Cumulative emissions drive peak global warming and determine the safe carbon budget compatible with staying below 2oC or 1.5oC. The safe carbon budget is lower if uncertainty about the transient climate response is high and risk tolerance low. Together with energy costs this budget determines...

The paper derives the optimal carbon tax in closed-form from an integrated assessment of climate change. The formula shows how carbon, temperature, and economic dynamics quantify the optimal mitigation effort. The model's descriptive power is comparable to numeric models used in policy advising....