The impact of government subsidy and tax policy on the competitive decision-making of remanufacturing supply chains

Abstract

In this paper, we consider a two-period competition model of a remanufacturing supply chain consisting of three members: a new product manufacturer, a recycler and a remanufacturer. The manufacturer supplies new products in the first period and the remanufacturer participates in the competition in the second period. We consider three scenarios in the second period: (1) there is no government subsidy in the competition; (2) there is only government subsidy in the competition; (3) there are both government subsidy and tax in the competition. First, we give the optimal decision-making of the manufacturer, the remanufacturer and the government in the three scenarios; second, we analyse changes in the decision-making of the manufacturer and remanufacturer in the three scenarios and compare their results. We analyse the effects of government subsidy and tax and their asymmetric use on manufacturers’ and remanufacturers’ decision-making variables and competitive performance. We also take consumer awareness of environmental protection into account and examine its impact on subjects’ decisions. Lastly, we operate a numerical example to show the results.

Keywords:

• Remanufacturing supply chain
• competition
• government subsidy
• government tax
• social welfare
• decision-making

1. Introduction

Today, many countries are destroying their natural environment in order to keep up with the pace of economic globalisation, which has brought a series of problems. For example, air pollution and energy shortages are two most concerned problems which must be solved. As a result, more and more attention has been paid to energy efficiency and emission reduction in recent years to protect our limited energy and reduce air pollution.

In order to implement energy conservation and emission reduction strategies effectively, enterprises must carry out remanufacturing activities. Remanufacturing is the process of disassembling used items, inspecting and repairing/reworking their components, and using these in the manufacture of new products (Pranab and Harry 2001). Remanufacturing can be the most suitable option for meeting multiple environmental objectives; it preserves most of the original product’s added value by giving it a second life and, typically, reduces energy use by eliminating production steps (Bernard 2010). Remanufacturing has the following important features: the quality and performance of remanufactured products meets or exceeds those of new products, the cost of remanufactured products does not exceed 50% of new products, remanufactured products use 60% less energy than new products, remanufactured products use 70% less material than new products, the negative environmental impact of remanufactured products is significantly smaller and remanufacturing can promote the creation of a resource-saving and environmentally friendly society. According to the statistics of the US’s ‘Remanufacturing Industry Development Report,’ we can save 5–9 kg of raw materials by remanufacturing 1 kg. The world saves 14 million tons of materials per year through remanufacturing, which would fill 230,000 railway carriages. The energy consumption of remanufactured products is just 15% of that of new products, which means we can save 16 million barrels of crude oil for 6 million cars per year. According to these statistics, the energy consumption involved in manufacturing a new car is six times that of remanufacturing a car, the energy consumption involved in producing a new vehicle generator is seven times that of remanufacturing a car. At the international level, remanufacturing plays a significant role in energy conservation and emission reduction.

Governments want enterprises to promote and develop remanufactured products due to concerns about environmental protection and energy conservation. They have introduced a variety of policies to encourage the remanufacturing industry. For example, the European Union (EU) enacted the End-of-Life Vehicles (ELVs) Directive (Directive 2000/53/EC) in 2000 and the Electronic Equipment Directive (2002/96/EC) in 2003. In the US states of Maryland and California, legislation puts a recycling fee on electronic products. Subsidy fees have been implemented in Canada and Japan (Wang, Chang, et al. 2014).

On the other hand, while governments promote remanufacturing activity, remanufactured products are always at a disadvantage when competing with new products. There are many difficulties involved in the process of remanufacturing. For example, the costs of recycling discarded products are too high, which means that remanufactured products offer no advantages in terms of production cost. In addition, consumers are always wary of remanufactured products. As a result, governments and researchers have paid more attention to the question of how to enhance the competitiveness of such products. There are certain real and urgent problems which must be resolved: How will remanufacturers make decisions in the competition with manufacturers in order to gain a competitive advantage? How should governments set reasonable subsidy and tax levels – two most popular means for governments to regulate competition among enterprises – in order to maximise social welfare? What effects will the asymmetric use of government subsidy and tax and consumer awareness of environmental protection have on manufacturers and remanufacturers?

In response to these problems, we construct a two-period model to describe the competition between manufacturers and remanufacturers with government participation. We consider three scenarios: (1) competition with no government involvement; (2) competition with only government subsidy; (3) competition with both government subsidy and tax. The rest of the paper is organised as follows: in Section 2, we summarise and review the relevant literature, and then explain the innovation and contribution of this paper. In Section 3, we give the optimal decision-making of manufacturers and remanufacturers, and calculate the optimal levels of government subsidy and tax in Scenario 2 and Scenario 3 in order to maximise social welfare. In Section 4, we analyse the changes in the decision-making of manufacturers and remanufacturers in the three scenarios and compare their results, and the effects of government subsidy, tax and the asymmetric use both on manufacturers’ and remanufacturers’ decision-making variables and competitive performance. In Section 5, we also take consumer’s awareness of environmental protection into account and examine its impact on subjects’ decisions. We operate a numerical example to show the results. In Section 6, a summary of the paper is given.

2. Literature review

New technology evolution, remanufacturing ratios and system holding costs are the three most significant factors influencing green supply chain control system (Chung and Wee 2011). This paper contributes to the research stream on remanufacturing supply chain. First of all, many studies have been published on the competition between manufacturer and remanufacturer. Market competing strategies include product cost, price, quality, design and so on. Some articles have proposed that pricing strategy plays a significant role in manufacturer–remanufacturer competition (Abbey, Blackburn, and Guide 2015; Chen and Chang 2013, Wang and Wang 2015, Zhang and Ren 2016). Considering connections between the price and cost of products, factors influencing product cost, like production rates (Kenné, Dejax, and Gharbi 2012) and the fraction available for remanufacturing (Pranab and Harry 2001), are also discussed in the literature. Competition modes are decided by law, like an individual or a collective take-back law (Webster and Mitra 2007), by patent license (Zhang and Ren 2016) and by contracts between manufacturer and remanufacturer (Yan 2010).

