What are the long-term effects of policies intended to equalize opportunities among different social classes of children? To find out, we study the stationary states of an intergenerational model where adults are either White or Blue collar employees. Both adults and the state invest in their children's education. Our analysis indicates that the major obstacle to equalizing opportunities in the long run is private educational investment. Next we examine economies where only the state invests in education, motivated by the Nordic experience. In a majority of these economies, no child lags behind regarding future prospects, a theoretical result confirmed by simulations.