We analyze how intergenerational mobility and inequality would change relative to the status quo if dynasties had access to optimal insurance against low ability of future generations. Based on a dynamic, dynastic Mirrleesian model, we find that insurance against intergenerational ability risk increases in the social optimum relative to the status quo. This implies less intergenerational mobility in terms of welfare but no quantitatively significant change in earnings mobility. Earnings mobility is thus similar across economies with different incentives and welfare, illustrating that changes in earnings mobility cannot be interpreted readily in welfare terms without further analysis.