Pranab and Harry (2001) considered a two-period competition model, including an original equipment manufacturer (OEM) and a local remanufacturer (L). During two agents’ competition, the OEM wants to increase L’s remanufacturing costs while it is in the interest of L to reduce the OEM’s remanufacturing cost. In order to enhance competition of remanufacturing, governments can incentivise OEMs to increase the fraction available for remanufacturing, or reduce remanufacturing costs. Webster and Mitra (2007) considered two different kinds of take-back method, collective WEEE take-back and individual WEEE take-back. These two methods have different effects on competitive, collective WEEE take-back, reduce the tax burden on society and can motivate remanufacturing activities. Individual WEEE take-back shows that the entrance of remanufacturers is also good for manufacturers. Wu (2012) considered a supply chain consisting of a manufacturer (OEM) and a remanufacturer and found that the design strategy of products affects the profits of both OEM and remanufacturer. He considered the disassembility of product designs, which is a key parameter that may affect remanufacturer–manufacturer competition. HE modelled a two-period competition structure and analysed manufacturers’ product design strategy and remanufacturers’ pricing strategy. Wu (2016) stated that manufacturers will compete not only on price but also on the incentives for consumers. He discussed certain problems which arise when manufacturer and remanufacturer share the same retailer, and competitors’ decision-making regarding prices and services, including remanufacturers’ efforts during the remanufacturing process. The profits of the whole supply chain vary due to different interactions between retailer prices and services.(Örsdemir, Kemahlıoğlu-Ziya, and Parlaktürk 2014) analysed how quality affects the competition between an OEM and an independent remanufacturer (IR). If the OEM is a stronger competitor in the market, it relies more on quality as a strategic lever. The IR’s entry into the market may reduce consumer surplus, so the benefits of remanufacturing are always overestimated if quality is absent in the competition model. Wei and Zhao (2015) considered the competition between two basic supply chains, one containing remanufacturer and retailer, and the other manufacturer and retailer. Competition arose in both. They studied five game decision models and different competing forms for exploring members’ optimal strategies on price and remanufacturing. Mitra (2016) considered a duopoly with new product manufacturer and remanufacturer in a price-sensitive secondary market. The results show that remanufacturing may cannibalise new product sales, the combined profitability and market share of the (re)manufacturer, but new product sales improved and remanufactured product sales were also good. So the remanufacturing strategy is competitive under a duopolistic environment.

The above studies concentrate mostly on manufacturer–remanufacturer competition, but are not concerned with the role of government, which has a rather important effect during market competition (Sheu 2011). For example, government subsidies may affect the pricing decisions of a home appliance remanufacturer (Gu and Gao 2012). Therefore, some researchers have studied subsidy proportion (Mitra and Webster 2008; Li et al. 2014a) and subsidies for remanufactured products (Li et al. 2014b; Wang, Zhao, et al. 2014). Mitra and Webster (2008) found that subsidies are an effective way to promote remanufacturing activity, they also that a policy of giving part of a subsidy to manufacturers was better than giving all of it to remanufacturers. Hong and Ke (2011) and Hong, Lee, and Chang (2014) presented Stackelberg-type models in which members make decisions according to their own interest and given the optimal Advanced Recycling Fee (ARF) and government subsidy. Ma, Zhao, and Ke (2013) introduced government consumption subsidy to a dual-channel closed-loop supply chain, and analysed the changes in decision-making before and after government consumer subsidy performance. Mitra and Webster (2008) analysed the proportion of government subsidy used to promote remanufacturing. When 100% of subsidies go to the remanufacturer, remanufacturing activity and profits will increase and the profits of manufacturer will simultaneously decrease. When a positive fraction of a subsidy is paid to the manufacturer, remanufacturing activity is generally higher and the profits of both firms increase. Li et al. (2014a) considered a carbon subsidy to encourage enterprises to reduce carbon emissions in three kinds of supply chain, including RCLSC. They studied the RCLSC carbon subsidy and argued that government should consider when and how carbon subsidy policy should be proposed. They provided a close form and found that both recycling price and carbon subsidy had reasonable ranges, and that the carbon subsidy is necessary under upper circumstances. Li et al. (2014b) studied the evolutionary stable strategies (ESS) of remanufacturers and retailers. Their results showed that government subsidies are quite important for the remanufacturing industry and clearly determine ESS. Beside government subsidies, product price also affected the ESS results. Wang, Zhao, et al. (2014) studied the optimal channel choice for a remanufacturing fashion supply chain with government subsidy. They studied remanufactured fashion products with two marketing channel structures: remanufacturers selling products to manufacturers or directly to consumers. They found that government subsidy stimulated the remanufacturer regardless of channel choice. Different subsidy standards had different effects on manufacturer–remanufacturer relationships. When the subsidy was ‘too high’ or ‘too low,’ there was competition between the two members, while an intermediate subsidy would result in cooperation between them. Wang, Chang, et al. (2014) examined the influences of subsidy policies on the development of the recycling and remanufacturing industries in China. They studied the Chinese auto-engine remanufacturing market. There are four kinds of subsidy policy: initial, recycling, R&D and production. By comparing these subsidies, they found that different subsidies have different incentive objectives and characteristics. The mixed-use of subsidy policies has a positive effect in promoting the remanufacturing industry. Yenipazarli (2016) considered the impact of emissions taxes for a manufacturer remanufacturing its own products, and found that it not only has a positive effect on his profits, but also has inherent economic, environmental and social benefits of remanufacturing.

The above indicates that government subsidy has been studied by many researchers. Actually, tax and subsidy are two basic means used by government, and always have great influence on both manufacturers and remanufacturers. Government tax is also used simultaneously with subsidy to balance market competition or to stimulate remanufacturing activities. Considering the current situation, governments may offer subsidies to remanufacturers and levy taxes on new product manufacturers. How do subsidies and taxes affect manufacturer–remanufacturer competition? How to balance this competition through the coexistence of subsidies and taxes? That is the key problem with which our research paper is concerned.

