This paper studies the design of child-care policies when redistribution matters. Traditional mothers provide some informal child care, whereas career mothers purchase full time formal care in the market. The sorting of women across career paths is endogenous and shaped by a social norm about gender roles in the family. Via this social norm traditional mothers' informal child care imposes an externality on career mothers, so that the market outcome is inefficient. Informal care is too large and the group of career mothers is too small.
In a first-best, full information word equity and efficiency are separable. Redistribution is performed via lump-sum transfers and taxes which are designed to equalize utilities across all couples. The efficient reduction of gender inequality is obtained by subsidizing formal child care at a Pigouvian rate.
However, in a second-best settings, we show that a tradeoff between the reduction of gender inequality and redistributive considerations emerge. The optimal uniform subsidy is lower than the "Pigouvian" level. Under a nonlinear policy the first-best "Pigouvian" rule for the (marginal) subsidy on informal care is reestablished. While the share of high career mothers continues to be distorted downward for incentive reasons, this policy is effective in reconciling the objectives of reducing the child care related gender inequalities and achieving a more equal income distribution across couples.