Optimal Taxation of Family Income with non-separable disutility of effort

This paper studies the optimal non linear income taxation for a couple with two earners, each with two possible productivity types. For the case of zero cross-elasticity of labor supply, I find the full solution in terms of type distribution and social welfare weights. Binding diagonal constraints are found to be relevant even with independent types. For the case of non zero cross elasticity, some partial results are obtained. No distortion at the top occurs only in families where both earners are at the top of their distribution. High types in heterogeneous families can be upward distorted, even when only downward incentive constraints bind. The sign of their marginal tax depend on the sign of cross elasticity of labor supply. An example with quadratic disutility of effort is solved using numerical optimization.