This article constructs a carbon emissions trading market based on a mixed oligopoly model, and calculates the equilibrium output decisions and changes in social welfare for firms before and after entering the carbon emissions trading market. The relationship between carbon quota allocation policies and social welfare is discussed. Our main research results show that in the carbon emissions trading market based on the mixed oligopoly model, the government can improve social welfare without sacrificing environmental effectiveness by appropriately optimizing carbon quota allocation policies. The main results of this article extend some of the previous research findings and enrich the analysis of social welfare in the carbon emissions trading system under the mixed duopoly model, providing some theoretical basis for the formulation of government industrial policies.