This paper presents a neoclassical growth model with three energy sectors and a climate externality. Energy is used in the production of the final consumption good. The energy sectors differ on the exhaustibility of the energy resource. Oil is an exhaustible resource, coal is an abundant resource, and a green energy sector uses labor. Oil and coal use increases the stock of carbon in the atmosphere, which generates a climate externality. Standard Pigouvian taxation prescribes that a uniform tax on all carbon energy inputs is optimal. This uniform tax must be equal to the social cost of carbon because this is the externality that the usage of these inputs generates. I consider a policymaker who cares about future generations and may discount the future less than the individuals in the economy. This paper's main theoretical result is that the uniform taxation rule does not carry over to an economy with a low social discount rate. In particular, the optimal carbon tax on oil does not equal the optimal carbon tax on coal. Moreover, while the optimal tax on coal equals the social cost of carbon, the optimal carbon tax on oil follows a more general formula.