How should a government price carbon when it cares about redistribution and emissions? I extend the dynamic Mirrlees model to two goods, one polluting, with privately observed skills that evolve over the life cycle. Under weakly separable preferences, the optimal carbon wedge equals the social cost of carbon while the labor and savings wedges keep their standard forms. The below-Pigou prescription of the second-best tradition disappears once the income tax is set optimally. Because real carbon taxes are linear, I also solve the problem when the instrument must be uniform and find that the restriction constrains redistribution but not externality correction. In a US calibration, the optimal energy wedge rises with skill, so the regressivity of real carbon taxes comes from their linearity. However, a flat tax at the social cost of carbon captures 98% of the welfare gain of the full optimum, so the income tax should focus on redistribution and the carbon price on externality correction.

Pollution raises climate risk in two ways. It can raise the probability of a discrete catastrophe, the "tipping point" already central to the climate-economics literature. It also shifts the entire distribution of everyday climate shocks, making extreme weather more frequent and more intense. I study this distributional channel and its consequences for the social cost of carbon (SCC). I introduce stochastic externalities: random damages whose distribution has parameters that depend on the pollution stock rather than staying fixed. Solving the social planner's problem, first in a three-period model and then in an infinite-horizon recursive one, I show that the optimal carbon tax adds a correction term to the standard Pigouvian tax, equal to expected marginal damages weighted by the distribution's sensitivity to pollution. The correction admits closed forms for standard distribution families and nests the Pigouvian tax as a special case. Under heavy-tailed shocks it can grow without bound faster than the Pigouvian term, sharpening Weitzman's Dismal Theorem. A calibrated DICE exercise quantifies the resulting increase in the SCC.

This project applies the fiscal rules and monetary rules methodology to study optimal "climate rules", where decision makers are present-biased and there is a need to balance commitment and flexibility.