Besides government subsidies and taxes, many factors influence customers. When they decide to buy a product, they do not consider price and quality alone. They are also affected by consumer desire (Wu 2016) and environmental preference. However, studies on competition rarely consider consumers’ environmental preference. Even if some researchers have referred to it, they have not analysed how environmental preference influences the decision-making of customers, remanufacturers and manufactures, and how consumers’ environmental preferences influence government subsidies and taxes. Wang, Zhao, et al. (2014) also considered customer preferences regarding new and remanufactured products. They found the realistic condition that consumers had low acceptance of remanufactured products and paid little attention to the environment, especially in developing countries. Their results show that if customers had higher acceptance of remanufactured products, it would be good for remanufacturers’ competition with manufacturers. Besides, remanufacturers’ channel choice was found to have no effects on social welfare or environmental protection. Wang and Wang (2015b) also considered manufacturer–remanufacture competition when the two parties share the same retailer in the supply chain. Customer acceptance of remanufactured products had a great effect on the supply chain of both parties. When the acceptance of remanufactured products increases, manufacturers’ profits drop and retailers’ profits grow steadily, but remanufacturers’ profits increase initially and then decrease. Qiang (2014) investigated a two-period closed-loop supply chain network in which manufacturer and remanufacturer compete for market share. Consumers are always conscious about product price and quality when facing remanufactured products, so manufacturer–remanufacturer competition faces asymmetrical demand markets. Shi, Sheng and Xu (2015) studied competition between an original manufacturer and a remanufacturer, especially focusing on how consumers’ willingness to pay (WTP) affects the competition process. A higher level of WTP is quite good for the remanufacturer, but always hurts the original manufacturer. So the original manufacturer should always choose an appropriate adjustment speed to gain new advantage. Sharma, Garg, and Sharma (2014) used a questionnaire-based survey to identify the major drivers and obstacles to the promotion of remanufacturing in India. In terms of obstacles, the major factor comes from customers, who are always concerned about product quality. Sharma, Garg, and Sharma (2014) advised Indian governments to come on several guidelines and laws to support remanufacturing. Zhao, Zhu, and Cui (2016) proposed a model considering both consumer acceptance of remanufactured products and government subsidy, but they did not consider the subsidy given by the government. In this paper, we consider both government subsidy and tax, and examine the impact of the asymmetric use of government subsidies and tax, and the effect of consumer preference regarding remanufactured products on the decision-making of members of remanufacturing supply chains.

3. Subjects’ optimal decisions in three scenarios

Consider a remanufacturing supply chain with three members, a manufacturer, a remanufacturer and a recycler. The recycler is authorised by the government or a qualified third party to recycle and dispose of waste products. In the first period, the manufacturer must pay the cost of recycling to the recycler as part of his extended producer responsibility. Then the recycler will sell the waste products to the remanufacturer for remanufacturing. So that the manufacturer does not profit from the recycler in that their extended producer responsibility. As a result, there was no profits getting from the recycler in it profit function. The recycler acts only as third party authorised by the government and is not involved in decisions. It is only responsible for the recovery of discarded materials and their sale to remanufacturers. The recycler profits from both manufacturer and remanufacturer.

In this paper, we assume a two-period play game supply chain model (Mitra and Webster 2008). The model is shown in Figure 1. The notions used in the paper are listed in Table 1. In the first period, the manufacturer provides new products. This period corresponds to the useful life of the product and there are no remanufactured products in the market during this period (Wang, Zhao, et al., 2014). It is very important for the recycler and the remanufacturer. The raw materials for remanufacturing in the second period come from the first period. The quantity of remanufactured products is affected by the recovery ratio and by the total amount of new products in the first period. Therefore, analysis in the first period is basic preparation for the second period, which makes analysis in the second period more straightforward. Let Q _r be the quantity of products in the market in the first period, which can be recycled in the second period.

Figure 1. Supply chain model.

Table 1. Parameters and definitions.

Notion	Definition
Q 0	Market size
Q r	The products that the manufacturer produced in the first period
p n , p r	The price of new products, remanufactured products
c n , c r	The cost of new products, remanufactured products
q n , q r	Demand for new products, remanufactured products
π m , π r , π h	Profits of the manufacturer, remanufacturer and recycler
d m	The fee paid by the manufacturer to the recycler per unit of discarded products
d h	The fee paid by the recycler to the customer per unit of discarded products
d r	The fee paid by the remanufacturer to the recycler per unit of discarded products
ρ	Coefficient of recovery
δ	Consumer awareness of environmental protection
s	Government subsidy per unit of remanufactured products
t	Government tax per unit of new products
v	Consumer expectations of a product

In the second period, the manufacturer still provides new products but does not participate in remanufacturing activities. The manufacturer authorises the recycler to recycle discarded products and the recycler gains d _m benefits per unit of discarded products from the manufacturer. Consumers can gain d _h benefits per unit of discarded product from the recycler. The remanufacturer must buy discarded products from the recycler and pay d _r benefits per unit discarded product to the recycler. We know that the quantity of discarded products in the first period is Q _r , and that it is impossible for consumers to sell all discarded products to the recycler, so ρ represents the coefficient of recovery, that is to say, the quantity of discarded products that can be used in remanufacturing in the second period is ρQ _r . c _n , c _r is the total cost per unit of new and remanufactured products (c _n , c _r ).

We assume that there are three scenarios in the second period. In the first scenario, we assume that the government does not participate in the manufacturer–remanufacturer competition, which means that there is no government subsidy or tax involved in the market. In the second scenario, the government offers a subsidy per unit of remanufactured products to the remanufacturer. We compare manufacturers’ and remanufacturers’ profits to those in the first scenario. Then we examine how government subsidy influences manufacturers’ and remanufacturers’ profits and decision-making. Last, we show the optimal government subsidy. In the third scenario, we assume that the government not only gives the remanufacturer a subsidy per unit of remanufactured products, but also levies a tax per unit of new products on the manufacturer. Then we compare manufacturers’ and remanufacturers’ profits in this third scenario to those profits in the second scenario. From the comparison of results, we analyse how the extra tax affects manufacturers’ and remanufacturers’ profits and decision-making. At the end of this third scenario, we also show the optimal government subsidy and tax. These three scenarios are discussed in detail later.

