Theory fails to predict clearly whether a greater public investment in the higher education system effectively decreases the inequality between the educational attainment of rich and poor students. It is assumed that a rich student enrolled at a university receives a monetary transfer from his parents and allocates it between private consumption and investment in private education. When private and public educational investments are substituted, it is found that a further public investment narrows the educational gap. This result is due to the behavior of rich households. Once public investment has increased, rich students and their parents reduce private investments and monetary transfer, respectively; this allows the education of the poor student to increase more than the education of the rich one. This result also holds under weak complementarity.