In the last 30 years wage inequality increased steeply while real minimum wages fell. In this paper I demonstrate that a general equilibrium model with endogenous skill choice is required to correctly evaluate the implications of minimum wage changes. The minimum wage not only truncates the wage distribution, but also affects skill prices and therefore changes the incentives that people face when making educational decisions. The calibrated model suggests, in line with recent empirical literature, that even though minimum wages affect the bottom end of the wage distribution more, their impact on the top end is significant as well.