Optimal Central Redistribution with Decentralized Redistribution

In an economy with both inter- and intra-region inequality and inconsistency between the objectives of local and central governments, this paper studies optimal non-linear federal (central) income tax under non-linear regional income taxes. Starting with a benchmark model without labor mobility, it uses the variation approach to derive a statistic-based optimal federal income tax formula, which turns out to be a function of social welfare weights, regional income distributions and labor income elasticities. Unlike the traditional Mirrleesian tax, the optimal federal income tax depends on the inter-government gap of preference instead of the central government's own preference. In particular, the optimal tax rate is non-negative (non-positive) when the central government has a relatively higher (lower) preference for equality. While in an economy without labor mobility the federal income tax is limited to remedy the inconsistency of objectives, introducing labor mobility activates federal income tax's role as a Pigovian tax which internalizes the horizontal revenue externality. The numerical analysis suggests that even if the decentralized redistribution is undesirable compared to the fully centralized redistribution, it is generally desirable when combined with the central redistribution