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

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2025-01-28 DOI:10.1016/j.matcom.2025.01.017

Xiaoliang Li , Jing Yang , Ally Quan Zhang

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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.

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不同规模收益下需求价格弹性对垄断博弈的影响

本文研究具有一般等弹性需求函数的垄断市场。利用垄断者的二次成本函数，我们探讨了需求的价格弹性在不同规模收益（递减、不变和递增）下对垄断行为的影响。一般等弹性需求和二次成本函数的结合导致了一个超越平衡方程，使得封闭形式的解无法实现。为了应对这一挑战，我们开发了一种创新的方法，利用边际收入和成本的特定结构进行全面的比较静态和稳定性分析。此外，我们还介绍了基于不同调节机制的两种动态模型：梯度和局部垄断近似（LMA）。我们的研究结果表明，与梯度模型相比，LMA模型在参数空间和状态空间上都更加稳定。值得注意的是，我们证明了LMA模型的唯一非消失平衡点是全局渐近稳定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

期刊介绍： The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.