IDEAS home Printed from https://ideas.repec.org/a/red/issued/v8y2005i4p877-901.html
   My bibliography  Save this article

The Optimality of a Control Band Policy

Author

Listed:
  • Jose M. Plehn-Dujowich

    (University of Buffalo)

Abstract

Consider a firm with an arbitrary profit function whose relative price follows a Brownian motion with negative drift. When the firm faces a fixed cost of price adjustment, we prove the optimal pricing policy is a control band if the following sufficient conditions are met: the profit function is continuous, strictly concave and single-peaked; moreover, together with its first and second derivatives, it is bounded in absolute value by a polynomial. We also demonstrate various ways of constructing the value function associated with the control band policy and show it has certain properties carried over from the profit function. Numerical examples are found to be consistent with empirical estimates regarding the frequency of price adjustments. (Copyright: Elsevier)

Suggested Citation

  • Jose M. Plehn-Dujowich, 2005. "The Optimality of a Control Band Policy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(4), pages 877-901, October.
    • Handle: RePEc:red:issued:v:8:y:2005:i:4:p:877-901
    DOI: 10.1016/j.red.2005.05.001
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1016/j.red.2005.05.001
    File Function: Full text
    Download Restriction: Access to full texts is restricted to ScienceDirect subscribers and ScienceDirect institutional members. See http://www.sciencedirect.com/ for details.
    File URL: https://libkey.io/10.1016/j.red.2005.05.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Levy, Daniel & Bergen, Mark & Dutta, Shantanu & Venable, Robert, 1997. "The Magnitude of Menu Costs: Direct Evidence from Large U.S. Supermarket Chains," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 112(3), pages 791-824.
    2. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    3. Abel, Andrew B & Eberly, Janice C, 1994. "A Unified Model of Investment under Uncertainty," American Economic Review, American Economic Association, vol. 84(5), pages 1369-1384, December.
    4. Giuseppe Bertola & Ricardo J. Caballero, 1990. "Kinked Adjustment Costs and Aggregate Dynamics," NBER Chapters, in: NBER Macroeconomics Annual 1990, Volume 5, pages 237-296, National Bureau of Economic Research, Inc.
    5. Andrew Caplin & John Leahy, 1991. "State-Dependent Pricing and the Dynamics of Money and Output," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 683-708.
    6. Blinder, Alan S, 1991. "Why Are Prices Sticky? Preliminary Results from an Interview Study," American Economic Review, American Economic Association, vol. 81(2), pages 89-96, May.
    7. Danziger, Leif, 1983. "Price Adjustments with Stochastic Inflation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 699-707, October.
    8. J. Michael Harrison & Thomas M. Sellke & Allison J. Taylor, 1983. "Impulse Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 454-466, August.
    9. Avner Bar-Ilan & Agnès Sulem, 1995. "Explicit Solution of Inventory Problems with Delivery Lags," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 709-720, August.
    10. Eytan Sheshinski & Yoram Weiss, 1977. "Inflation and Costs of Price Adjustment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 287-303.
    11. Bar-Ilan, A. & Sulem, A., 1991. "Explicit Solution in Inventory Problems with Delivery Lags," Papers 5-91, Tel Aviv - the Sackler Institute of Economic Studies.
    12. Eytan Sheshinski & Yoram Weiss, 1983. "Optimum Pricing Policy under Stochastic Inflation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(3), pages 513-529.
    13. Dixit, Avinash, 1991. "A simplified treatment of the theory of optimal regulation of Brownian motion," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 657-673, October.
    14. Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
    15. George M. Constantinides & Scott F. Richard, 1978. "Existence of Optimal Simple Policies for Discounted-Cost Inventory and Cash Management in Continuous Time," Operations Research, INFORMS, vol. 26(4), pages 620-636, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yiannis Kamarianakis & Anastasios Xepapadeas, 2006. "Stochastic impulse control with discounted and ergodic optimization criteria: A comparative study for the control of risky holdings," Working Papers 0709, University of Crete, Department of Economics.
