We develop a unifying framework for optimal income taxation in multi-activity economies with general production technologies. Agents are characterized by an N-dimensional skill vector that captures intrinsic abilities in N activities. The private return to each activity depends on individual skill and an aggregate activity-specific return, which is a general function of the economy-wide distribution of efforts across activities. The optimal tax schedule features a multiplicative income-specific correction to an otherwise standard tax formula. Because taxes affect the relative returns to different activities, this correction diverges, in general, from the weighted average of the Pigouvian taxes that would align private and social returns in each activity. We characterize this divergence as a function of relative return elasticities, and its implications for the shape of the income tax both generally and in a number of applications, including externality-free economies with general equilibrium effects, economies with increasing or decreasing returns to scale, zero-sum activities such as bargaining or rent extraction, and positive or negative spillovers.
income taxation general equilibrium multidimensional screening multi-sector economies