Optimal Commodity Taxation Under Non-linear Income Taxation

I characterize the optimal linear commodity taxes when households differ in multiple characteristics, in presence of an optimal non-linear tax schedule on the households' labour incomes. The optimal distortions caused by a linear commodity tax are larger if, conditional on labour income, more deserving individuals consume more of that commodity. This is the case for merit goods, or if the government otherwise seeks to compensate individuals who consume larger quantities of that commodity. Furthermore, the government wishes to tax commodities at different rates to the extent that doing so reduces the distortions caused by the labour income tax. This is the case when individuals with different incomes have different preferences, or when individuals who supply different quantities of labour have different consumption patterns. I extend these findings to the case where households earn multiple incomes