Carbon pricing is a policy with the potential to reduce CO2 emissions in the household sector and support the European Union in achieving its environmental targets by 2050. However, the policy faces acceptance problems from the majority of the public. In the framework of the project Role of technologies in an energy efficient economy–model-based analysis of policy measures and transformation pathways to a sustainable energy system (REEEM), financed by the European Commission under the Horizon 2020 program, we investigate the effects of such a policy in order to understand its challenges and opportunities. To that end, we use a recursive-dynamic multi-regional Computable General Equilibrium model to represent carbon pricing as a cap-and-trade system and calculate its impacts on consumption of energy goods, incidence of carbon prices, and gross income growth for different income groups. We compare one reference scenario and four scenario variations with distinct CO2 reduction targets inside and outside of the EU. The results demonstrate that higher emission reductions, compared to the reference scenario, lead to slower Gross Domestic Product growth, but also produce a more equitable increase of gross income and can help reduce income inequalities. In this case, considering that the revenues of carbon pricing are paid back to the households, the gross income of the poorest quintile grows as much as, or even more in some cases, than the gross income of the richest quintile.