Subsidies versus public provision of private goods as instruments for redistibution

The literature on the use of differential commodity taxes/subsidies and that on quantity controls to supplement income taxation have developed separately from each other. The purpose of this paper is to combine these two strands in the standard framework of optimal non-linear income taxation. We start from a simple model in which there are two types of households, the government has access to both subsidy policy and public provision of a good substitutable with leisure, and households can supplement the publicly provided good from the market. We present conditions when optimal policy should involve a mix of these two instruments alongside income taxation or only one of them. We also consider alternative settings, including the extension to many types of households and the inability of households to supplement in-kind transfers.