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

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E-pub ahead of print
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<mark>Journal publication date</mark>31/07/2025
<mark>Journal</mark>Mathematics and Computers in Simulation
Volume233
Number of pages24
Pages (from-to)75-98
Publication StatusE-pub ahead of print
Early online date3/02/25
<mark>Original language</mark>English

Abstract

This paper examines a monopoly market featured by a general isoelastic demand function. Assuming that the monopolist's cost function is quadratic, we investigate the influence of the price elasticity of demand on the behavior of monopoly games under various (decreasing, constant, and increasing) returns to scale. Note that the assumption of a general isoelastic demand function and a quadratic cost function results in the equilibrium equation becoming transcendental, which makes the closed-form solutions unattainable. To overcome this obstacle, we adopt an innovative approach that utilizes the special structure of the marginal revenue and the marginal cost to conduct the comparative static analysis and the stability analysis. This paper also introduces two boundedly rational dynamic models based on different (gradient and LMA) mechanisms of adjusting the output. Our findings reveal that the LMA model is more stable in both the parameter space and the state space than the gradient model. In particular, it is proved that the unique non-vanishing equilibrium of the LMA model is globally asymptotically stable.