Comparisons of initial carbon allowance allocation rules in an O2O retail supply chain with the cap-and-trade regulation

Author’s Accepted Manuscript Comparisons of initial carbon allowance allocationrules in an O2O retail supply chainwith the cap-and-trade regulation Jingna Ji, Zhiyong Zhang, Lei Yang www.elsevier.com/locate/ijpe

PII: DOI: Reference:

S0925-5273(17)30038-5 http://dx.doi.org/10.1016/j.ijpe.2017.02.011 PROECO6660

To appear in: Intern. Journal of Production Economics Received date: 12 July 2016 Revised date: 20 January 2017 Accepted date: 21 February 2017 Cite this article as: Jingna Ji, Zhiyong Zhang and Lei Yang, Comparisons of initial carbon allowance allocationrules in an O2O retail supply chainwith the cap-and-trade regulation, Intern. Journal of Production Economics, http://dx.doi.org/10.1016/j.ijpe.2017.02.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Comparisons of initial carbon allowance allocationrules in an O2O retail supply chainwith the cap-and-trade regulation Jingna Ji,Zhiyong Zhang, Lei Yang School of Economics and Commerce, South China University of Technology, Guangzhou 510006, P.R. China 

Corresponding author. [email protected]

ABSTRACT

This paper focuses on an O2O retail supply chain in the context of low-carbon environment. The decision models are constructed under three cases: without cap-and-traderegulation, cap-and-trade regulation based on grandfathering mechanism, and cap-and-trade regulation based on benchmarking mechanism. The emission reduction strategies of the supply chain members in the three cases are then discussed. The paper compares the effects of the grandfathering and benchmarking mechanisms on the firm’s decisions, profits and social welfare. Firstly, the results show that the unit carbon quota plays a decisive role in firm’s decisions. Compared with the grandfathering methodology, the benchmarking one can more effectively push manufacturers to produce low-carbon products and motivate retailers to promote low-carbon products. Secondly, it is profitable for the retailer to cooperate with a manufacturer who has lower emission reductioncost. Simultaneously, the retailer will prefer the benchmarking mechanism to the grandfathering mechanism. Thirdly, for the government, it is beneficial to use grandfathering mechanism for low-carbon-emission firms and use benchmarking mechanism for high-carbon-emission firms. Also, the paper provides government and firms with conditions where the benchmarking allocation method is more suitable for sustainable development. The government’s decision on benchmarks is a critical factor in maximizing the social welfare. Keywords: cap-and-trade; supply chain; O2O; dual-channel; carbon allowances allocation

1. Introduction Carbon emissions associated with economic development have caused serious issues such as the greenhouse effect (Ding et al., 2016). Environmental degradation issue has attracted worldwide attention since it has become a great threat to the survival and health of human beings (Jiang and Shao, 2014). In China, most big cities have been shrouded in thick haze, thereby causing public’s high attention on environmental protection (Du et al., 2016a). Now adopting an effective mechanism to alleviate the effect of global warming on human activities has become an important task for governments around the world. To this end, many regions and countries have developed and applied relevant low-carbon policies and regulations, such as cap-and-trade and carbon tax. Cap-and-trade regulation is proved to be one of the most effective mechanisms to control the emission of carbon dioxide (Giarola et al., 2012; Zhang and Xu, 1

