Under the influence of the carbon tax-carbon trading policy and taking a low-carbon supply chain consisting of a leading retailer and subordinate small and medium-sized manufacturers(SMM)as research object,this study explores the fair concern decision-making of SMM and the coordination of the supply chain by constructing a decentralized decision-making model for whether SMM has fair concern behavior and a centralized decision-making model and by comparing and analyzing the optimal decision-making of each model.The impact of fair concern coefficient,carbon reduction rate and carbon tax rate on supply chain pricing and profits under SMM fair concern is studied while a"Nash negotiation-two part pricing"contract is designed to achieve systematic coordination.It is found that under the influence of carbon tax-carbon trading policy,the profits of supply chain members decrease with carbon tax rates increasing,but the profits of supply chain members present two different changing directions with carbon reduction rates changing.The fair concern behavior of SMM can increase wholesale prices and self profits,reduce retailers'profits,but has no impact on retail prices and system profits;as the fair concern coefficient of SMM increases,the profit gap between retailers and SMM narrows.The"Nash negotiation-two part pricing"contract designed in this study can achieve systematic coordination.