Section S1 shows that a given path of earnings (z0 (n) , z1 (n)) is implementable. Section S2 provides conditions for the existence of a solution to the maximization problem. Section S3 discusses conditions ensuring no bunching in the optimum. Section S4 discusses the outcome of a more general model with heterogeneity in both work costs and home production abilities. Section S5 provides technical details of the simulations.