We present a simple dynamic model based on on-the-job human capital accumulation affecting the dynamic of wage rates and labor earnings. We show how these dynamics are determined by the interplay between the supply and demand sides of the labor market. The model can generate and explain the different dynamics of women's earnings after childbirth documented in the empirical literature on child penalties. We show that the temporary negative shock in labor supply due to childbearing may create a wage trap and a permanent divergence of labor earnings between genders. Even when the wage trap is avoided, and working mothers are on a path toward a high-wage equilibrium, slow convergence can permanently lose earnings. We use this model to study the impact of different policies on the gender wage gap and child penalties. We show that mandatory maternal leave exacerbates the shock which pleads against long leaves. Similarly, cash transfers to mothers via the income effect on labor supply aggravate gender wage differences. By contrast, temporary subsidies to mothers' wages (possibly in the form of Income Tax Credits) are not only useful to exit the wage trap, but also to speed up recovery and reduce the child penalty when the shock in labor supply is small enough to avoid the wage trap. Other family policies, like formal child-care subsidies and in-kind provision of formal childcare, are potentially useful because they reduce the mothers' cost of labor supply, but they affect mothers' choices only indirectly.