We analyze, in this paper, DSNK general equilibrium model with indivisible 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. The presence of monopoly unions introduces real wage rigidity in the model and this implies a trade-off between output stabilization and inflation stabilization i.e., as in Blanchard and Galì (2005), the so called "divine coincidence" does not hold. 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 sector. The larger is this number, the smaller are these effects. We derive a welfare based objective function as a second order Taylor approximation of the expected utility of the economy's representative agent and we analyze optimal monetary policy under discretion and under constrained commitment. We show that the larger is the number 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 affected 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.
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