social cost of oil is less than that of renewables, there are two regimes starting with oil. The first one occurs if the oil stock is not too small and not too large and the initial capital stock is below its steady state in which case it is optimal to follow the oil-only phase with a renewables-only phase. The second regime occurs if the initial oil stock is large enough. It is then optimal to follow an oil-only phase with an oil-renewables phase. If it is optimal to start with renewables, a third and fourth regime emerge. The third one occurs if the initial oil stock takes on an intermediate value and the capital stock exceeds its steady-state value. It is then optimal to start with renewables and end with a phase where oil is used alongside renewables. The fourth regime occurs if the initial oil stock is low enough. Renewables are then used throughout. We also offer some policy simulations for the first and second regime, which illustrate that with a lower discount rate more oil is left in situ and renewables are phased in more quickly. In the first regime the optimal carbon tax rises during the oil-only phase, but in the second regime the optimal carbon tax can fall. Subsidizing renewables (without a carbon tax) induces more oil to be left in situ and a quicker phasing in of renewables, but oil is depleted more rapidly initially. The net effect on global warming is ambiguous