Atkinson-Stiglitz theorem in directed technological change (DTC-AABH model) with Ramsey–Mirrlees–Pigou policy system

Three forces: Externality (Pigou), Inequality (Mirrlees), Innovation direction (Acemoglu DTC-AABH) along with Ramsey (planner must raise tax revenue only through imposition of tax on commodities only) will be combined in this paper. Total optimal environmental tax includes Pigou + redistribution, Ramsey–Mirrlees term is pure redistribution correction driven by: non-separability inequality aversion . Ramsey-Mirrlees term shows: how dirty consumption correlates with ability and whether taxing pollution also redistributes income. Covariance term on the other hand is structural meaning:If high-weight individuals (poor) consume more dirty goods leads to positive covariance.If rich consume more dirty goods leads to negative covariance. Ramsey–Mirrlees term is: Positive if high-ability types consume more dirty goods, negative if low-ability types consume more dirty goods.