Jacobs, B. and van der Ploeg, F. (2019). Redistribution and pollution taxes with non-linear Engel curves Journal of Environmental Economics and Management, 95:198--226.

This paper analyses optimal corrective taxation and optimal income redistribution. The Pigouvian pollution tax is higher if pollution damages disproportionally hurt the poor due to equity weighting of pollution damages. Moreover, under general utility functions, optimal pollution taxes should be set below the Pigouvian tax if the poor spend a disproportionate fraction of their income on polluting goods. However, if Engel curves are linear, optimal pollution taxes should follow the first-best rule for the Pigouvian corrective tax even if the government wants to redistribute income and the poor spend a disproportional part of their income on polluting goods. The often-used quasi-linear, CES and Stone-Geary utility functions all have linear Engel curves. If Engel curves are linear, and if pollution taxes are not optimised, Pareto-improving green tax reforms exist that move the pollution tax closer to the Pigouvian tax. Simulations demonstrate that optimal corrective taxes should be Pigouvian if the demand for polluting goods is derived from a LES demand system, but deviate from the Pigouvian taxes if demand for polluting goods demand is derived from a PIGLOG demand system.