Price Setting With Menu Cost for Multiproduct Firms

Abstract

We model the decisions of a multiproduct 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 both increase with the number of products; they more than double as the number of products goes from 1 to 10, quickly converging to the response of Taylor's staggered price model.

Not all beef‐cut price shocks are alike: Disentangling supply and demand shocks in the US beef market

“…The second identifying assumption is that restaurants and other FAFH outlets want to maintain relatively stable prices-in other words, they face nonzero menu costs (e.g., Alvarez & Lippi, 2014) or otherwise "sticky" prices, which implies the exclusion restriction, b = 0 23 . This exclusion restriction says shocks to FAFH expenditure are independent of contemporaneous shocks to wholesale prices.…”

Dispersed information and the non-neutrality of money: fifty years after Lucas, 1972

“…In particular, considering multi-product firms would allow to weaken the 'selection effect' which is inherent in state-dependent pricing models, and which explains why these models usually deliver much less monetary non-neutrality than their time-dependent counterparts. Alvarez and Lippi (2014) notably show that when the number of different goods priced by each firm tends to infinity, the selection effect vanishes and the amount of monetary non-neutrality generated by state-dependent models is as high as that generated by the popular model of Taylor (1980).…”

The Real Effects of Monetary Shocks: Evidence from Micro Pricing Moments

“…F.1 The Sufficient Statistic in Alvarez et al (2016Alvarez et al ( , 2020 The analytical menu cost model in Alvarez et al (2016aAlvarez et al ( , 2020 is set in continuous time and features no stochastic monetary shocks, random menu costs, Gaussian idiosyncratic productivity shocks, no trend inflation, and firm quadratic objective functions, among other ingredients. This model captures the essence of many pricing models including Taylor (1980), Calvo (1983), Reis ( 2006), Golosov and Lucas (2007), Nakamura and Steinsson (2010), Midrigan ( 2011) and Alvarez and Lippi (2014). 16 In Alvarez et al (2016aAlvarez et al ( , 2020, they summarize monetary non-neutrality M by the following expression when monetary shocks are small:…”