3.1. Demand model

In this paper, we assume that the market size is Q ₀ and represent consumer expectations of a new product as v (v is uniformly distributed on [0,Q ₀]), and so consumer expectations of remanufactured products is δv (δ is a variable in the range of [0,1]). Consumers are willing to buy remanufactured products only when δv is greater than or equal to their expectations. We assume that the distribution function of consumer expectations is F(v) = v (Debo, Toktay, and Van Wassenhove 2005). p ₁ denotes the price of a new product in the first period. Consumers will consider buying a new product only when v ≥ p ₁. The manufacturer demand function in the first period is as follows: $Q_r=\underset{p_1}{\overset{Q_0}{\int }}dF(v)=Q_0-p_1$. Then the profit function of the manufacturer is as follows:

(1) $$\underset{p_1}{max}{{\pi }_m}^1=(p_1-c_n)(Q_0-p_1)=p_1{Q}_0-p_1^2-c_n{Q}_0+c_n{p}_1$$(1)

According to formula (1), the optimal price for the manufacturer is as follows:

(2) $$p_1^{\ast }=\frac{1}{2}{Q}_0+\frac{1}{2}{c}_n$$(2)

the optimal demand for the manufacturer is as follows:

(3) $$Q_r^{\ast }=Q_0-\frac{(Q_0+c_n)}{2}=\frac{1}{2}{Q}_0-\frac{1}{2}{c}_n$$(3)

There are both new products and remanufactured products in the second period, and consumers will consider buying a new product only when v − p _n  > 0, v − p _n  ≥ δv − p _r , that is, $v\ge p_n,v\ge \frac{p_n-p_r}{1-\delta }$． Similarly, consumers will consider buying remanufactured products only when δv − p _r  ≥ 0, v − p _n  < δv − p _r , that is, $v\ge \frac{p_r}{\delta },v<\frac{p_n-p_r}{1-\delta }$．Based on the above, if p _r  ≥ δp _n , people only demand new products. Similarly, people only demand remanufactured products when p _r  ≤ p _n  − (1 − δ). However, if we take into account demands not only for new products but also for remanufactured products, p _n  − (1 − δ) < p _r  < δp _n . Based on the above range of parameters, production demands for new products and remanufactured products can be obtained as follows:

(4) $$q_n=\underset{\frac{p_n-p_r}{1-\delta }}{\overset{Q_0}{\int }}dF(v)=Q_0-\frac{p_n-p_r}{1-\delta }$$(4)

(5) $$q_r=\underset{\frac{p_r}{\delta }}{\overset{\frac{p_n-p_r}{1-\delta }}{\int }}dF(v)=\frac{\delta p_n-p_r}{\delta (1-\delta )}$$(5)

3.2. Consumer surplus

Consumer surplus occurs whenever the price a consumer actually pays is lower than they are prepared to pay. CS _n , CS _r denotes consumer surplus when consumers buy both new and remanufactured products. Based on the above demand functions, CS _n , CS _r is expressed as follows:

(6) $$C{S}_n=\underset{0}{\overset{q_n}{\int }}vdv-p_n{q}_n=\left(\frac{Q_0+(p_n-p_r)/(1-\delta )}{2}-p_n\right)q_n$$(6)

(7) $$C{S}_r=\underset{0}{\overset{q_r}{\int }}\delta vd(\delta v)-p_r{q}_r=\left(\frac{\delta (p_n-p_r)/(1-\delta )+p_r}{2}-p_r\right)q_r$$(7)

3.3. Scenario 1: There is no government in the competition

In this scenario, there are no government subsidies or taxes in the market, which means that the government does not interfere with the market economy. Manufacturers and remanufacturers make decisions based only on their own profit. Their profit functions are given as follows (The recycler only acts as a third party commissioned by the manufacturer, its profits are eliminated when calculating social welfare. It is assumed that the manufacturer derives no profit from the recycler in that their extended producer responsibility. As a result, there was no profits getting from the recycler in it profit function. Therefore, the influence of the recycler on the decisions of the manufacturer and remanufacturer will not be taken into account.):

(8) $${\pi }_m=(p_n-c_n)q_n-d_m\rho Q_r$$(8)

(9) $${\pi }_r=(p_r-c_r-d_r)q_r$$(9)

Based on the maximisation of their profits, we take first derivatives of π _m with respect to p _n and take first derivatives of π _r with respect to p _r , and let $\frac{d{\pi }_m}{d{p}_n}=0$, $\frac{d{\pi }_r}{d{p}_r}=0$. Then we obtain the equilibrium price decisions of the game as follows:

(10) $$p_n^{\ast }=\frac{2Q_0(1-\delta )+2c_n+c_r+d_r}{4-\delta }$$(10)

(11) $$p_r^{\ast }=\frac{\delta Q_0(1-\delta )+\delta c_n+2c_r+2d_r}{4-\delta }$$(11)

As mentioned above, we can substitute the optimal price $p_n^{\ast },p_r^{\ast }$ for q _n , q _r and then obtain the optimal demand as follows:

(12) $$q_n^{\ast }=Q_0-\frac{p_n^{\ast }-p_r^{\ast }}{1-\delta }=\frac{2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r}{(4-\delta )(1-\delta )}$$(12)

(13) $$q_r^{\text{*}}=\frac{\delta p_n^{\text{*}}-p_r^{\text{*}}}{\delta (1-\delta )}=\frac{\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r}{\delta (4-\delta )(1-\delta )}$$(13)

Finally, we substitute formulae (10), (11), (12) and (13) into the profit functions (8) and (9), and can then obtain the optimal profits of the manufacturer and the remanufacturer as follows:

(14) $${\pi }_m^{\ast }=(p_n^{\ast }-c_n)q_n^{\ast }-d_m\rho Q_r=\frac{{[2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r]}^2}{{(4-\delta )}^2(1-\delta )}-d_m\rho Q_r$$(14)

(15) $${\pi }_r^{\ast }=(p_r^{\ast }-c_r-d_r)q_r^{\ast }=\frac{{[\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r]}^2}{\delta {(4-\delta )}^2(1-\delta )}$$(15)

3.4. Scenario 2: There is only government subsidy in the competition

In this scenario, the government determines the subsidy s^* per unit of remanufactured products to be given to the remanufacturer. Based on s^*, the manufacturer and remanufacturer will determine the prices of their products. Their respective profits are given as follows:

