The reduction of GHG emissions is one of the most important policy objectives worldwide. Nonetheless, concrete and effective measures to reduce them are hardly implemented. One of the main reasons for this deadlock is the fear that unilateral actions will reduce a country’s competitiveness, and will benefit those countries where no GHG mitigation measures are implemented. This kind of argument is also often used to explain why some governments and many business leaders are not in favour of the EU 30% GHG mitigation target that has been proposed to replace the previous 20% GHG emission reduction objective approved by the EU within the well-known 20-20-20 climate and energy package. By developing and applying a recursive, dynamic, very detailed CGE model with energy generation from both fossil fuel and renewable sources, we address this issue by estimating the cost for different EU countries and industries of the EU climate and energy package under a set of alternative international scenarios on global GHG mitigation efforts. Results show that, thanks to the EU economic recession, achieving a 20% GHG emission reduction entails a moderate cost for the European Union - about 0.5% of EU GDP – even in the case of EU unilateral action. This cost could be reduced to almost zero if not only the European Union, but also the other major world economies, comply with the “low pledge” Copenhagen Accord. A 30% GHG emission reduction target would certainly be more costly: the total loss in the European Union would be 1.26% of EU GDP in the case of EU unilateral action, whereas the total cost would be 0.55% of EU GDP if all major economies reduce their own GHG emissions according to the “low pledge” Copenhagen Accord. Both border tax adjustments and free allocation of carbon permits are shown to be successful in reducing some adverse competitiveness effects of the EU GHG mitigation policy into energy intensive sectors, but at the expenses of the other economic sectors.