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