Nonlinear and piecewise linear income taxation, and the subsidization of work-related goods

We investigate how the social welfare gain of subsidizing work-related goods depends on whether the underlying income tax system is linear, piecewise linear or fully nonlinear, focusing on child care services as a paradigmatic example of goods/services that are complements with labor supply. Our quantitative analysis employs an empirically relevant labor supply model and shows that the welfare gain of an optimally chosen subsidy is negligible when the optimal income tax is restricted to be linear but about the same as under fully nonlinear taxation when the optimal income tax is restricted to be piecewise linear. Our findings enhance the policy relevance of the optimal tax argument in favor of providing subsidies to work-related goods and also shed light on the relative welfare gains of employing piecewise linear rather than fully nonlinear income taxes.