Price setting with menu cost for multi-product firms

We model the pricing decisions of a multi-product firm that faces a fixed 'menu' cost: once the cost is paid, the firm can adjust the price of all its products. We characterize analytically the steady state firm’s decision 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 that are 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 cumulative response of output to a monetary shock is the product of three terms: the steady state standard deviation of price changes, the average time elapsed between price changes, and a function of both the number of products and the size of the monetary shock. The size of the cumulative response of output and the length of the half-life of the response of aggregate prices to a monetary shock increase with the number of products, both of them more than double as the number of products goes from 1 to ten, quickly converging to the ones of Taylor’s staggered price model.