4.1. Model N (Free Recycling Mode)
In this model, the manufacturers first decide both the quantity of new products and the level of recycling effort simultaneously, and then the remanufacturers determine the ratio of outsourcing . The specific decision functions are shown below.
The manufacturers’ recycling decision and new product output decision are:
The decision for the ratio of outsourcing is:
These problems are typical of the Cournot duopoly and Stackelberg game model. We solve (1) and (2) according to the backward induction method. The optimal solutions under mode N are shown in
Table 2. By analyzing the above results, the relationships between each decision variable and the main parameters are obtained, as shown in
Table 3. See
Appendix A for the solution process.
According to the recycling rate, the development of the remanufacturing industry can be classified into the germination and mature periods. The larger
τ is, the more developed the remanufacturing industry is. In this paper, the development of the remanufacturing industry is based on the per unit production cost for the remanufacturers. The lower
is, the higher the development level is. In addition, in order to facilitate reading and understanding, the costs of remanufacturing in the (N-1) and (N-2) intervals in this article are sequentially reduced. When
is in the (N-1), it means the remanufacturer’s capability to produce remanufactured products is strong. When
is in the (N-2), it means the remanufacturer’s capability is weak.
Proposition 1. are negatively related to , while is positively related to . When , is negatively related to ,
is positively related to ; when , is negatively related to , .
Proposition 1 shows that as the remanufacturers’ ability continues to increase, the remanufacturers adopts a strategy of using a greater amount outsourcing to produce remanufactured products. At the same time, the manufacturers adopt a strategy of recycling more waste products and producing fewer remanufactured products. When the remanufacturers are in the development period, the recycling rate continues to increase as the decreases and the manufacturers choose to produce fewer new products. Based on the aforementioned assumption that the manufacturers choose to produce fewer remanufactured and new products, the manufacturers’ total output is reduced. Hence, the remanufacturers’ increased output means that the market share for the manufacturers is reduced and their leading status is weakened; when the remanufacturing cost for the remanufacturers is in the range of (N-2) (that is, the remanufacturing industry enters a mature period), the recycling volume of waste products is equal to the volume of new products, whereby the recycling volume of waste products and the output of new products are both increasing while is declining.
Proposition 2. are negatively related to . When , are positively related to . When , are negatively related to .
Proposition 2 shows that as continues to increase, the manufacturers apply a strategy to lower their output of both new products and total products. The remanufacturers’ output remains stable, leading to the market share and leading status of the manufacturers declining. When is in the range of (N-1), whereby the manufacturers’ per unit cost for new products increases, the manufacturers would focus on their remanufacturing business and improving their recycling efforts. The manufacturers would adopt strategies to increase their own output of remanufactured products, hence the recycling rate would increase accordingly. When is in the range of (N-2), as the manufacturers’ per unit cost for new products increases, the remanufacturers will increase the amount of outsourcing. In the range of (N-2), the manufacturers apply a strategy to fully recycle all used products, so the output for recycling products is equal to the output for new products. When the output of new product declines, the manufacturers’ recycling activities and output of remanufactured products also decline.
Proposition 3. are negatively related to . When , and are positively correlated. When , and are negatively correlated.
Proposition 3 shows that as decreases, the manufacturers tend to increase their recycling efforts, thereby recycling more waste products. The amount of remanufactured products and the total capacity increase, along with the manufacturers’ market share and dominance. When is in the interval range of (N-1), as continues to decrease, the manufacturers produce fewer new products. When is in the interval range of (N-2), the recycling rate is maintained at 100% and the recycle amount is equal to the output of new products. The output of new products and the amount of recycling increase while decreases.
4.2. Model G (Government Regulation Model Based on Reward–Penalty Mechanism)
In real-life operations, when the remanufacturing industry is in its initial period, if there is a lack of external incentives, manufacturers are often reluctant to be involved in recycling activities. Hence, government regulation and intervention are important. To promote the implementation of the EPR system, the government needs to take certain measures to encourage manufacturers to recycle waste products. In this model, by setting up the reward–penalty mechanism based on the benchmark recycling rate, the government regulates the recycling activities.
The manufacturers’ recycling decision and new product output decision are:
The decision for the ratio of outsourced business is:
According to the backward induction method used to solve the problems expressed in (3) and (4), when
is in different ranges, we can derive the optimal decisions for model G, as shown in
Table 4. By analyzing the solution results, the relationships between each decision variable and the main parameters are obtained. The results are shown in
Table 5. The solution process is the same as for model N, and so will not be described in detail here.
Obviously, the relationship between the optimal solution and the parameters under model G is basically the same as that under model N. Therefore, the following proposition mainly analyzes the relationships between variables and parameters in model G.
Proposition 4. When , and are positively related; and are negatively related; is negatively related with ; and the relationship between and is uncertain.
Proposition 4 shows that when the remanufacturing industry is in the germination period, the more intensive the reward–penalty mechanism is and the higher the recycling rate is, the more likely the manufacturers will be to increase their recycling efforts, recycling volume, and output of remanufactured products while reducing the output of new products. During this period, these two regulatory measures can incentivize the manufacturers to increase their recycling rate. The remanufacturers will lower their outsource ratio to maintain their output.
Proposition 5. When , , and are positively related, while all are negatively related with ; is negatively related with and positively related with .
