Abstract: In this paper,the problem of choosing low-carbon technologies under carbon trading market mechanism is investigated by dividing the carbon emissions of a product into the manufacturing stage and the usage stage. It is we assumed that the supplier can make efforts to reduce the carbon emission in each of the two stages and the efficiencies in terms of reducing the carbon emission in the two stages by the supplier's efforts are different. It is Further assumed that consumers prefer to low-carbon products.The technology characteristics of low carbon with cost and efficiency are analyzed and a dynamic supply chain optimization model with low carbon technology investment and cooperation is set up. The optimal decision for the supplier (i.e., the efforts that made in two carbon emission stages) is derived and obtain the corresponding profits of the chain members are obtained by solving a Hamilton Jacobi Bellman Equation. The optimal trajectory of product carbon emission is obtained. In view of the limited choice about technical features in practice and the willing cooperation level of the retailer, the market condition for promoting the retailer cooperation is derived. The study shows that:(1) In the short term, the margin profit of emission reduction can improve both emission and profit; while in the long term, if the efforts are selected properly in the two carbon emission stages, a win-win result can be achieved. (2) The revenue from the market is crucial to cooperation, and has a positive impact on the cooperation between the two chain members. (3) Dividing emissions in the two carbon emission stages under carbon trading market can encourage carbon reduction efforts. Additionally, numerical experiments are used to analyze the influence of critical factors. In this paper, the question about which kind of technologies should be adopted is answered and a basic idea and framework is provided for supply chain carbon emission reducing.

Key words: cap and trade, low-carbon preference, low-carbon technology selection, differential game