(16) $${\pi }_m=(p_n-c_n)q_n-d_m\rho Q_r$$(16)

(17) $${\pi }_r=(p_r-c_r+s-d_r)q_r$$(17)

Based on the maximisation of their profits, we take first derivatives of π _m with respect to p _n and take first derivatives of π _r with respect to p _r , and then let $\frac{d{\pi }_m}{d{p}_n}=0$, $\frac{d{\pi }_r}{d{p}_r}=0$. Then we obtain the equilibrium price decisions of the game as follows:

(18) $$p_n^{\ast }=\frac{2Q_0(1-\delta )+2c_n+c_r+d_r-s^{\ast }}{4-\delta }$$(18)

(19) $$p_r^{\ast }=\frac{\delta Q_0(1-\delta )+\delta c_n+2c_r+2d_r-2s^{\ast }}{4-\delta }$$(19)

As mentioned above, we can substitute the optimal price $p_n^{\ast },p_r^{\ast }$ for q _n , q _r and then obtain the optimal demand as follows:

(20) $$q_n^{\ast }=Q_0-\frac{p_n^{\ast }-p_r^{\ast }}{1-\delta }=\frac{2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r-s^{\ast }}{(4-\delta )(1-\delta )}$$(20)

(21) $$q_r^{\text{*}}=\frac{\delta p_n^{\text{*}}-p_r^{\text{*}}}{\delta (1-\delta )}=\frac{\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r+(2-\delta )s^{\ast }}{\delta (4-\delta )(1-\delta )}$$(21)

Lastly, we substitute formulae (18), (19), (20) and (21) into the profit functions (16) and (17), and then obtain the optimal profits of the manufacturer and the remanufacturer, respectively, as follows:

(22) $${\pi }_m^{\ast }=(p_n^{\ast }-c_n)q_n^{\ast }-d_m\rho Q_r=\frac{{[2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r-s^{\ast }]}^2}{{(4-\delta )}^2(1-\delta )}-d_m\rho Q_{r_r}$$(22)

(23) $${\pi }_r^{\ast }=(p_r^{\ast }-c_r+s^{\ast }-d_r)q_r^{\ast }=\frac{{[\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r+(2-\delta )s^{\ast }]}^2}{\delta {(4-\delta )}^2(1-\delta )}$$(23)

TS denotes total social welfare, which is the sum of producer surplus, consumer surplus and tax/subsidy revenue (Hong, Lee, and Chang 2014). Social welfare is given as follows:

(24) $$TS={\pi }_m+{\pi }_r+{\pi }_h+C{S}_n+C{S}_r-s{q}_r$$(24)

Because π _m  = (p _n  − c _n )q _n  − d _m ρQ _r , π _r  = (p _r  − c _r  + s − d _r )q _r and π _h  = d _m ρQ _r  + d _r q _r , social welfare can be expressed as follows:

(25) $$TS=\left(\frac{Q_0+(p_n-p_r)/1-\delta }{2}-c_n\right)q_n+\left(\frac{\delta (p_n-p_r)/1-\delta +p_r}{2}-c_r\right)q_r$$(25)

Then we substitute formulae (18), (19), (20) and (21) into profit function (25), and take first derivatives of TS with respect to s. Finally, we let $\frac{\mathit{dTS}}{\mathit{ds}}=0$, the optimal government subsidy can be given as follows:

(26) $$s^{\ast }=\frac{{\delta }^2{Q}_0(1-\delta )+2\delta (\delta -2)c_n+(4-3\delta +{\delta }^2)c_r+(3\delta -4)d_r}{3\delta -4}$$(26)

3.5. Scenario 3: There are both government subsidy and tax in the competition

Based on the first and second scenarios, the government not only gives the remanufacturer a subsidy but also levies taxes on the manufacturer. We denote the tax per unit of new products by t, and simultaneously assume that the tax t is a times higher than the subsidy s(a > 0). That is to say, t = as. Next, the profits of the manufacturer and remanufacturer, respectively, are given as follows:

(27) $${\pi }_m=(p_n-c_n-t)q_n-d_m\rho Q_r$$(27)

(28) $${\pi }_r=(p_r-c_r+s-d_r)q_r$$(28)

Based on the maximisation of their profits, we take first derivatives of π _m with respect to p _n and take first derivatives of π _r with respect to p _r , and then let $\frac{d{\pi }_m}{d{p}_n}=0$, $\frac{d{\pi }_r}{d{p}_r}=0$. Then we obtain the equilibrium price decisions of the game as follows:

(29) $$p_n^{\ast }=\frac{2Q_0(1-\delta )+2c_n+c_r+d_r+(2a-1)s^{\ast }}{4-\delta }$$(29)

(30) $$p_r^{\ast }=\frac{\delta Q_0(1-\delta )+\delta c_n+2c_r+2d_r-(2-a\delta )s^{\ast }}{4-\delta }$$(30)

As mentioned above, we can substitute the optimal price $p_n^{\ast },p_r^{\ast }$ for $p_n^{\ast },p_r^{\ast }$ and then obtain the optimal quantity as follows:

(31) $$q_n^{\ast }=Q_0-\frac{p_n^{\ast }-p_r^{\ast }}{1-\delta }=\frac{2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r-(2a+1-a\delta )s^{\ast }}{(4-\delta )(1-\delta )}$$(31)

(32) $$q_r^{\text{*}}=\frac{\delta p_n^{\text{*}}-p_r^{\text{*}}}{\delta (1-\delta )}=\frac{\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r+(2-\delta +a\delta )s^{\ast }}{\delta (4-\delta )(1-\delta )}$$(32)

Finally, we substitute formulae (29), (30), (31) and (32) into profit functions (27) and (28), and obtain the optimal profit of the manufacturer and the remanufacturer, respectively, as follows:

(33) $${\pi }_m^{\ast }=(p_n^{\ast }-c_n-t)q_n^{\ast }-d_m\rho Q_r=\frac{{[2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r-(2a+1-a\delta )s^{\ast }]}^2}{{(4-\delta )}^2(1-\delta )}-d_m\rho Q_r$$(33)

