This paper investigates if the optimal green tax is still equal to the Pigouvian rate, in a context of endogenous productivity, or the distributive / efficient impact should be remove. In a Mirrlees partial equilibrium model, we introduce endogenous productivities through investment in education. Each household differs by ability and chooses whether to acquire an education and become a high-skilled worker or remain unskilled. Given these assumptions, our economy is characterized by an ability cut-off such as those with education cost parameter strictly above will invest in education and become skilled. It determines endogenously the proportion of skilled and unskilled workers in the economy that is directly impacted by the government policy instruments. We derive the optimal carbon tax in conjunction with the optimal redistributive income tax and lumps sum transfers. We found that discriminating lump sum tax transfers between high and low skilled workers is necessary to allow the government to reach the first best pollution tax (the Pigouvian one). Tax subsidies on education have the same advantage. Yet, this result holds only under the homothetic properties of the human capital production function. Otherwise, neither lump-sum transfers, nor education subsidies allow reaching the first best pollution tax.