[Running title: Intergenerational Mobility]

A large literature on ‘endogenous inequality’ has argued that persistent differences in macroeconomic performance across countries can be explained by historical inequality, owing to indivisibilities in occupational choice and borrowing constraints. These models are characterized by homogenous agents, a continuum of steady states and lack of mobility in every steady state. We show that introducing (even a little) heterogeneity in order to generate steady state mobility shrinks the steady state set dramatically. Mobile steady states are generically locally unique and finite in number. Sufficient conditions for global uniqueness and convergence of competitive equilibrium dynamics are provided.