关键词: 再制造, 政府税收, 蚕食, 环境影响, 社会福利

Abstract: Although remanufactured products reduce demands on energy and materials, they can still bring some environmental problems. Meanwhile, recent research has proved that remanufacturing is not a one-size-fit-all approach and may also lead to bad results, either economically or environmentally. Therefore, whether remanufactured products should be taxed has attracted people’s attention. So far, there is no literature which clarifies the impact mechanism of incorporating the tax on remanufactured products. To solve this problem, we construct a two-stage Stackelberg game model including government and manufacturer. In the context of a game model, we consider two different cases, namely the case with tax on remanufactured products and the case without tax on remanufactured products. We set the case without tax on remanufactured products as a benchmark and compare the two different cases in order to better analyze the impact of incorporating remanufactured products tax on production decision, environment, economy and social welfare. According to reverse induction, we first use Karush-Kuhn-Tucker conditions to solve the manufacturer’s profit function and determine the optimal quantities of new and remanufactured products. Then, we solve the regulator’s welfare function and determine the tax price. We analyze the effects of incorporating remanufactured products through the comparison of two cases and list the main results as follows.From the perspective of effective tax price region, incorporating the tax on remanufactured products expands the adjustable tax region under inactive constraint condition and shrinks the adjustable tax region under active constraint. In the whole, incorporating the tax on remanufactured products causes the shrink of the whole adjustable tax region.From the perspective of production decision, when the tax price is low, incorporating tax onremanufactured product weakens the cannibalization effect of remanufactured product on new products, thereby increasing the demand for new products. It has a positive impact on the manufacturer’s production activities. When the tax price is high, incorporating tax on remanufactured product decreases the demands for new and remanufactured products, while the change of new products is higher than that of remanufactured products as a result of decreasing in available cores. It has a negative effect on the manufacturer’s production activities and inhibits manufacturers’ production of new and remanufactured products.From the perspective of economic profit, incorporating tax onremanufactured product leads to a worse economic performance. Note that profit difference between two cases is continuous and strictly concave and the change of profit difference between two cases is affected by the tax price.From the perspective of environmental performance, incorporating tax onremanufactured product does not necessarily lead to a better environmental impact. When the tax pricing is high enough, incorporating tax on remanufactured product must lead to a better environmental impact. It is because that high tax price curbs the manufacturer’s production activity. When the tax pricing is low or moderate, the change of environmental impact after incorporating tax on remanufactured product is related to environmental impact of remanufactured products and the environmental awareness of consumers. When the environmental awareness of consumers is higher than environmental impact of remanufactured products, incorporating the tax on remanufactured products inversely lead to a worse environmental impact. Note that under this condition, incorporating tax on remanufactured product brings a "lose-lose" situation where the economic and environmental performances of the manufacturer are simultaneously damaged. This warns regulators that there is no need to impose the tax on remanufactured products when the environmental awareness of consumers is strong enough. On the contrary, if consumers consider remanufactured products are not environment-friendly, incorporating the tax on remanufactured products leads to better environmental impact. At the moment, it results in a "lose-win" situation where economic profit gets worse, but environmental impact gets better. In order to better understand the effect of tax policy implementation, the regulator should use social welfare-maximization as a criterion to determine whether or not to incorporate tax onremanufactured products. From the perspective of social welfare, welfare function integrates consumer surplus, manufacturer’s profit, government revenue and environmental externalities. We examine the nature of the welfare function to investigate the impacts of tax price on the balance among economy, environment and social welfare. The welfare function is continuous and strictly concave in the tax price. The cases RN and Rboth exist the unique maximum tax price tRN* and tR*with the goal of welfare-maximization, respectively. According to different environmental cost values of the product, the regulator imposes the optimal tax price and chooses the optimal tax policy, thereby determining whether incorporating tax on remanufactured product or not. When the environmental cost of a product is over-low, there is no need to impose the environmental tax under two cases. On the contrary, if the environmental cost of the product is over-high, the regulator should impose the strictest tax price and eliminate the product from the market. It is noted that incorporating the tax on remanufactured products results in raising the initial threshold of taxable environmental cost. Thus, taxing only on new product is stricter than that on both new and remanufactured products, and the product of the manufacturer is more likely to trigger the former.There are also some interesting conclusions through analyzing the impact of the tax on social welfare by numerical examples: When the environmental cost of products is moderate under certain conditions, if consumers considerremanufactured product is not environment-friendly enough, there is a situation in which only imposing the tax on new products leads to better social welfare. However, if consumers consider remanufactured product is environment-friendly enough, there exists a situation where the legislative efficiency of two policies is same. This demonstrates that imposing the tax on remanufactured products shares the tax burden of new products. When the environmental cost of products is high under certain conditions, the social welfare of incorporating the tax on remanufactured products is relatively better. The regulator should choose to impose the tax on remanufactured products.

Key words: remanufacturing, government tax, cannibalization, environmental impact, social welfare