We use a labor search model with worker experience to assess the effects of minimum wage increases. Minimum wages can have nonlinear effects on unemployment as higher minimum wages become binding for larger portions of the underlying productivity distribution. The model is used to assess the increases proposed by the Obama Administration from $7.25 an hour to $9.00 and then to $10.10 per hour. We find that minimum wage increases have large effects on youth unemployment. These large effects cast doubt on using past empirical estimates of the effects of minimum wages that do not account for potential nonlinearities. (JEL E24, J08, J24, J64)