Optimal nonlinear taxes for families

The problem faced by a taxation authority choosing a tax schedule for families is modeled as a multi-dimensional screening problem. A description of the possible constrained Pareto-efficient mechanisms is given. The implications of a standard redistributive assumption on the sign of marginal tax rates is explored. In contrast to unidimensional taxation models, the redistributive assumption does not imply that marginal tax rates are everywhere non-negative. The qualitative features of optimal tax schedules are discussed. It is concluded that taxation based solely on total family income is rarely optimal.