New-Keynesian Phillips Curve with Bertrand Competition and Endogenous Entry

We derive a New Keynesian Phillips Curve under Calvo staggered pricing and price competition. Firms strategic interactions induce price adjusters to change their prices less when there are more firms that do not adjust. This reduces the slope of the Phillips curve and generates an additional source of real rigidity that magnifies the impact of monetary shocks on the economic activity. Endogenous entry amplifies the impact of both monetary and real shocks. We study the design of the optimal Taylor rule in the case of a fixed number of firms and we characterize the optimal monetary policy to restore the social planner allocation and the optimal Ramsey steady state in the case of endogenous entry.