Inefficient taxation of sin goods

Within an O'Donoghue and Rabin (2006) style model, we study the optimal sin taxes that a government wants to implement when consumers are time-inconsistent, and taxation is inefficient in terms of administrative, collection and compliance costs. We find that, if the inefficiency of taxation is not too large, the optimal tax is positive and it may be higher or lower than the first best depending on the elasticity of demand with respect to taxation. Finally, the extent of the distortion depends on the degree of inefficiency of taxation.