Our paper contributes to explore differences in high-education systems, and to highlight the role of competition among tertiary education providers and more generally of tertiary education systems viewed from a general equilibrium perspective to explain changes in returns to skill, wage inequalities and output. An objective function is introduced for universities who seek to maximize their reputations and face a trade-off between research and teaching activities. We propose an explanation to the stratification of higher education providers engaged in a competition process, which preserves the positive competitive effect of admission requirement, both on the size of the students' body and on the quality of the research. We show that competition among higher education providers may have strong benefits on economic activities and output in particular. (Contains 2 tables, 3 figures and 18 notes.)