<p>Low carbon has emerged as a contentious topic in both academic discourse and governmental policy agendas, demanding urgent attention to mitigate carbon emissions. In this paper, a supply chain model is constructed that includes the new product manufacturer and the remanufacturer, which are in perfect competition in the market. With the help of game theory analysis, the study examines the carbon emission reduction decisions of new and remanufacturing product manufacturers under different carbon cap-and-trade policies. In the face of diverse consumers with low carbon sensitivity, manufacturers also make different carbon reduction and pricing decisions to maximize their interests. The results of this study show that lower carbon quotas while favoring remanufacturers, pose a serious threat to the interests of new product manufacturers. Based on this, this study proposes a reasonable interval for the government’s carbon quota setting, aiming to protect the profitability level of new product manufacturers. Moreover, an appropriate carbon quota is equivalent to subsidizing the remanufacturer while enhancing the carbon emission reduction rate of the new product manufacturer, thus achieving a win–win situation. This study also found that too much low carbon sensitivity of consumers may constrain the development of the industry. On the contrary, when consumers’ low carbon sensitivity is maintained at a moderate level, manufacturers are incentivized to increase their carbon reduction rates. Therefore, based on setting a reasonable carbon quota, the government should work with industry regulators to maintain consumers’ low carbon sensitivity at an appropriate level through education and advertising. This will effectively stimulate market vitality and enhance the profitability of manufacturers, thereby promoting the building of an environmentally friendly society.</p> Graphical abstract <p></p>