(34) $${\pi }_r^{\ast }=(p_r^{\ast }-c_r+s^{\ast }-d_r)q_r^{\ast }=\frac{{[\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r+(2-\delta +a\delta )s^{\ast }]}^2}{\delta {(4-\delta )}^2(1-\delta )}$$(34)

TS represents total social welfare, which is the sum of producer surplus, consumer surplus and tax/subsidy revenue (Hong, Lee, and Chang 2014). Social welfare is given as follows:

(35) $$TS={\pi }_m+{\pi }_r+{\pi }_h+C{S}_n+C{S}_r-s{q}_r+t{q}_n$$(35)

Based on all the above, social welfare can be expressed as follows:

(36) $$TS=\left(\frac{Q_0+(p_n-p_r)/1-\delta }{2}-c_n\right)q_n+\left(\frac{\delta (p_n-p_r)/1-\delta +p_r}{2}-c_r\right)q_r$$(36)

Then we substitute formulae (29), (30), (31) and (32) into profit function (36), and take first derivatives of TS with respect to s. Finally, we let $\frac{\mathit{dTS}}{\mathit{ds}}=0$, and the optimal government subsidy and tax, respectively, can be given as follows:

(37) $$\begin{array}{c}{s}^{\ast }=\frac{\delta [4a+(1-7a)\delta +(3a-1){\delta }^2]Q_0-\delta [4+4a-(2+3a)\delta +a{\delta }^2]c_n}{3\delta -4-4a^2\delta -2a{\delta }^2+3a^2{\delta }^2}\\ +\frac{[4+(4a-3)\delta +{\delta }^2(1-2a)]c_r+(3\delta -a{\delta }^2-4)d_r}{3\delta -4-4a^2\delta -2a{\delta }^2+3a^2{\delta }^2}\\ \end{array}$$(37)

(38) $$\begin{array}{c}{t}^{\ast }=a{s}^{\ast }=a\left\{\frac{\delta [4a+(1-7a)\delta +(3a-1){\delta }^2]Q_0-\delta [4+4a-(2+3a)\delta +a{\delta }^2]c_n}{3\delta -4-4a^2\delta -2a{\delta }^2+3a^2{\delta }^2}\right.\\ \left.+\frac{[4+(4a-3)\delta +{\delta }^2(1-2a)]c_r+(3\delta -a{\delta }^2-4)d_r}{3\delta -4-4a^2\delta -2a{\delta }^2+3a^2{\delta }^2}\right\}\\ \end{array}$$(38)

4. The influence of government subsidy and tax on subjects’ decision-making

Based on the above calculations, the results can be compared from three angles (Table 2).

Table 2. Calculated results.

	Scenario 1	Scenario 2	Scenario 3
$p_n^{\ast }$	$\frac{2Q_0(1-\delta )+2c_n+c_r+d_r}{4-\delta }$	$\frac{2Q_0(1-\delta )+2c_n+c_r+d_r-s^{\ast }}{4-\delta }$	$\frac{2Q_0(1-\delta )+2c_n+c_r+d_r+(2a-1)s^{\ast }}{4-\delta }$
$q_n^{\ast }$	$\frac{2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r}{(4-\delta )(1-\delta )}$	$\frac{2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r-s^{\ast }}{(4-\delta )(1-\delta )}$	$\frac{2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r-(2a+1-a\delta )s^{\ast }}{(4-\delta )(1-\delta )}$
$p_r^{\ast }$	$\frac{\delta Q_0(1-\delta )+\delta c_n+2c_r+2d_r}{4-\delta }$	$\frac{\delta Q_0(1-\delta )+\delta c_n+2c_r+2d_r-2s^{\ast }}{4-\delta }$	$\frac{\delta Q_0(1-\delta )+\delta c_n+2c_r+2d_r-(2-a\delta )s^{\ast }}{4-\delta }$
$q_r^{\ast }$	$\frac{\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r}{\delta (4-\delta )(1-\delta )}$	$\frac{\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r+(2-\delta )s^{\ast }}{\delta (4-\delta )(1-\delta )}$	$\frac{\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r+(2-\delta +a\delta )s^{\ast }}{\delta (4-\delta )(1-\delta )}$
${\pi }_m^{\ast }$	$\frac{{[2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r]}^2}{{(4-\delta )}^2(1-\delta )}-d_m\rho Q_r$	$\frac{{[2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r-s^{\ast }]}^2}{{(4-\delta )}^2(1-\delta )}-d_m\rho Q_r$	$\frac{{[2Q_0(1-\delta )-(2-\delta )c_n+c_r+d_r-(2a+1-a\delta )s^{\ast }]}^2}{{(4-\delta )}^2(1-\delta )}-d_m\rho Q_r$
${\pi }_r^{\ast }$	$\frac{{[\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r]}^2}{\delta {(4-\delta )}^2(1-\delta )}$	$\frac{{[\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r+(2-\delta )s^{\ast }]}^2}{\delta {(4-\delta )}^2(1-\delta )}$	$\frac{{[\delta Q_0(1-\delta )+\delta c_n-(2-\delta )c_r-(2-\delta )d_r+(2-\delta +a\delta )s^{\ast }]}^2}{\delta {(4-\delta )}^2(1-\delta )}$

According to Table 2, from comparison between Scenario 2 and Scenario 1, we know that the remanufacturer gets a subsidy per unit of remanufactured products from the government. In order to gain an advantage in the price competition, the remanufacturer tends to reduce prices. Government subsidies are often able to help the remanufacturer to gain advantages in the price competition. As a result, sales of remanufactured products will show an upward trend. The manufacturer must adapt to the competition with the remanufacturer by lowering the prices of its products. However, sales of new products still show a downward trend when compared with the scenario in which there is no government involvement. That is to say, the subsidy for remanufactured products can change the competition equilibrium between the manufacturer and the remanufacturer. There is no doubt that the profits of the manufacturer will decrease when both prices are cut and sales of new products decrease. Although the remanufacturer also lowers the prices of remanufactured products, its per unit product profit rises due to government subsidy. From a comparison between $p_r^{\ast }+s^{\ast }$ in Scenario 2 and $p_r^{\ast }$ in Scenario 1, we use $p_r^{\ast }+s^{\ast }$ in Scenario 2 minus $p_r^{\ast }$ in Scenario 1 and then obtain $\frac{(2-\delta )}{4-\delta }{s}^{\ast }$. It is obvious that the value of $\frac{(2-\delta )}{4-\delta }{s}^{\ast }$ is greater than zero. In other words, government subsidies will increase the marginal profits of remanufactured products. As sales of remanufactured products increase, the profits of the remanufacturer will increase on the basis of maximising social welfare.