2013). Under a cap-and-trade system, firms get a predetermined amount of carbon quotas (a carbon cap) from a government (Xu et al., 2016a). Firms could sell/buy carbon quotas in carbon trading market when they have surplus/lack quotas where carbon emission price is determined by market. Chinese government also established 7 carbon trading pilot regions, such as Beijing, Shanghai and Shenzhen. The reduction of carbon emission has become an inevitable trend and a world-wide consensus (Wang and Wang, 2015). Initial allowance allocation mechanism is fundamental in the mechanism design of carbon trading mechanism (Liao et al., 2015). In the international community, various initial allocation mechanisms of carbon emission allowances have been proposed (Pan et al., 2014). Free allocation, fixed-price and auction are the three main initial allocation methods. There are two mainly free carbon quota allocation mechanisms: “Grandfathering” and “Benchmarking”. The European Union Emissions Trading System (EU-ETS), which is the largest emission trading market in the world, used the grandfathering method based on historical emissions for the first two phases. However, starting in 2013, allocation to industrial facilities is based on benchmarking①-②.California’s program, which began operation at the beginning of 2013, follows the example of the current phase of the EU-ETS and primarily uses benchmarking for allocation③. In China, the carbon trading pilot regions adopt allocation rules, like benchmarking and grandfathering under the cap-and-trade system. Currently, Shanghai, Beijing, Guangdong, Tianjin and Hubei use both the benchmarking and grandfathering rules (Zhang et al., 2015). Now relevant authorities are discussing to design a unified carbon emissions trading market mechanism and national carbon allowance allocation rules, which are expected to implement in 2017. As more and more environmental norms and compliance standards are enforced, an increasing number of manufacturers devote attention to produce low-carbon product and take actions to curb ①

http://www.c2es.org/publications/key-considerations-industrial-benchmarking-theory-practice http://www.epa.ie/pubs/advice/air/climatechange/phase/guidancedocumentno2ontheharmonizedfreeallocationmethodologyfortheeu.html ③ http://www.c2es.org/us-states-regions/key-legislation/california-cap-trade ②

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emissions, so as to conform to the norms and survive competition (Kumar et al., 2014). The improving environmental awareness of consumers also provides a strong incentive for manufacturers to engage in green innovation. In 2008, Gree invest more than one billion yuan in carbon reduction technologies④. It also focuses on the design and innovation of energy-saving products. As one of the important member in the supply chain, retailer also plays an important role in switching consumer-purchasing habits to low-carbon alternatives. For example, some giant retailers, such as Walmart and Suning, have taken actions to display and promote energy-saving products in their offline shops. Suning cooperates with Siemens, Midea, Haier and others to provide more green products for consumers and improve the market share of green products. In 2013, the sales of energy-saving air-conditioner accounted for about 70% of the total air-conditioner sales in Suning. In 2014 Corporate Social Responsibility (CRS) Report of Suning, they have set their ambitious goal, which was to increase market share of energy-saving air-conditioner to 85%. In addition, Suning uses the LED light instead of power-consuming ones in the offline shops, so as to create a green atmosphere for consumers and save electric energy. The development of Internet has also provided an available option for many enterprises to sale and promote green product in online channel (Li et al., 2016). Obviously, the opening of online channel can contribute to a larger demand of energy-saving product. The exponential growth of smart phones and mobile APPs enables people to virtually purchase any product from any corner of the world as long as consumers have its information (He et al., 2016). In this context, a new commerce model emerged in recent years, which is called online to offline (O2O) business. Attracted by the huge profit potential, an increasing number of companies are endeavoring to enter into this new market (Xiao and Dong, 2015). For example, Zara, Metersbonwe and other manufacturing enterprises devote attention to integrating their own retail stores and online shops, which is regarded as the vertical manufacturer’s O2O supply ④

http://www.gree.com.cn/public/200908/pop_jsp_catid_1261_id_44306.shtml

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chain. In fact, some retailers such as Walmart and Suning have had their own online shops. This is treated as the horizontal retailer’s O2O supply chain. Compared with manufacturer’s O2O case, retailer’s O2O pattern has received more academic attention. That is because the research on manufacturer’s O2O supply chain is similar to that of the centralized dual-channel supply chain, which has been extensively studied before. Therefore, this paper focuses on the retailer’s O2O supply chain. Previous studies on dual-channel supply chain focused on the channel competition and price competition. However, the dual-channel supply chain under O2O mode completely changes the competition situation in the traditional market. Firstly, O2O pattern emphasizes the combination of online and offline channels. For example, Suning integrates the online and offline resources from the perspective of distribution. Their offline hypostatic stores are treated as the warehouse and delivery terminal of the online sales. The principle of proximity in the distribution will help realize the optimal allocation of resources and relieve the impact on the environment. Secondly, as the development of O2O pattern, consistent pricing is usually adopted by firms, which can help avoid price competition between two channels and thus alleviate channel conflict. The consistent pricing strategy means that the online price is equal to the offline price. In reality, Suning has developed O2O mode with consistent pricing strategy. In addition, in November 2015, Amazon opened the first offline bookstore ‘Amazon Books’ in Seattle University Village. The price in ‘Amazon Books’ are the same as that in online sales. In the same month, dangdang.com also announced that they will open 1000 offline bookstore in the following 3 years. The consistent pricing strategy will also be used by them. Therefore, the research scope of this paper is narrowed by observing an O2O retail supply chain with consistent pricing strategy. As discussed above, this paper considers the supply chain in which the retailer opens his own online channel and offline channel. Based on the cap-and-trade regulation with two different carbon allowance 4

