This paper investigates the effects of a binding minimum wage in an economy which exhibits multiple unemployment equilibria. For this purpose, we develop a theoretical model based on the simple imperfectly competitive model of Manning [In Conference Papers, Economic Journal 100, 151–162 (1990)], in which we introduce labor heterogeneity and knowledge spillovers in the individual production technology. Then, using numerical simulations, we show that a binding minimum wage rules out the occurrence of an inefficient equilibrium. Last, we analyze the effects of a minimum wage increase on the labor market's outcomes.