We develop a general method to study the effects of non-linear taxation in dynamic settings using variational arguments. We first derive general theoretical formulas that characterize the welfare effects of local tax reforms and, in particular, the optimal tax system, potentially restricted within certain classes (e.g., age-independent, linear, separable). These formulas are expressed in terms of intuitive parameters, such as the labor and capital income elasticities and the hazard rates of the income distributions. Second, we apply these formulas to various specific settings. In particular, we decompose the gains arising from each element of tax reform, starting from a simple baseline system, as the available tax instruments becomes more sophisticated. We further show that the design of tax systems obeys a common general principle, namely that more sophisticated tax instruments (e.g., age-dependent, non-linear, non-separable) allow the government to fine-tune the tax rates by targeting higher distortions to the segments of the population whose behavior responds relatively little to those taxes.

We study the incidence of nonlinear labor income taxes in an economy with a continuum of endogenous wages. We derive in closed form the effects of reforming nonlinearly an arbitrary tax system, by showing that this problem can be formalized as an integral equation. Our tax incidence formulas are valid both when the underlying assignment of skills to tasks is fixed or endogenous. We show qualitatively and quantitatively that contrary to conventional wisdom, if the tax system is initially suboptimal and progressive, the general‐equilibrium “trickle‐down” forces may raise the benefits of increasing the marginal tax rates on high incomes. We finally derive a parsimonious characterization of optimal taxes.

Golosov and Tsyvinski thank the NSF for financial support. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

We develop a model of political competition with endogenous turnout and endogenous platforms. Parties trade off incentivizing their supporters to vote and discouraging the supporters of the competing party from voting. We show that the latter objective is particularly pronounced for a party with an edge in the political race. Thus, an increase in political support for a party may lead to the adoption of policies favoring its opponents so as to asymmetrically demobilize them. We study the implications for the political economy of redistributive taxation. Equilibrium tax policy is typically aligned with the interest of voters who are demobilized. (JEL D63, D72, H23, H24)