Decreasing carbon emissions becomes essential for maximizing social welfare in power systems. This study investigates the market clearing strategy for maximizing participants' benefits in both economic and environmental power systems, considering renewable energy certificates (RECs). The proposed problem formulation is solved by a particle swarm optimization algorithm and applied to a modified IEEE 30-bus system. The study shows that a combined supply offer that includes supply costs, carbon emission costs (CEC), renewable energy (RE) costs, and REC pricing resulted in the greatest cost savings. This paper demonstrates the efficiency of thorough optimization approaches. In addition, a more effective model is obtained by including demand-sided bidding in the optimization framework in addition to CEC, RE costs, and REC prices, leading to higher social welfare and encouraging the adoption of sustainable energy utilization. These results emphasize the importance of incorporating various environmental and economic factors into optimization frameworks for low-carbon power systems. Implementing this comprehensive strategy promotes substantial enhancements in social welfare and the progression of sustainable energy methodologies.