This paper finds that accounting for the human capital development of children has a quantitatively large effect on the true costs and benefits of providing cash assistance to single mothers in the United States. A dynamic model of work, welfare participation, and parental investment in children introduces a formal apparatus for calculating costs and benefits when individuals respond to incentives. The model provides a tractable outcome equation in which a policy's effect on child skills can be understood through its impact on two economic resources in the household--time and money--and the share of each resource as factors in the production of skills. These key causal parameters are cleanly identified by policy variation through the 1990s. The model also admits simple and interpretable formulae for optimal nonlinear transfers in the style of Mirrlees (1971), with novel features arising when child skill formation is accounted for. Using a broadly conservative empirical strategy, estimates imply that optimal transfers are about 20% more generous than the US benchmark, and shaped very differently. In contrast to current policies, the optimal policy discourages labor supply at the bottom of the income distribution due to the costly estimated impacts of work on child development. The finding underscores the importance of reconciling results in the literature on the developmental effects of maternal employment. Finally, a counterfactual model exercise suggests that changes to the welfare and tax environment after 1996 had negative average effects both on maternal welfare and child skill outcomes, with a significant degree of redistribution across latent dimensions.