Equity considerations play an important role in international climate negotiations. While policy analysis has often focused on equity as it relates to mitigation costs, there are large regional differences in adaptation costs and the level of residual damage. This paper illustrates the relevance of including adaptation and residual damage in equity considerations by determining how the allocation of emission allowances would change to counteract regional differences in total climate costs, defined as the costs of mitigation, adaptation, and residual damage. We compare emission levels resulting from a global carbon tax with two allocations of emission allowances under a global cap-and-trade system: one equating mitigation costs and one equat...