The expansion of higher education in the Western countries has been accompanied by a marked widening of wage differentials and increasing over-qualification. While the increase in wage differentials has been attributed to skill-biased technological change that made advanced skills scarce, this explanation does not fit well with the observed increase in over-qualification which suggests that advanced skills are in excess supply. By "Reder-competition" I refer to the simultaneous adjustment of wage offers and hiring standards in response to changing labor market conditions. I present a simple model of Reder competition that depicts wages as driven by labor heterogeneity, rather than scarcity. The mechanism may give rise to a simultaneous increase in wage differentials and over-qualification.