New-Keynesian Phillips curve with Bertrand competition and endogenous entry

We derive a New Keynesian Phillips curve under Calvo staggered pricing and endogenous market structures with Bertrand competition. Both strategic interactions and endogenous business creation strengthen the nominal rigidities. Price adjusters change their prices less when there are more direct competitors that do not adjust, which reduces the slope of the Phillips curve. Current and future firms entering in the markets decrease current inflation because they reduce markups and the welfare-based price index. Endogenous entry amplifies the impact of both monetary and supply shocks. We also characterize the optimal social planner allocation, that can be replicated with a labor subsidy and a dividend tax (both decreasing in the number of firms) and zero producer price inflation. The optimal Ramsey allocation implies zero inflation tax in steady state.