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In the last decade, a few papers have analysed the consequences of achieving the greenhouse gas concentration levels necessary to maintain global temperature increases below 2 degrees Celsius above preindustrial levels. Most models and scenarios assume that future trends in global GDP will be similar to the growth experienced in the past century, which would imply multiplying current output nineteen-fold in this century. However, natural resource and environmental constraints suggest that future global economic growth may not be so high. Furthermore, the environmental implications of such growth depend on how it is distributed across countries. This paper studies the implications on GHG abatement policies of different assumptions on global GDP growth and convergence levels. A partial equilibrium model (POLES) of the world´s energy system is used to provide detailed projections up to 2050 for the different regions of the world. The results suggest that while low stabilisation is technically feasible and economically viable for the world in all the scenarios considered, it is more likely to occur with more modest global growth. Convergence in living standards on the other hand places greater pressures in terms of the required reduction in emissions. In general we find that there are major differences between regions in terms of the size and the timing of abatement costs and economic impact.