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with the increasing popularity of ecological civilization and sustainable development,enterprises should consider environmental protection measures in their operations in addition to pursue their economic interests.This paper establsihes a closed-loop supply chain network model composed of multiple suppliers,manufacturers,retailers,recyclers,and demand markets—regarding their dual goals of the profit maximization and the minimization of carbon emissions.The conditions necessary for establishing overall equilibrium and an equilibrium model of the entire closed-loop supply chain network are determined by applying variational inequality and dual theory.A modified projection contraction algorithm is used to design a model-solving program.Finally,using numerical examples,the paper conducts a comparative static analysis on important parameters such as the weight co-efficients of environmental protection objectives and consumers\' awareness of low-carbon environmental pro-tection and attains some beneficial enlightenment on management.The results indicate that when the environmental protection objectives of a certain type of enterprise increases,both the economic benefits and environmental protection performance will improve;when the environmental protection objectives of all en-terprises increases simultaneously,environmental protection performance improves significantly,but the changes in economic benefits of different enterprises are inconsistent and profit coordination is more complex.Although consumers\' awareness of low-carbon preference could improve environmental performance,it reduces the overall profits of network members and the entire closed-loop supply chain network as a whole.The above conclusions can be used as a reference for the government in designing low-carbon environmental protection policy and in closed-loop supply chain research.