Dynamic analysis of the decision of authorized remanufacturing supply chain affected by government subsidies under cap-and-trade policies

In this paper, we apply nonlinear dynamics to analyse the influence of government subsidies on the stability of the authorized remanufacturing supply chain pricing system. We build a bounded rational decision model in the context of a supply chain consisting of new product manufacturers, new product retailers, and re-manufacturers. New product manufacturers charge remanufacturers an authorization fee. And government subsidizes remanufacturers. The government subsidies need to balance the social welfare and environmental development. The main findings of the study: (i) When the carbon emissions of remanufactured products are below a certain threshold, the government can increase subsidies to help reduce the carbon emissions of the system; The size of the threshold positively correlates with the cross-price elasticity. (ii) Government subsidies are beneficial to increase the stable range of the price adjustment speed of remanufactured and new products. In contrast, government subsidies exceeding a certain threshold will reduce the stable range of authorization fee adjustment speed. The stable range of the authorization fee adjustment speed parameter is more sensitive to government subsidies, therefore, the stability of the supply chain decision system decreases with the increase of government subsidies; (iii) Remanufacturers' profits fluctuate wildly when manufacturers adjust authorization fees quickly causing system into chaos; When the market followers (retailers or remanufacturers) adjust decision quickly causing the system into chaos, the profit of the followers is lower than that of the equilibrium state.