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The Optimality of a Control Band Policy

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
    8. 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.
    9. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
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    Cited by:

    1. Yiannis Kamarianakis & Anastasios Xepapadeas, 2006. "Controlling the risky fraction process with an ergodic criterion," Working Papers 0710, University of Crete, Department of Economics.
    2. 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.

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    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

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