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Price setting with menu cost for multi-product firms

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  • Alvarez, Fernando E
  • Lippi, Francesco

Abstract

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.

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 8863.

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Date of creation: Feb 2012
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Handle: RePEc:cpr:ceprdp:8863

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Keywords: economies of scope in price changes; fixed costs; impulse responses; menu cost; monetary shocks; optimal control in multiple dimensions; quasi-variational inequalities;

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References

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  1. Mark Gertler & John Leahy, 2006. "A Phillips curve with an Ss foundation," Working Papers 06-8, Federal Reserve Bank of Philadelphia.
  2. Martin S. Eichenbaum & Nir Jaimovich & Sergio Rebelo & Josephine Smith, 2012. "How Frequent Are Small Price Changes?," NBER Working Papers 17956, National Bureau of Economic Research, Inc.
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  8. Fernando Alvarez & Francesco Lippi & Luigi Paciello, 2013. "Monetary Shocks with Observation and menu Costs," EIEF Working Papers Series 1310, Einaudi Institute for Economics and Finance (EIEF), revised May 2013.
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Cited by:
  1. Joseph Vavra, 2013. "Inflation Dynamics and Time-Varying Volatility: New Evidence and an Ss Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 129(1), pages 215-258.
  2. Julio Blanco & Isaac Baley, 2013. "Learning to Price," 2013 Meeting Papers 663, Society for Economic Dynamics.
  3. Emi Nakamura & J�n Steinsson, 2013. "Price Rigidity: Microeconomic Evidence and Macroeconomic Implications," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 133-163, 05.
  4. Alvarez, Fernando & Dixit, Avinash, 2014. "A real options perspective on the future of the Euro," Journal of Monetary Economics, Elsevier, vol. 61(C), pages 78-109.
  5. Martin S. Eichenbaum & Nir Jaimovich & Sergio Rebelo & Josephine Smith, 2012. "How Frequent Are Small Price Changes?," NBER Working Papers 17956, National Bureau of Economic Research, Inc.
  6. Joseph Vavra, 2011. "Inflation Dynamics and Time-Varying Uncertainty: New Evidence and an Ss Interpretation," 2011 Meeting Papers 126, Society for Economic Dynamics.

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