Abstract: As a result of global warming, low-carbon economic development is widely accepted, thereby the low-carbon supply chain management has come up as an important research paradigm in operations management. Due to the environmental pressures and the guidance of the government, the low-carbon consciousness of consumers is increasing and low-carbon consumption is becoming more and more popular in the whole society. Through literature review, it is found that the consumer preference to low carbon and reference effect have strong impacts on the supply chain management. Therefore, it is important to study low-carbon supply chain management considering these two types of consumers' behavior. In this paper, for one manufacture-one supplier supply chain, a dynamic optimization and coordination about joint emission reduction is discussed. The reference low-carbon level for a product is assumed to be a weighted average of the historical low-carbon level. In addition, the low-carbon level is assumed to have a positive effect on the market demand, and the reference low-carbon level is assumed to have a negative effect on the market demand. Based on the differential game theory and method, the manufacturer and the supplier's optimal emission reduction strategy, revenue and the total revenue of the supply chain in decentralized and centralized decision making mode are investigated and compared. The results show that cooperative game equilibrium has more Pareto advantage. According to the comparison, a two-way subsidy contract is proposed. With this contract, both the manufacturer and the supplier achieve the Pareto improvement in a certain condition. Finally, based on the parameter values chosen from the previous literature (e.g. Liu et al., 2015^[7]), a numerical example verifies the main conclusions of this paper and the sensitivity analysis of key parameters is also presented. The research shows that the manufacturer and supplier's revenue increases as the increase of the level of consumers' preference to low carbon under the condition that the two-way subsidy contract can coordinate the supply chain. The initial reference low-carbon level can affect the tendency of the manufacturer and supplier's revenue with the reference low-carbon level parameter in decentralized and decision making and two-way subsidy contract mode. Although the initial reference low-carbon level can affect the tendency of the reference low-carbon level with time, the reference low-carbon level tends to the same stable value for the same channel structure. In this study, the scope and content of the low-carbon supply chain management problem under the consideration of the consumers' behavior are enriched, and the guidance for the related study on the behavioral operation problem is provided.

Key words: supply chain coordination, joint emission reduction, differential game, reference low-carbon level effect, preference to low carbon