The success of climate change mitigation depends on the modalities for the extension of the Kyoto protocol after 2020. This refers to the appropriate level of GHG reduction imposed as emissions quotas in line with the 2 °C commitment. We perform a parametric analysis where increasingly stringent cumulative and global emission quota bounds are applied using the integrated TIMES and MERGE model (ITMM). The model integrates in one set of equations two hybrid top-down and bottom-up models both able to analyze technological change. The study assumes efficient policies and measures where all world regions accept a binding protocol in 2020 while mitigation policies will start already in 2015. However, this early introduction of efficient policies needs capital transfers for a fair burden sharing in favor of countries with low income and in that sense the model assumptions are critical. Marginal cost of carbon control of these optimistic policies are high (600–1000 $/t of carbon by 2050) but global GDP losses remain moderate and below 1.5 % per year.