The (Q,S,s) Pricing Rule

We introduce menu costs in the search-theoretic model of imperfect competition of Burdett and Judd. When menu costs are not too large, the equilibrium is such that sellers follow a (Q,S,s) pricing rule. According to the rule, a seller lets inflation erode the real value of its nominal price until it reaches some point s. Then, the seller pays the menu cost and resets the real value of its nominal price to a point randomly drawn from a distribution with support [S, Q], where s< S < Q. A (Q, S, s) equilibrium differs with respect to a standard (S, s) equilibrium: (1) in a (Q,S,s) equilibrium, sellers sometimes keep their nominal price constant to avoid paying the menu cost, other times because they are indifferent to changes in the real value of their price. An exploratory calibration reveals that menu costs account less than half of the observed duration of nominal prices. (2) in a (Q,S,s) equilibrium, higher inflation leads to higher real prices, as sellers pass onto buyers the cost of more frequent price adjustments, and to lower welfare.