    2. Yiannis Kamarianakis & Anastasios Xepapadeas, 2006. "Controlling the risky fraction process with an ergodic criterion," Working Papers 0710, University of Crete, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Erwan Gautier, 2009. "Les ajustements microéconomiques des prix : une synthèse des modèles théoriques et résultats empiriques," Revue d'économie politique, Dalloz, vol. 119(3), pages 323-372.
    2. Bonomo, Marco, 2000. "Are One-Sided S,s Rules Useful Proxies For Optimal Pricing Rules?," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 20(1), May.
    3. Emmanuel Dhyne & Jerzy Konieczny & Fabio Rumler & Patrick Sevestre, 2009. "Price rigidity in the euro area - An assessment," European Economy - Economic Papers 2008 - 2015 380, Directorate General Economic and Financial Affairs (DG ECFIN), European Commission.
    4. Levy, Daniel & Müller, Georg & Chen, Haipeng (Allan) & Bergen, Mark & Dutta, Shantanu, 2010. "Holiday Price Rigidity and Cost of Price Adjustment," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 77(305), pages 172-198.
    5. Alexander L. Wolman, 2007. "The frequency and costs of individual price adjustment," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(6), pages 531-552.
    6. Hansen, Per Svejstrup, 1996. "Permanent effects of monetary policy in a dynamic menu cost model," Economics Letters, Elsevier, vol. 52(1), pages 61-66, July.
    7. Wilko Letterie & Øivind Anti Nilsen, 2016. "Price Changes - Stickiness and Internal Coordination in Multiproduct Firms," CESifo Working Paper Series 5701, CESifo.
    8. Bar-Ilan, Avner & Sulem, Agnes & Zanello, Alessandro, 2002. "Time-to-build and capacity choice," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 69-98, January.
    9. Dutta, Shantanu, et al, 1999. "Menu Costs, Posted Prices, and Multiproduct Retailers," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(4), pages 683-703, November.
    10. Le, Duc Thuc & Jones, John Bailey, 2005. "Optimal investment with lumpy costs," Journal of Economic Dynamics and Control, Elsevier, vol. 29(7), pages 1211-1236, July.
    11. Leif Danziger, 1999. "A Dynamic Economy with Costly Price Adjustments," American Economic Review, American Economic Association, vol. 89(4), pages 878-901, September.
    12. Jaime Casassus & Pierre Collin-Dufresne & Bryan R. Routledge, 2005. "Equilibrium Commodity Prices with Irreversible Investment and Non-Linear Technology," NBER Working Papers 11864, National Bureau of Economic Research, Inc.
    13. Carlos Borondo, 1994. "La rigidez nominal de los precios de la Nueva Economía Keynesiana: una panorámica," Investigaciones Economicas, Fundación SEPI, vol. 18(2), pages 245-288, May.
    14. Christian R. Ahlin, 2001. "Optimal Pricing Under Stochastic Inflation: State:Dependent (s,S) Policies," Vanderbilt University Department of Economics Working Papers 0127, Vanderbilt University Department of Economics.
    15. Kevin X. D. Huang & Jonathan L. Willis, 2018. "Sectoral Interactions and Monetary Policy under Costly Price Adjustments," Annals of Economics and Finance, Society for AEF, vol. 19(2), pages 337-374, November.
    16. Claus Thustrup Kreiner, 2002. "Do the New Keynesian Microfoundations Rationalise Stabilisation Policy?," Economic Journal, Royal Economic Society, vol. 112(479), pages 384-401, April.
    17. Attila Rátfai, 2007. "The frequency and size of price adjustment: microeconomic evidence," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(7), pages 751-762.
    18. repec:awi:wpaper:0477 is not listed on IDEAS
    19. House, Christopher L., 2014. "Fixed costs and long-lived investments," Journal of Monetary Economics, Elsevier, vol. 68(C), pages 86-100.
    20. Andrew W. Lo & Harry Mamaysky & Jiang Wang, 2004. "Asset Prices and Trading Volume under Fixed Transactions Costs," Journal of Political Economy, University of Chicago Press, vol. 112(5), pages 1054-1090, October.
    21. Virgiliu Midrigan, 2011. "Menu Costs, Multiproduct Firms, and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(4), pages 1139-1180, July.

    More about this item

    Keywords

    stochastic control; menu cost;

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:red:issued:v:8:y:2005:i:4:p:877-901. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christian Zimmermann (email available below). General contact details of provider: https://edirc.repec.org/data/sedddea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.