Optimal carbon tax with a dirty backstop: Oil, coal, or renewables?

Optimal climate policy is studied. Coal, the abundant resource, contributes more CO2 per unit of energy than the exhaustible resource, oil. We characterize the optimal sequencing oil and coal and departures from the Herfindahl rule. 'Preference reversal' can take place. If coal is very dirty compared to oil, there is no simultaneous use. Else, the optimal outcome starts with oil, before using oil and coal together, and finally coal on its own. The 'laissez-faire' outcome uses coal forever or starts with oil until it is no longer profitable to do so and then switches to coal. The optimum requires a steeply rising CO2 tax during the oil-only phase and a less steeply rising CO2 tax during the subsequent oil-coal and coal-only phases to avoid the abrupt switch from oil to coal thus leaving a lot of oil in situ. Finally, we analyze the effects on the optimal transition times and carbon tax of a carbon-free, albeit expensive backstop (solar or wind). Without a carbon tax, a prohibitive coal tax leads to less oil in situ, substantially delays introduction of renewable, and thus curbs global warming substantially. Subsidizing renewables to just below the cost of coal does not affect the oil-only phase. The gain in green welfare dominates the welfare cost of the subsidy if the subsidy gap is small and the global warming challenge is acute.