Optimal linear commodity taxation under optimal non-linear income taxation

This paper analyzes optimal linear commodity taxes joint with non-linear income taxes. We provide optimal tax rules based on empirically observable elasticities. We demonstrate that commodities should be taxed/subsidized if doing so boosts labor supply. The critical role of commodity taxation is to alleviate distortions on labor supply caused by income taxation. In addition, we extend the standard formula for optimal non-linear income taxation for the presence of optimal linear commodity taxes. We correct parts of the literature that suggest that the optimal tax rules for commodity taxes derived by Atkinson and Stiglitz (1976, 1980) apply as well to linear tax commodity taxes. We show that the optimal second-best allocation cannot be implemented with linear commodity taxes and non-linear income taxes.