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

Xiaoliang Li, Jing Yang and Ally Quan Zhang

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 233, issue C, 75-98

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.

Keywords: General isoelastic demand; Quadratic cost; Local asymptotical stability; Global asymptotical stability (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475425000175
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:233:y:2025:i:c:p:75-98

DOI: 10.1016/j.matcom.2025.01.017

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().