The implications of individual heterogeneity for the evolution of wealth distribution are studied in a standard model of occupational choice with financial market imperfections and local non convexities in education investment technology. We consider heterogeneity in the cost of educational investment, interpreted as genetic variation at the level of lineage. Ergodicity of the wealth distribution is obtained whenever the (exogenous) distribution of education costs entails the presence of ability types for which the educational investment is inefficient vis a vis financial investment, regardless of how ”large” the support is. Conversely, poverty traps can emerge only if investment is efficient for every single agent in the economy. We show that under quite general conditions, the accumulation of wealth at the lineage level does not eliminate financial market imperfections over the long run, motivating our exploration of policy implications. In particular heterogeneity requires more persitent policies to achieve similar results as in the standard case. On the other hand policies can be effective in environments where they would fail under the assumption of homogeneous costs. JEL classification: D31, D91, I21, J24, O15 Keywords : Intergenerational Mobility, Inequality Dynamics, Occupational Choice, Educational Investment, Borrowing Constraints