In 2015, the 21st Conference of the Parties reaffirmed the target of keeping the global mean temperature rise below 2 ∘C or 1.5 ∘C by 2100 while finding no consensus on how to decarbonize the global economy. In this regard, the speed of decarbonization reflects the (in)flexibility of transforming the energy sector due to engineering, political, or societal constraints. Using economy–energy–climate-integrated assessment models (IAMs), the maximum absolute rate of change in carbon emission allowed from each time step to the next, so-called carbon emission inertia (CEI), governs the magnitude of emission change, affecting investment decisions and economic welfare. Employing the model of investment and endogenous technological development (MIND), we conduct a cost-effectiveness analysis and examine anthropogenic global carbon emission scenarios in line with decarbonizing the global economy while measuring the global mean temperature. We examine the role of CEI as a crucial assumption, where the CEI can vary in four scenarios from 3.7% to 12.6% p.a. We provide what-if studies on global carbon emissions, global mean temperature change, and investments in renewable energy production and show that decarbonizing the global economy might still be possible before 2100 only if the CEI is high enough. In addition, we show that climate policy scenarios with early decarbonization and without negative emissions may still comply with the 2 ∘C target. However, our results indicate that the 1.5 ∘C target is not likely to be reached without negative emission technologies. Hence, the window of opportunity is beginning to close. This work can also assist to better interpret existing publications on various climate targets when altering CEI could have played a significant role.