Sustainable pricing and production policies for two competing firms with carbon emissions tax

This paper studies the incentive for a firm's sustainable pricing and production policies with carbon dioxide emissions tax policy. We consider two competing firms who have different operation efficiencies and produce a same product to the end-users. Based on game theory models, we derive the competing firms' optimal pricing and production policies, and show that the high-efficiency firm will set a lower retail price than that of the low-efficiency firm, either with same carbon emissions tax or without carbon emissions tax. When the two competing firms absorbed same carbon emissions tax, we show that both of them will set higher retail price than that without carbon emissions tax, and the high-efficiency firm's both profit reduction and carbon emissions reduction percentages are lesser than that of low-efficiency firm. In addition, we find that when a firm incurs a higher carbon emissions tax, the firm gains a higher carbon emissions reduction percentage, but the competing firm gains a lower carbon emissions reduction percentage. We also find that in order to achieve a certain desired carbon emissions reduction percentage, the carbon emissions tax imposed on the high-efficiency firm should be more than that on the low-efficiency firm.