Environment protection and green development is of great importance. Therefore, this paper attempts to propose an environmentally friendly and sustainable development model that depends on environmental economics and game theory. This paper employs an analytical approach to show that the effects of carbon tax on environment regulation in case of the duopoly market structure. Some interesting conclusions are obtained. Firstly, factors affecting carbon tax, such as the importance of environment to the government, are captured. Secondly, this paper shows that low efficiency firm has more stimulation to reduce product substitutability and more motivation to practice product efficiency improving innovations. Thirdly, optimal carbon tax is compared between tax on energy input and unit carbon tax. The results show that unit tax is lower than energy input tax under optimal condition. More importantly, the numeric results of the paper clearly demonstrate that those countries committed to environment prefer input tax since it is more efficient in reducing energy consumption, while a profit maximization approach leads to the unit carbon tax. The findings of this paper can be helpful to those who are responsible for the environment and sustainable progress.

中文翻译：

---

双头垄断下碳税对环境的影响

环境保护和绿色发展具有重要意义。因此，本文试图提出一种以环境经济学和博弈论为基础的环境友好型可持续发展模式。本文采用分析方法来说明双头垄断市场结构下碳税对环境规制的影响。得到了一些有趣的结论。首先，捕捉影响碳税的因素，例如环境对政府的重要性。其次，本文表明，低效率企业对降低产品可替代性有更多的刺激，更有动力去实践提高产品效率的创新。第三，比较了能源投入税和单位碳税的最优碳税。结果表明，在最优条件下，单位税低于能源进项税。更重要的是，论文的数值结果清楚地表明，那些致力于环境的国家更喜欢进项税，因为它在减少能源消耗方面更有效，而利润最大化的方法导致单位碳税。本文的研究结果可以帮助那些对环境和可持续发展负责的人。