Joint Implementation (JI) calls for cooperation between industrialized and developing countries in the mitigation of greenhouse gas (GHG) emissions. However, a major concern of potential host countries is that, if they utilize their low-cost options for JI now, they will be left with only high cost options in the future, thereby penalizing them at a time when they may be obligated to mitigate GHGs themselves. This paper formalizes this hypothesis by utilizing an optimal control framework analogous to the Hotelling model of non-renewable resource extraction. The results are that cumulative abatement effects can impose costs on the future, but that they can be offset by technological change, market power, or compensation.