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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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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. Etienne Gagnon, 2006. "Price Setting during Low and High Inflation: Evidence from Mexico," 2006 Meeting Papers 300, Society for Economic Dynamics.
  2. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
  3. Fredrik Wulfsberg, 2009. "Price adjustments and inflation - evidence from Norwegian consumer price data 1975-2004," Working Paper 2009/11, Norges Bank.
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  8. Marco Bonomo & Carlos Carvalho, 2004. "Endogenous Time-Dependent Rules and Inflation Inertia," Macroeconomics 0402005, EconWPA, revised 19 May 2005.
  9. Saroj Bhattarai & Raphael Schoenle, 2011. "Multiproduct firms and price-setting: theory and evidence from U.S. producer prices," Globalization and Monetary Policy Institute Working Paper 73, Federal Reserve Bank of Dallas.
  10. Ricardo Reis, 2005. "Inattentive Producers," NBER Working Papers 11820, National Bureau of Economic Research, Inc.
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  12. F. Alvarez & F. Lippi & L. Paciello, 2010. "Optimal price setting with observation and menu costs," 2010 Meeting Papers 478, Society for Economic Dynamics.
  13. repec:nbr:nberre:0126 is not listed on IDEAS
  14. Cavallo, Alberto & Rigobon, Roberto, 2011. "The Distribution of the Size of Price Changes," Working Papers 2011-011, Banco Central de Reserva del Perú.
  15. 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.
  16. 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.
  17. Ernesto Pasten, 2012. "Rational Inattention, Multi-Product Firms and the Neutrality of Money," 2012 Meeting Papers 346, Society for Economic Dynamics.
  18. Mark Gertler & John Leahy, 2008. "A Phillips Curve with an Ss Foundation," Journal of Political Economy, University of Chicago Press, vol. 116(3), pages 533-572, 06.
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  20. Klenow, Peter J. & Malin, Benjamin A., 2010. "Microeconomic Evidence on Price-Setting," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 6, pages 231-284 Elsevier.
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Citations

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Cited by:
  1. 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.
  2. Joseph S. Vavra, 2013. "Inflation Dynamics and Time-Varying Volatility: New Evidence and an Ss Interpretation," NBER Working Papers 19148, National Bureau of Economic Research, Inc.
  3. Martin Eichenbaum & Nir Jaimovich & Sergio Rebelo & Josephine Smith, 2014. "How Frequent Are Small Price Changes?," American Economic Journal: Macroeconomics, American Economic Association, vol. 6(2), pages 137-55, April.
  4. Julio Blanco & Isaac Baley, 2013. "Learning to Price," 2013 Meeting Papers 663, Society for Economic Dynamics.
  5. 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.

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