2020 Dynamic Models of Pollution Penalties and Rewards with Time Delays
Akio Matsumoto, Ferenc Szidarovszky
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Abstr. Appl. Anal. 2020: 1-10 (2020). DOI: 10.1155/2020/3162634


In cases of nonpoint pollution sources, the regulator can observe the total emission but unable to distinguish between the firms. The regulator then selects an environmental standard. If the total emission level is higher than the standard, then the firms are uniformly punished, and if lower, then uniformly awarded. This environmental regulation is added to n-firm dynamic oligopolies, and the asymptotical behavior of the corresponding dynamic systems is examined. Two particular models are considered with linear and hyperbolic price functions. Without delays, the equilibrium is always (locally) asymptotically stable. It is shown how the stability can be lost if time delays are introduced in the output quantities of the competitors as well as in the firms’ own output levels. Complete stability analysis is presented for the resulting one- and two-delay models including the derivations of stability thresholds, stability switching curves, and directions of the stability switches.


The first author highly acknowledges the financial supports from the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (C) 20K01566) and Chuo University (Grant for Special Research). The usual disclaimers apply.


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Akio Matsumoto. Ferenc Szidarovszky. "Dynamic Models of Pollution Penalties and Rewards with Time Delays." Abstr. Appl. Anal. 2020 1 - 10, 2020. https://doi.org/10.1155/2020/3162634


Received: 13 April 2020; Accepted: 1 June 2020; Published: 2020
First available in Project Euclid: 28 July 2020

Digital Object Identifier: 10.1155/2020/3162634

Rights: Copyright © 2020 Hindawi


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