Abstract:This paper studies the problem consisting of multiple manufacturers, multiple retailers, multiple random market demand supply chain network equilibrium decision based on carbon cap constraints, consider the carbon tax policy. We use the equilibrium theory and variational inequality research tools, describe the competitive behavior of each layer in the decision network, give each layer equilibrium and network equilibrium conditions, construct the stochastic demand closed-loop supply chain network equilibrium model with cap constraints and carbon tax policy. Research shows that: the optimal carbon tax in the network to ensure that there is no carbon emissions the manufacturer's equilibrium exceed the government's limit; when the government relaxed on the carbon limits the closed-loop supply chain in the network, the manufacturers take the increase in the cost of recycling to increase the recovery amount and lower wholesale price increase products wholesale volume, improve the profit, the carbon emissions are also increasing, which indicates that the company's environmental and economic performance of the existence of the conflict, in order to achieve certain environmental goals need to give up part of economic interests.