Optimal Commodity Taxation When Households Earn Multiple Incomes

I characterize the optimal linear commodity taxes when households differ in multiple characteristics and earn multiple incomes, in presence of an optimal non-linear tax schedule on the households' labour incomes. The government should tax a commodity more heavily if, conditional on labour income, more deserving individuals consume larger quantities 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 with different labour supplies also have different consumption pattern