allocation methodologies, we try to answer the following research questions.

a)

What is the impact of the two allocation methods on the supply chain members’ emission reduction behaviors, the firm’s profit and social welfare?

b)

With the target of social welfare maximization, which allocation method is more beneficial to the low-carbon supply chain and environment?

To address these issues, this work uses the Stackelberg game model to analyze the O2O retail supply chain. In order to analyze social welfare which is associated with carbon emissions of the supply chain, this paper uses carbon footprint to describe the different carbon emissions in online and offline channels. The paper also considers the different delivery ways in the offline channels, which can effectively highlight the characteristics of the O2O retail supply chain. This work models the optimal pricing and emission reduction decisions with and without cap-and-trade regulation. On this basis it focuses on the comparison between the grandfathering and benchmarking mechanisms. Some managerial insights for supply chain members and governments are obtained from the analysis. The remainder of this paper is structured as follows: Section 2 provides a literature review and Section 3 presents assumptions and notations. Section 4 shows the models considering different carbon allowance allocation mechanisms, and obtains the optimal strategies. Section 5 provides the comparative analysis of the three models. Section 6 conducts numerical experiments to provide more insights. Conclusions and outlooks are finally presented in Section 7. To make the paper more readable, all proofs are presented in Appendices.

2. Literature review The relevant literature can be divided into three areas: operations management under the 5

cap-and-trade regulation, dual-channel with environmental issue and free carbon allowance allocation mechanisms. To highlight our contribution, we review only the literature that is representative and particularly relevant to our study.

2.1. Operations management under the cap-and-trade regulation Operations management under the ‘cap-and-trade’ regulation is an important topic in the low-carbon environment. It is also relevant to our study. The existing literature on the operations management in the cap-and-trade regulation contains the research on pricing, production, inventory and carbon emission reduction decisions. In the view of pricing and production decisions, Xu et al. (2016b) explored the joint production and pricing problem of a manufacturer under cap-and-trade and carbon tax policies. They compared the effects of the two policies on the total carbon emissions, the firm’s profit and social welfare. They showed that, under the cap-and-trade system, both the emission trading prices and the cap play decisive role in the optimal production quantity. Similarly, we also adopt a Stackelberg model to analyze the effect of cap-and-trade regulation on the supply chain member’s profit and social welfare. However, their research only considered the operational decisions of a single manufacturer; in this aspect, this model differs from ours. Xu et al. (2017b) considered the production and pricing problems in make-to-order supply chain with cap-and-trade regulation. The impact of emission trading price on the production decisions and firms’ profits are analyzed. Their model only considers the carbon emission incurs in the production activities. By contrast, we calculate the total carbon emissions from the aspects of production, inventory and transportation. Gong et al. (2013) presented the optimal production strategy under carbon trading policy through a dynamic model. By contrast, our study investigates the emission reduction strategies of the supply chain members. Du et al. (2016a) delved the impacts of carbon footprint and 6

