In the absence of globally coordinated action to combat climate change, governments are concerned that ambitious carbon pricing could harm the competitiveness of emission-intensive industries. A prominent measure to prevent that manufacturing producers relocate to countries with laxer environmental regulation are carbon border adjustments often referred to as carbon tariffs. Several studies have discussed this policy tool, but mostly neglected an important fact: firms are not homogeneous but differ along several dimensions. This firm heterogeneity has important implications for the effectiveness of carbon border adjustments. By limiting the reallocation of market shares across firms, carbon border adjustments can have an adverse effect on the emission intensity of the economy. While shown in theory, the size of this emission intensity effect has not been quantified so far. In this study, I develop a general equilibrium trade model with heterogeneous firms which allows me to investigate the quantitative importance of the emission intensity effect.