Extended oligopolies with pollution penalties and rewards
type: Item
instance of: scholarly article
title: Extended oligopolies with pollution penalties and rewards
zbMATH Open document ID: 1422.91469
DOI: 10.1155/2018/7861432
author: F. Szidarovszky
author: Hirokazu Takizawa
author: Akito Matsumoto
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: An extended \(n\)-firm oligopoly with product differentiation is considered. It is assumed that the government selects an emission standard for the industry and based on the output and technology of each firm it selects a maximum allowed amount of emission for each firm. If the actual amount is higher than the allowed maximum, then the firm has to pay a constant multiple of the excess to the government; otherwise it is rewarded similarly based on the saved emission amount. The existence of the unique interior equilibrium is first proved, and then the effect of the level of penalty or reward and that of the emission standard on the industry output and therefore on the total emission level is also examined. Time delay is introduced into the penalties the firms have to pay and into the rewards the firms receive. In analyzing the stability of the equilibrium both discrete and continuous time scales are considered. For mathematical simplicity the case of symmetric firms is analyzed. In the discrete case the various values of the delay length are examined. The equilibrium is stable if either the total industry output is sufficiently large or the common speed of adjustment of the firms is sufficiently small. In the continuous case, either the equilibrium is always stable or stability occurs if the delay is sufficiently small and at the critical value Hopf bifurcation occurs.
Mathematics Subject Classification ID: 91B54
Mathematics Subject Classification ID: 91B76
zbMATH DE Number: 7026685
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/7861432
OpenAlex ID: W2809220603
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Wikidata QID: Q129653076
description: scientific article; zbMATH DE number 7026685