Optimal carbon taxation is evaluated in a model where climate change affects productivity. With a numerical US economy model with preexisting taxes, the optimal carbon tax is found to exceed marginal social damage by 53 percent and "marginal private damage" (the sum of households' marginal willingness to pay) by 73 percent. The welfare gain from optimal carbon taxation is estimated at $3.58 billion per year when marginal damages are $40/ton; employment also increases. Setting the carbon tax at the Pigouvian rate raises welfare by only $3.17 billion. The contrasting results in the "tax interaction" literature are due to the use of "marginal private damage" when applied to amenity externalities