We present a DSGE New Keynesian model with indivisible labor and a dual labor market: a walrasian one where wages are fully ‡exible and a unionized one charaterized by real wage rigidity. We show that the negative e¤ect of a productivity shock on in ‡ation and the positive e¤ect of a cost-push shock are crucially determined by the proportion of …rms that belong to the unionized sector. The larger this number, the larger are these e¤ects. Consequently, the larger the union coverage, the larger should be the optimal response of the nominal interest rate to exogenous productivity and cost-push shocks. The optimal in ‡ation and output gap volatility increases as the number of the unionized …rms in the economy increases. JEL codes: E24, E32, E50, J23, J51