We analyze, in this paper, a DSGE New Keynesian model with indi- visible labor where firms may belong to two different final goods producing sectors one where wages and employment are determined in competitive labor markets and the orther where wages and employment are the result of a contractual process between unions and firms. Bargaining between firms and monopoly unions implies real wage rigidity in the model and, in turn, an endogenous trade-off between output stabilization and infla- tion stabilization. We show that the negative effect of a productivity shock on inflation and the positive effect of a cost-push shock is crucially determined by the proportion of firms that belong to the competitive sec- tor. The larger is this number, the smaller are these effects. We derive a welfare based objective function as a second order Taylor approxima- tion of the expected utility of the economy's representative agent and we analyze optimal monetary policy. We show that the larger is the num- ber of firms that belong to the competitive sector, the smaller should be the response of the nominal interest rate to exogenous productivity and cost-push shocks. If we consider, however, an instrument rule where the interest rate must react to inflationary expectations, the rule is not af- fected by the structure of the labor market. The results of the model are consistent with a well known empirical regularity in macroeconomics, i.e. that employment volatility is larger than real wage volatility.