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Price-taking behavior versus continuous dynamic optimizing

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  • Huang, Weihong

Abstract

In a quantity-competition oligopoly, previous studies have shown that a price-taking firm can outperform any rival with identical technology that produces at a different output level at any intertemporal equilibrium. This research seeks to examine this seemingly counter-intuitive fact in a heterogeneous duopoly consisting of an adaptive price-taker and a dynamic optimizer who dynamically optimizes its either absolute or relative profit stream over an infinite planning horizon. With conventional economic assumptions, the Hamiltonian system always converges to a saddle point. If goal of the dynamic optimizer is absolute profit, the price-taker produces more than the dynamic optimizer at the equilibrium, around which there exists a long-run relative profitability portion for the price-taker. Consequently, the price-taker unconsciously makes higher relative profit than the dynamic optimizer in the long-run. In contrast, if the dynamic optimizer pursues the relative profit, both firms produce at the competitive level at the equilibrium while the whole optimal path lies in the relative profitability regime of the dynamic optimizer so that it will enjoy a higher profit than the price-taker before reaching equilibrium. These results provide economical justification for ever-growing evolutionary game theoretical literatures in appreciating price-taking behavior and additionally clarify possible misunderstandings in interpreting their conclusions.

Suggested Citation

  • Huang, Weihong, 2011. "Price-taking behavior versus continuous dynamic optimizing," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 37-50.
  • Handle: RePEc:eee:jeborg:v:78:y:2011:i:1:p:37-50
    DOI: 10.1016/j.jebo.2010.12.006
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    References listed on IDEAS

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    1. Huang, Weihong, 2008. "The long-run benefits of chaos to oligopolistic firms," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1332-1355, April.
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    Cited by:

    1. Accinelli, Elvio & Covarrubias, Enrique, 2015. "Evolution in a Walrasian setting," MPRA Paper 64736, University Library of Munich, Germany.
    2. Yu Zhang & Weihong Huang, 2018. "Impact of strategy switching on wealth accumulation," Journal of Evolutionary Economics, Springer, vol. 28(4), pages 961-983, September.
    3. Anufriev, Mikhail & Kopányi, Dávid, 2018. "Oligopoly game: Price makers meet price takers," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 84-103.
    4. Hirth Hans & Walther Martin, 2018. "Strategic Effects between Price-takers and Non-price-takers," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(2), pages 1-18, July.

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    More about this item

    Keywords

    Price-taking; Dynamic optimization; Oligopoly; Duopoly; Optimal control; Hamiltonian; Saddle point;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory

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