Price Setting with menu cost for Multi-product firms

We model the decisions of a multi-product firm that faces a fixed "menu" cost: once it is paid, the firm can adjust the price of all its products. We characterize analytically the steady state firm's decisions in terms of the structural parameters: the variability of the flexible prices, the curvature of the profit function, the size of the menu cost, and the number of products sold. We provide expressions for the steady state frequency of adjustment, the hazard rate of price adjustments, and the size distribution of price changes, all in terms of the structural parameters. We study analytically the impulse response of aggregate prices and output to a monetary shock. The size of the output response and its duration increase with the number of products, they more than double as the number of products goes from 1 to ten, quickly converging to the ones of Taylor's staggered price model.