Optimal monetary policy under Calvo pricing with Bertrand competition

We consider a NK model characterized by a small and fixed number of firms competing in prices à la Bertrand and we study the implications for monetary policy under both exogenous and endogenous market concentration. We find that the implied NKPC has a lower slope compared to a standard NK model with atomistic firms, and the determinacy region enlarges assuming a standard Taylor rule. We characterize the impact of competition on the optimal monetary rules within the linear-quadratic approach of Rotemberg-Woodford. The optimal monetary rule requires a less aggressive reaction to inflationary shocks compared to monopolistic competition, but an increase in competition, due to either an increase in substitutability between the goods or in the number of firms, makes it optimal to adopt a more aggressive reaction in front of inflationary shocks. Finally, more competition increases the gains from commitment.