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Influence of price elasticity of demand on monopoly games under different returns to scale

Author

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  • Li, Xiaoliang
  • Yang, Jing
  • Zhang, Ally Quan

Abstract

This paper examines a monopoly market featured by a general isoelastic demand function. With a quadratic cost function for the monopolist, we explore how the price elasticity of demand influences monopolistic behavior under different (decreasing, constant, and increasing) returns to scale. The combination of the general isoelastic demand and quadratic cost functions leads to a transcendental equilibrium equation, making closed-form solutions unattainable. To address this challenge, we develop an innovative approach that leverages the specific structure of marginal revenue and cost to conduct a comprehensive comparative static and stability analysis. Additionally, we introduce two dynamic models based on distinct adjustment mechanisms: gradient and local monopolistic approximation (LMA). Our findings reveal that the LMA model is more stable in both parameter and state spaces compared to the gradient model. Notably, we prove that the unique non-vanishing equilibrium of the LMA model is globally asymptotically stable.

Suggested Citation

  • Li, Xiaoliang & Yang, Jing & Zhang, Ally Quan, 2025. "Influence of price elasticity of demand on monopoly games under different returns to scale," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 75-98.
    • Handle: RePEc:eee:matcom:v:233:y:2025:i:c:p:75-98
    DOI: 10.1016/j.matcom.2025.01.017
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