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 taxpayers’ labour incomes. The government should tax a commodity more heavily if, conditional on labour income, more deserving taxpayers 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 households with different incomes have different consumption preferences, or when households with different labour supplies also have different consumption patterns.