Proposition 5 shows that when the remanufacturing industry is in the mature period, the manufacturers will recycle all waste products, so the number of waste products will be equal to the number of new products. When the government increases the regulation intensity, the manufacturers will increase their recycling efforts, producing more new products and more remanufactured products (increasing the total output). The remanufacturers will outsource less of their remanufacturing business, while their own remanufactured product output will remain unchanged, so the manufacturers’ market share and market dominance will increase accordingly. When the government increases the basic recycling rate, the manufacturers reduce their output of new products and remanufactured products (reducing the total output). At this time, the remanufacturers increase the contracting share of the remanufacturing business so that its output is unchanged, meaning the manufacturers’ market share and market dominance decline accordingly.
4.3. Model GF (Government Dual-Intervention Mode)
The environmental pollution and energy consumption caused by manufacturing activities can be partially alleviated by remanufacturing. In reality, the market is composed of two types of consumers: normal consumers, who prefer to purchase new products, and green consumers, who view remanufactured products as a cost-effective choice. Therefore, the government is motivated to adopt certain incentives based on the EPR principles to encourage consumers to purchase remanufactured products. This study discusses the government’s development of a green subsidy scheme to motivate green customers to fulfill the EPR principles, which were originally developed for manufacturers. In this scenario, the government aims for maximum social benefits. The manufacturers indirectly fulfill the EPR principles by paying taxes on new products to the government, while green consumers qualify for a certain purchasing subsidy on remanufactured products provided by the government.
In this model, we present a three-layer game model, which incorporates the government, manufacturers, remanufacturers, and green and non-green consumers. The government as a leader determines the tax per unit on new products to maximize overall social welfare. On this basis, according to this tax amount, the manufacturers determine their output of new products and their recycling efforts so as to maximize profits. The remanufacturers thereafter determine their level of outsourcing based on their own profit maximization.
The social welfare component consists of four parts: the manufacturers’ profits, remanufacturers’ profits, consumer surplus, and government expenditure.
The government’s tax decision for new products is:
The manufacturers’ recycling decisions and new product decisions are:
The decision for the ratio of outsourcing is:
The backward induction method is still applied here. For
in different ranges, the relations between the optimal government tax level and the parameters are shown in
Table 6. (In the stage of incomplete manufacturer recycling, the tax expression f is more complicated, so f is not substituted in
Table 7. For the value of f, see
Appendix B.) The optimal decisions for the GF model are shown in
Table 7. By analyzing the solution results, the relationships between each decision variable and the parameters are obtained. The results are shown in
Table 8.
Proposition 6. When , is positively related to , and negatively related to .
Proposition 6 shows that when the remanufacturing industry is in the development period, when the manufacturers’ new product cost increases, in order to achieve the goal of maximizing social benefits, the government should increase the tax on new products; while the remanufacturer or manufacturers’ remanufactured product cost decreases, in order to maximize social benefits, the government should reduce taxes. When the government increases the benchmark recycling rate or intensity, the government should reduce taxes.
Proposition 7. When , is positively related to , and negatively related to . And has no relationship with .
Proposition 7 shows that when the remanufacturing industry is at the mature stage, when the government adopts a greater level of intensity for the reward and punishment mechanism, the government should increase taxes, while if the government increases the benchmark recycling rate, the government should reduce the taxes.
Proposition 8. When , is positively related with , is negatively related with .
Proposition 8 shows that when the remanufacturing industry is in the development period, under the dual regulations, as the government increases the benchmark recycling rate, the manufacturers adopt a lower level of recycling effort and the remanufacturers increase their proportion of outsourcing, so the number of remanufactured products produced by the manufacturers is also reduced.
Proposition 9. When , are not related with .
Proposition 9 shows that when the remanufacturing industry is at the mature stage, under the dual regulations, the government reward–penalty mechanism does not work.
4.4. Comparison of the Three Modes
In
Section 4.1,
Section 4.2 and
Section 4.3, we analyzed and found solutions for the three models in sequence, but did not compare the different models. In this section, by further comparing and analyzing the optimal decision-making processes for the three models, the following propositions were obtained.
Proposition 10. When manufacuterer recycles part of the waste products , when the manufacturer recycles all the waste, . And .
Proposition 10 shows that when the remanufacturing industry is in the early stage of development, government regulation can effectively enhance the manufacturers’ recycling activity, and among the two government regulation models, the government’s dual-regulation model is better in terms of environmental performance. When the remanufacturing industry is at the mature stage, the government’s implementation of rewards and punishments based on the recycling rate can encourage the manufacturers to recycle waste products. Under models GF, G, and N, the cost threshold for complete recycling of waste products is successively reduced, showing that even if the remanufacturering industry is in the development period, government regulations can effectively encourage the manufacturers to fully recycle.
Proposition 11. , when the manufacturer recycles all the waste products, .
Proposition 11 shows that when the manufacturers partially recycle, under models G and GF, the output of remanufactured products is higher than under model N. This shows that government regulations can effectively guide the manufacturers to pay attention to their own remanufacturing business and produce more remanufactured products, and that the effects of dual interventions are more obvious. In the case of full recycling, the total output from the manufacturers in model G is higher than the total output of the manufacturers in model N, indicating that government regulation based on the reward and punishment model of recycle can encourage the manufacturers to increase their output.