@article{oai:chuo-u.repo.nii.ac.jp:00008144,
 author = {MATSUMOTO, Akio and SZIDAROVSZKY, Ferenc and TAKIZAWA, Hirokazu},
 journal = {経済研究所 Discussion Paper, IERCU Discussion Paper},
 month = {Mar},
 note = {application/pdf, An extended n-…rm 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 …rm it selects a maximum allowed amount of emission for each fi…rm. 
If the actual amount is higher than the allowed maximum, then the …rm 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 time delay is introduced into the penalties the …rms have to pay and into the rewards the …rms receive.
In analyzing the stability of the equilibrium both continuous and discrete time scales are considered.
 For mathematical simplicity the case of symmetric …rms is analyzed.
 In the continuous case the equilibrium is either always stable or stable if the delay is sufficiently small and at the critical value Hopf bifurcation occurs. 
In the discrete case the delay is assumed to be unity.
 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. 
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.},
 title = {Extended Oligopolies with Pollution Penalties and Rewards},
 volume = {275},
 year = {2017}
}