We study optimal nonlinear income taxation when earnings can differ because of both ability and luck, so the income tax has both a redistributive role and an insurance role. A substantial literature on optimal redistribution in the absence of uncertainty has evolved since Mirrlees' original...

An optimal commodity tax approach is taken to compare trade taxes and VATs when some commodities are produced informally. Trade taxes apply to all imports and exports, including intermediate goods while the VAT applies only to sales by the formal sector and imports. The VAT can achieve...