This dissertation is composed of two essays and studies the optimal taxation of carbon emissions.In the first essay, I set up an economy where an externality arises from the consumption of an exhaustible resource (oil) and a technology exists to mitigate the externality. I focus on the implications for policy design of assuming social preferences differ from private preferences regarding future generations. In particular, I consider a welfare function that places direct Pareto weights on unborn generations, as opposed to future generations receiving weight only through the altruism of their ancestors. This specification delivers a social discount rate which is lower than that of private individuals. I first show that standard policies, such as price or quantity controls on the net emissions of carbon, are insufficient to achieve the social optimum: When social and private discounting differ, more sophisticated policies are necessary. The main results of the chapter characterize these sophisticated policies. I show that an optimal tax scheme requires subsidizing the mitigation technology and taxing carbon emissions, but each at different rates: the optimal subsidy for removing a ton of carbon from the atmosphere will in general not equal the optimal tax for creating a ton of carbon. I also show that an optimal cap and trade system must include a cap on carbon offset allowances.In the second essay, I study the optimal taxation of carbon emissions in an intergenerational model with imperfect altruism. This means that the current generations discount tradeoffs in the near future more than those which happen in the distant future. As a result, a problem of time inconsistency arises. I study if standard carbon policies are sufficient to control emissions in this economy. I first show that, when society can successfully resolve the inconsistency problem by committing itself to following a climate plan, standard carbon taxes coupled with a subsidy on oil reserves are enough to induce future generations to follow it. However, an initial period of sophisticated policies are required to induce the current generation to abide by it as well. When no commitment technology is available, I solve for the Markov perfect equilibrium of the dynamic game between generations and show that sophisticated policies are always required to implement the constrained social optimum.