We analyze the consequences of an increase in the supply of highly educated workers on relative and real wages in a search model where wages are set by Nash-bargaining. The key insight is that an increase in the supply of highly educated workers improves the firms? outside option. As a consequence, the real wage of all workers decreases in the short-run. Since this decline is more pronounced for less educated workers, wage inequality increases. In the long-run a better educated work force induces firms to invest more in physical capital. Wage inequality and real wages of highly educated workers increase while real wages of less educated workers may decrease. These results are consistent with the U.S. experience in the 70s and 80s. Based upon differences in legal employment protection we also provide an explanation for the diverging evolution of real and relative wages in Continental Europe.