A necessary condition of an efficient global climate change mitigation policy is to equate marginal abatement costs across world regions to ensure use of the cheapest abatement options available. The welfare economic justification for such an approach rests on lump sum transfers between regions to compensate for any unwanted distributional consequences of such a policy. I contrast this efficient solution with a second best situation in which lump sum transfers between regions are impossible. I derive that in a dynamic setting optimal taxes are different in such a case for regions with different per capita consumption. I estimate the optimal tax rates with the integrated assessment model FUND and find that optimal mitigation is less stringent when equity is explicitly considered for widely used parameter choices of a utilitarian social welfare function.