Comparing Scenario 3 to Scenario 1, the government implements a policy of the coexistence of subsidy and tax. The asymmetric use of government subsidy and tax will have effects on the decision-making and related performance of the main body of the system. We can divide the asymmetric use of government subsidy and tax into three cases under the condition of optimal subsidy: $\left(a\in \left(0,\frac{1}{2}\right)\right)$, $\left(a\in \left(\frac{1}{2},\frac{2}{\delta }\right)\right)$ and $\left(a\in \left(\frac{2}{\delta },\infty \right)\right)$.

The remanufacturer will lower the price of remanufactured products when the government gives it a subsidy per unit of remanufactured product. However, the production cost of new products will not greatly increase when $a\in \left(0,\frac{1}{2}\right)$, but the manufacturer lowers the price of new products under the pressure of price competition. There is no doubt that sales of the remanufacturer’s products will rise under the policy of subsidy and tax. Though the new product manufacturer has also lowered its prices, its competitiveness has declined when $a\in \left(0,\frac{1}{2}\right)$, which leads to declining profits from new products. From the comparison between $p_r^{\ast }+s^{\ast }$ in Scenario 3 and $p_r^{\ast }$ in Scenario 1, we use $p_r^{\ast }+s^{\ast }$ in Scenario 3 minus $p_r^{\ast }$ in Scenario 1 and then obtain $\frac{[2+(a-1)\delta ]s^{\ast }}{4-\delta }$. It is obvious that the value of $\frac{[2+(a-1)\delta ]s^{\ast }}{4-\delta }$ is greater than zero. In other words, as sales of remanufactured products increase, the profits of the remanufacturer will increase on the basis of maximising social welfare.

The cost of new products will greatly increase when $a\in \left(\frac{1}{2},\infty \right)$. The manufacturer will choose to raise the prices of new products in order to maximise profits. The magnitude of these price increases is not large when $a\in \left(\frac{1}{2},\frac{2}{\delta }\right)$. In addition, the remanufacturer will further reduce the prices of remanufactured products in order to gain competitive advantage. When $a\in \left(\frac{1}{2},\frac{2}{\delta }\right)$, the new product manufacturer will set higher prices due to the rapid escalation of costs. In doing this, the manufacturer becomes less competitive, and the remanufacturer will raise its prices to increase marginal profits. The simultaneous implementation of tax and subsidy policies can reconstruct the competition equilibrium between manufacturer and remanufacturer and reduce the competitiveness of new products. As a result, the remanufacturer’s competitiveness will improve. This means that sales of new products will decrease, sales of remanufactured will increase, the profits of the new product manufacturer will fall and those of the remanufacturer will increase.

5. Numerical case

5.1. Influences of consumer environmental awareness

Based on the above, we examine the impacts of consumer awareness of environmental protection (δ ∊ (0, 1)) on the remanufacturing supply chain under the context of the government’s asymmetric use of subsidy and tax. We use manipulation of the value of a (a = 0.2, a = 0.6) to stimulate the government’s asymmetric use of subsidy and tax. We set the parameters ρ = 0.6, Q ₀ = 150000, c _n  = 40000, c _r  = 3000, d _r  = 8000 and d _m  = 1250.

In order to ensure that all parameters are greater than zero, δ takes the range of (0.2, 0.75). The effects of both a and δ on producers’ sale price, sales volume, profits and social welfare and subsidy are shown in Figures 2–6.

Figure 2. Price evolution trend with different levels of consumer environmental awareness.

Figure 3. Demand evolution trend with different levels of consumer environmental awareness.

Figure 4. Profit evolution trend with different levels of consumer environmental awareness.

Figure 5. Social welfare evolution trend with different levels of consumer environmental awareness.

Figure 6. Government subsidy evolution trend with different levels of consumer environmental awareness.

The figures show that as consumer awareness of environmental protection increases, government subsidy always shows an upward trend, regardless of whether there is only government subsidy in play, as in Scenario 2, or both government subsidy and tax, as in Scenario 3. As shown in Figure 2, in the absence of government tax, the optimal government subsidy is highest. However, the optimal subsidy in the situation where a = 0.2 is higher than when a = 0.6 when subsidy and tax coexist. Therefore, the amount of the optimal subsidy will drop with the introduction of government tax. At the same time, the greater the proportion of government tax and subsidy, the smaller the difference between them, and the smaller the optimal subsidy.

As shown in Figure 5, social welfare also shows an upward trend in three scenarios. In general, as consumer awareness of environmental protection increases, the government can choose to give a small subsidy for remanufactured products, or not. However, the study suggests that increasing consumer awareness of environmental protection and government subsidy play a dual role in promoting the competitiveness of remanufactured products. In this situation, in order to further improve social welfare, the government should further increase its subsidy as awareness of environmental protection increases, rather than reducing it. Social welfare is lower when there is no government tax regardless of the fact that subsidy is highest here. This shows that government tax has important effects in improving social welfare. When government subsidy and tax coexist, the smaller a, the greater the social welfare as consumer awareness of environmental protection increases.

Under the influences of increasing awareness of environmental protection and optimal subsidy, the price of remanufactured products shows a relatively stable trend of rising at first and then declining when subsidy and tax coexist, but the sales volume of remanufactured products always increases. In this competition, the price of new products shows a trend of rapid decline and the sales volume of new products also decreases, as shown in Figures 2 and 3. As consumer awareness of environmental protection increases, the demand for remanufactured products becomes apparent in the market. Although the new products manufacturer has dropped its prices under pressure from competition, the prices of new products are less competitive than those of remanufactured products. The remanufacturer will raise the prices of its products in order to maximise profits during this time. As the prices of new products are lower, the remanufacturer must move to win competition by dropping the prices of its own products.

