This paper calculates the quantitative significance of the welfare costs of union wage compression. This is done in a dynamic general equilibrium model with overlapping generations where agents choose both schooling (human capital) and assets (physical capital). The labor market in this model is characterized as a right-to-manage contract, which allows unions to compress wage differentials between high- and low-skilled workers, by implementing a binding minimum wage. This paper shows that when labor markets are competitive even low levels of wage compression lead to large welfare losses, since wage compression creates costly unemployment among low-skilled workers. The effect of wage compression on the supply of skilled labor, however, is rather small, since the disincentive effect of a lower, high-skilled wage is, to a large extent, offset by a lower opportunity cost of schooling due to higher unemployment.