Redistribution or education?: the political economy of the social race

In an overlapping generations model with two social classes, rich and poor, parents of the different social classes vote on two issues: redistributive policies for them and education investments for their kids. Public education is the engine for growth through its effect on human capital; but it is also the vehicle through which kids born from poor families may exchange their positions with kids born from rich families. This is because education reduces the probability of the mismatch, i.e. individuals with low talent but coming from rich families being placed in jobs which should be reserved to people with high talent (and vice-versa). We find a political economy equilibrium of the voting game using probabilistic voting. When the poor are more politically influent, the economy is characterized by a higher level of education, growth and social mobility than under political regimes supported by the rich; pretax inequality is greater in the first case, but post-tax is lower.