Dynamic Models of Pollution Penalties and Rewards with Time Delays
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 u...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2020/3162634 |
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| _version_ | 1832554111926534144 |
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| author | Akio Matsumoto Ferenc Szidarovszky |
| author_facet | Akio Matsumoto Ferenc Szidarovszky |
| author_sort | Akio Matsumoto |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bb7de70e6a8546c0899ed29b6e3aa52a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bb7de70e6a8546c0899ed29b6e3aa52a2025-02-03T05:52:29ZengWileyAbstract and Applied Analysis1085-33751687-04092020-01-01202010.1155/2020/31626343162634Dynamic Models of Pollution Penalties and Rewards with Time DelaysAkio Matsumoto0Ferenc Szidarovszky1Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji, Tokyo 192-0393, JapanDepartment of Mathematics, Corvinus University, Budapest, Fövám tér 8, 1093, HungaryIn 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.http://dx.doi.org/10.1155/2020/3162634 |
| spellingShingle | Akio Matsumoto Ferenc Szidarovszky Dynamic Models of Pollution Penalties and Rewards with Time Delays Abstract and Applied Analysis |
| title | Dynamic Models of Pollution Penalties and Rewards with Time Delays |
| title_full | Dynamic Models of Pollution Penalties and Rewards with Time Delays |
| title_fullStr | Dynamic Models of Pollution Penalties and Rewards with Time Delays |
| title_full_unstemmed | Dynamic Models of Pollution Penalties and Rewards with Time Delays |
| title_short | Dynamic Models of Pollution Penalties and Rewards with Time Delays |
| title_sort | dynamic models of pollution penalties and rewards with time delays |
| url | http://dx.doi.org/10.1155/2020/3162634 |
| work_keys_str_mv | AT akiomatsumoto dynamicmodelsofpollutionpenaltiesandrewardswithtimedelays AT ferencszidarovszky dynamicmodelsofpollutionpenaltiesandrewardswithtimedelays |