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Monopolistic competition, sticky prices, and the minimal mark-up in steady state

This note reports the rate of inflation that minimizes the mark-up of prices over marginal costs in the steady-state solution of a monopolistic competition model with either Taylor (1980) or Calvo (1983) pricing. The minimal mark-up is always found at a positive and low rate of inflation for any sensible parameter calibration. Actually, the rate of inflation that minimizes the mark-up is very close to ratio between the real rate of discount and the Dixit-Stiglitz elasticity. This result is robust to altenative sticky-price specifications.