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This paper is the first attempt, to the best of our knowledge, to study the impact of a carbon tax by means of a heterogeneous agents model. The objectives of the paper are two: i) To assess how the results of a representative agent model compare to those coming from a model accounting for heterogeneity across agents when evaluating aggregate economic and environmental impacts of a carbon tax; ii) To assess the distributional implications of a carbon tax (and equivalent cap) and how they can be mitigated through different recycling schemes or allocations.