low-carbon preference on the manufacturer’s production strategy under the cap-and-trade regulation. They pointed out that the firm’s emission reduction decision is determined by the benefit of emission permits and the added value brought by the consumers’ low-carbon preference. We also take the carbon footprint and consumers’ low-carbon preference into account, but we formulate a dual-channel model for the retailer. From the inventory perspective, Hua et al. (2011) investigated how firms manage carbon footprints in inventory management under the carbon-trading regulation. They demonstrated that both the carbon cap and carbon price have a great influence on the retailer’s order decisions, carbon footprints, and total costs. Benjaafar et al. (2013) developed relatively simple models under low-carbon policies, including strict emission caps, taxes on emissions, cap-and-offset, and cap-and-trade, to discuss their impact on production and inventory decisions. Their study aimed to present the comparison of different low-carbon policies. Differently, we focus on the comparison between the grandfathering and benchmarking methodologies under the cap-and-trade regulation. Within this literature of supply chain considering cap-and-trade regulation, there are growing studies taking note of firms’ emission reduction behaviors. Xu et al. (2017a) focused on the emission abatement decisions in a make-to-order supply chain. Their study aimed to analyze the impacts of cap-and-trade regulation on manufacturers’ abatement level. They conclude that with the increase of carbon trading price, the optimal abatement levels firstly increase and then remain constant. Ren et al. (2015) investigated the issue of allocating the carbon emission abatement target on product level in a make-to-order supply chain. Four scenarios based on different bargaining power are considered in their paper. The results show that it is always not bad to let the leader allocate the product-related carbon emission abatement target. He et al. (2015) addressed the impact of cap-and-trade regulation on firm’s 7

carbon emission decisions. They pointed out that the differentiated permits trading prices play a decisive role in firm’s decisions of optimal emissions and permits trading. Our model is similar to the above in the sense that we too consider a managerially relevant framework that takes firms’ emission reduction behaviors into account. Conclusively, almost all the above papers are restricted to a single channel supply chain and neglect to consider the dual-channel mode. Therefore, our paper addresses these limitations in current research by studying the supply chain members’ emission reduction behaviors from the perspective of dual-channel supply chain.

2.2. Dual-channel with environmental issue

With the rapid development of e-commerce and increasing acceptance of low-carbon economic, the academic world began to pay attention to the research on dual-channel with environmental issue. This area is closely related to our study. In empirical research field, Williams and Tagami (2002) showed that in suburban and rural areas, the energy consumption of the e-commerce and the conventional retail is nearly equal. However, in dense urban areas, the e-commerce uses considerably more energy because of additional packaging. Weber et al. (2008) performed a case study for buy.com and find that the total amount of carbon emissions for a traditional retailer is higher than that typically associated with e-commerce delivery. They also pointed out that if the goods are delivered by air shipping, then the energy usage for the online channel and retail channel is roughly comparable. Loon et al. (2015) developed a framework to analyze the carbon emissions from retail and e-commerce activities. The results indicate that online retailing can lower the environmental impact of shopping under specific circumstances. In order to identify the different carbon

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emissions in the online and offline channels, we explicitly consider the carbon footprint in the supply chain related to consumer’s behavior such as shopping mode and choice of delivery method. However, there is rarely literature introduced dual-channel into low-carbon supply chain management from a micro perspective, such as the impact on firm’s operational decisions. In this area, Carrillo et al. (2014) developed a dual-channel mode for a retailer and discussed the pricing decisions and channel choice with considering the environmental issue. The deterministic and stochastic models were both analyzed in their paper. Li et al. (2016) established a Stackelberg game to delve the pricing and greening strategies for the supply chain members. They concluded that when the greening cost is higher than a threshold, the manufacturer does not open direct channel. Although the background of the above two studies are similar to that in our model, their focus was the channel choice of the retailer or the manufacturer and they do not consider the influence of the low-carbon policy. Ji et al. (2017) incorporated cap-and-trade regulation, firm’s emission reduction strategies and consumers’ low-carbon preference into a dual-channel supply chain. In their model, the grandfathering mechanism is adopted. By contrast, we in this paper concentrate on the comparisons between the grandfathering and benchmarking mechanisms.