The increase in consumer awareness of environmental protection, the increase in government subsidy and the manufacturer becoming less competitive results in a rising trend in the remanufacturer’s profits. Thus, the profits of the remanufacturer and the growth rate of its profits are both higher when there is government subsidy and no tax. This means that the effects of coexistence of government subsidy and tax are better than high subsidies alone on enhancing the competitiveness of the remanufacturer.

In addition, when a = 0.2, the optimal subsidy level for remanufactured products is higher than when a = 0.6. Therefore, lower prices and higher sales volume lead to higher profits for the remanufacturer when comparing a = 0.2 to a = 0.6. It can be seen that the asymmetric use of government subsidy and tax will have different effects on decision-making and corresponding performance indicators.

Consumers have a low awareness of environmental protection, which means that they show low recognition for remanufactured products. In this context, the government should let $a\in \left(0,\frac{1}{2}\right)$ to reduce market intervention.

5.2. Influences of tax to subsidy ratio

In order to make a no longer a specific value, we let a ∊ (0, 7) and $\delta =0.65$. The effects of the tax to subsidy ratio on sales prices, sales volume, profits and social welfare and subsidy are shown as follows (Figures 7 and 8):

Figure 7. Social welfare, subsidy and tax trends.

Figure 8. Trends of price, demand and profit.

Social welfare will continuously decrease as the value of a increases; the greater the tax to subsidy ratio, the more detrimental will be the effect social welfare when the government levies taxes on the manufacturer and gives subsidy from the remanufacturer. The government aims to maximise social welfare, and as the value of a increases, the subsidy will reduce gradually and tax will rise first and then decline. The amount of subsidy is greater than the amount of tax and the difference between them decreases gradually when a ∊ (0, 1). However, as the value of a increases, the difference between subsidy and tax will increase and then reduce when a ∊ (1, 7).

As the value of a increases, the prices of remanufactured products will increase gradually, the prices of new products will increase first then decrease and the prices of new products will always be higher than those of remanufactured products. The sales volume of new products decreases slightly then rises, while that of remanufactured products will decrease gradually. The profits of the remanufacturer decrease gradually, but the profits of the manufacturer will decrease lightly and then increase gradually. The profits of the manufacturer will be greater than the remanufacturer when the value of a increases to a certain extent.

The government subsidy will reduce gradually when the value of a increases, and tax will rise then decline. The prices of new products rise gradually as tax level increases, which leads the sales volume of new products to decrease. At the same time, the remanufacturer raises the prices of its products in order to maximise profits under the circumstances of reduced subsidy. However, remanufactured products will still lose their ‘low price’ advantages in the competition with new products when the prices of new products rise. Based on this, sales of remanufactured products will drop significantly in the market, the profits of the remanufacturer will decrease gradually and the profits of the manufacturer will rise gradually. As the value of a increases, remanufactured products will lose their price advantage further and the profits of the remanufacturer will be caught by the manufacturer when subsidy and tax decrease gradually.

As a result, the greater a is, the worse it will be for the remanufacturer and for total social welfare in the competition. Thus, if the government wants to guarantee the level of social welfare and improve remanufacturer competitiveness, ‘more subsidies, less tax’ is the best way to proceed.

6. Conclusions

Under the circumstances of rapid development in the remanufacturing industry, we assume that a remanufacturing supply chain consists of three members, a manufacturer, a remanufacturer and a recycler. Based on this, we set up a two-period model. In the first period, the manufacturer produces new products which can be recycled for remanufacture in the second period. The remanufacturer competes with the manufacturer in the second period.

Through comparing three governmental policies (no intervention, remanufacturer subsidy and the asymmetric use of subsidy and tax), we analysed changes in manufacturers’ and remanufacturers’ decision-making. We discovered that the sales of remanufactured products are best when subsidy and tax coexist. In this equilibrium, we identified the optimal government subsidy. Based on this, we analysed changes in manufacturer and remanufacturer decision-making under the asymmetric use of subsidy and tax. We found that the remanufacturing industry will develop fast when the government implements both subsidy and tax at the same time.

We also found that consumer awareness of environmental protection plays a significant role in the remanufacturing industry. As a result, it is important for a remanufacturer that consumers are highly aware of environmental protection. This means that the remanufacturer must improve the quality of its products to attract consumers. Only thus will the remanufacturer earn greater profits.

From the perspective of the government, in order to guarantee the level of social welfare and improve remanufacturer competitiveness, the tax to subsidy ratio should be small, which means ‘less tax, more subsidy.’

We consider competition with a single manufacturer and a single remanufacturer. In future research, we can consider conditions where there are many manufacturers and remanufacturers.

Funding

This work was supported by the National Natural Science Foundation of China [grant number 71501084], [grant number 71671078], [grant number 71301062], [grant number 71471076], [grant number 71401082]; by Senior Personnel Scientific Research Foundation of Jiangsu University [grant number 15JDG108] and Youth Backbone Teacher Training Project of Jiangsu University.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes on contributors

Zhen Li is an associate professor in the School of Management, The Jiangsu University. Her research interests include remanufacturing supply chain management. She is young academic leader in “Young Teachers Training Project” of Jiangsu University, Evaluation expert of Faculty of Management in National Natural Science Foundation of China(NNSFC), until now she has presided two projects of NNSFC. She has published some articles in International journals such as International Journal of Production Economics, Neural Computing & Applications and so on.

Wei Zheng is a graduate student at Jiangsu University and majoring in Logistics Engineering. His research interests include remanufacturing and green supply chain management.

Qingfeng Meng is an associate professor in the School of Management, The Jiangsu University. He received his PhD degree from Department of Management Science and Engineering, Nanjing University. His research interests include operation management. He is young academic leader in “Young Teachers Training Project” of Jiangsu University, Deputy director of “Big Data and Sustainable Development Research Center in Jiangsu University”, Evaluation expert of Faculty of Management in National Natural Science Foundation of China.

Shuai Jin is an associate professor in the School of Management, The Jiangsu University. His research interests include environment management. He is young academic leader in “Young Teachers Training Project” of Jiangsu University.