A Beckerian Theory of Taxation

We study taxation in matching environments in which both equilibrium sorting and the sharing of match surplus are endogenous. Tax reforms lead to complex adjustments in sorting and surplus sharing patterns across the whole economy. We develop a general approach for characterizing these equilibrium adjustments using matching elasticities, which are primitive objects that describe how agents' matching choices are affected by pecuniary payoffs in partial equilibrium. Applying this approach to a workhorse model of family formation, we first show that the sorting and surplus sharing responses are closely linked to complementarities in the creation of economic surplus, as first emphasized by Becker (1973). We then describe the effects of arbitrary tax reforms on tax revenues, the utilities of different agents, and social welfare; design tests to assess Pareto efficiency of existing tax systems; derive formulas that characterize optimal taxes; and propose numerical techniques to compute them. In a calibrated model, we find that optimal marginal tax rates are substantially lower and less progressive than in the Mirrleesian benchmark.