Heterogeneous human capital, inequality and growth: the role of patience and skills

We extend the Lucas' 1988 model introducing two classes of agents with heterogeneous skills, discount factors and initial human capital endowments. We consider two regimes according to the planner's political constraints. In the first regime, that we call meritocracy, the planner faces individual constraints. In the second regime the planner faces an aggregate constraint, redistributing. We find that heterogeneity matters, particularly with redistribution. In the meritocracy regime, the optimal solution coincides with the BGP found by Lucas (1988) for the representative agent's case. In contrast, in the redistribution case, the solution for time devoted to capital accumulation is never interior for both agents. Either the less talented agents do not accumulate human capital or the more skilled agents do not work. Moreover, social welfare under the redistribution regime is always higher than under meritocracy and it is optimal to exploit existing differences. Finally, we find that inequality in human capital distribution increases in time and that, in the long run, inequality always promotes growth.