Abstract:

With the increasing pressure of resources shortage and environmental pollution， the government and manufacturer are seeking measures to promote the sustainable development of economy. By-product synergy （BPS） is an effective way to achieve waste utilization and resources conservation. To encourage manufacturer to consider resource utilization of waste， environmental tax policy is designed by government. It aims to investigate the optimal production decision of manufacturer with the consideration of BPS and environmental tax policy in this paper.A manufacturer is considered that produces prime product A and generates a certain proportion of waste which may cause environment pollution. The government levies environmental tax on manufacturer to improve waste treatment and reduce environmental impact. Besides discharging waste into environment and paying the tax to the government， the manufacturer can also invest to implement BPS and convert waste into by-product B which will be sold in another market. Considering two cases：the manufacturer does not implement BPS， the manufacturer implements BPS，Stackelberg game models of the government and the manufacturer are established. As the leader， the government makes decision on tax rate to maximize social welfare， while the manufacturer decides the quantity of the prime product and by-product. The backward induction method is applied to get the equilibrium solutions of the models. By comparing the two cases， the impact of by-product synergy strategy of manufacturer on social welfare and environmental benefits is analyzed. Whether the manufacturer would choose BPS strategy under environmental tax policy is also discussed.The results show that　the environmental tax will reduce the waste emissions of manufacturer by reducing the output of prime product and accelerate the utilization of waste by increasing the output of by-product. When the environmental damage cost is relatively small， the government will be inclined to set higher tax to stimulate manufacturer to implement BPS. When the manufacturer chooses BPS strategy， the social welfare and environmental benefits are better than that without BPS. So， BPS strategy is always conducive to environmental protection and social welfare improvement. The tax policy may affect the choice of manufacturer about BPS strategy. There is a threshold value of investment cost coefficient. When the investment cost coefficient is less than this value，the profit of manufacturer will be always improved if BPS strategy is chosen. On the contrary， when the coefficient is greater than this value， BPS strategy may not be chosen because the profit of the manufacturer who chooses BPS strategy may decrease when the environmental damage cost of waste is moderate.

Key words: by-product synergy, production decision, social welfare, tax policy, environmental benefits