A new IAM is used to calculate the optimal tradeoff between, on the one hand,locking up fossil fuel and curbing global warming, and, on the other hand,sacrificing consumption now and in the near future. This IAM uses the Oxford carbon cycle, which differs from DICE, FUND and PAGE in that cumulative emissions are the key driving force of changes in temperature. We highlight how time impatience, intergenerational inequality aversion and expected trend growth affect the time paths of the optimal global carbon tax and the optimal amount of fossil fuel reserves to leave untapped. We also compare these with the adverse and deleterious global warming trajectories that occur if no policy actions are taken. (authors' abstract) / Series: Ecological Economic Papers