2.3. Carbon allowance allocation mechanisms

Many studies have been published which analyzed the impact of carbon allowance allocation methods from a macro perspective. For example, Cong et al. (2010) addressed the impact of different allocation options of allowances on China’s power sector. To be specific, the emission-based allocation and the output-based allocation are included. Their results indicate that the emission-based allocation brings about both higher electricity and carbon prices than by output-based allocation. Therefore, they concluded that the output-based allocation would be more conductive to reducing emissions. Liao et al. 9

(2015) argued that the grandfathering method, which is based on historical emissions, is inequitable. In particular, it is unfair to high efficiency and low emission enterprises. They believed that the grandfathering method can be adopted in the introduction of experimental stage. Though it is difficult to establish benchmarks, the benchmarking mechanism should be prepared and adopted at the appropriate time. More related articles in this issue are presented by Cramton and Kerr (2002) and Pan et al. (2014). Existing studies focus on the impact of allocation rules from the micro perspective is still scarce. Zetterberg (2014) investigated abatement incentives for allowance allocation and show the impact of benchmarking method on firm’s price decisions. They found that benchmarking with updated output and updated benchmarks reduces abatement incentives somewhat, but less so than updated grandfathering. Zhang et al. (2015) used a multi-stage profit model to analyze firms’ price and emission reduction strategies based on the current carbon allocation rules in China. They confirmed that under the rules of grandfathering, self-declaration and auctioning, the firms will focus on maximizing current stage profit when deciding the optimal price and emission reduction; while under the benchmarking method, the firms will care more about the impact of current decisions on the profit in next stage. Although the above papers on grandfathering and benchmarking methods are relevant to our study, none of them considers the effect of the two methods from the perspective of social welfare. Our key contribution lies in the following three aspects. First, our paper contributes to the low-carbon supply chain management literature by investigating the cooperation between manufacturer and retailer. Although the literature on firms’ optimal decisions under cap-and-trade policy is rich as illustrated above, most of them do not consider firms’ low-carbon cooperation mechanism except Wang et al. (2016) and Ji et al. (2017). Our model is more practical by considering decisions of both manufacturer’s emission reduction and retailer’s low-carbon promotion. Second, we introduce O2O 10

mode into low-carbon supply chain management. We no longer emphasize the channel and price competition, but we combine the online and offline channels into one unit to operate them synergistically. To this end, we assume that the offline stores play the role of warehouse in the online sales, which is one of the important characters in O2O mode. At the same time, the consistent pricing strategy is adopted in our model. Third, our contributions are in addressing the different impact of the grandfathering and benchmarking methods on the supply chain members’ emission reduction behaviors, the firm’s profit and social welfare through the model analysis. We identify the carbon emissions incur in online and offline activities, so as to analyze the different environmental effect between the two channels. Up to now, the literature containing both the operations management, environmental and social problems in the supply chain is sparse. Our work aims to provide decision-makers and policy-makers with some new managerial insights under the cap-and-trade regulation.

3. Prerequisites and assumptions This paper investigates the pricing strategies and emission reduction decisions of supply chain members under the ‘cap-and-trade’ system. A two-echelon supply chain consisting of an upstream manufacturer and a downstream retailer is considered. In our model, the manufacturer is regulated by cap-and-trade regulation and has to take actions to curb emissions. The manufacturer’s emission reduction effort includes the investment in green innovation and replacing energy consuming equipment with energy saving equipment. Meanwhile, the retailer has both the online and offline shops and adopts consistent pricing strategy. Consumers can buy products through either the online channel or the offline channel depending on their preference. In the low-carbon supply chain, the retailer’s advertisement and promotion are indispensable to ensure low-carbon products receive maximum extension (Zhou et al., 2016). Thus, we consider the case that the retailer implements low-carbon promotion strategy in the 11

offline shop, so as to motivate consumers to purchase low-carbon products. The retailer’s low-carbon promotion can be regarded as the effort in providing place for consumers to investigate low-carbon products, as well as providing detailed environmental information of products for consumers. It is assumed that all information is common knowledge to both supply chain players. For lucidity and simplicity, we summarize the model parameters and decision variables in Table 1. Table 1 Model parameters and decision variables Model Parameters a

Potential market size

p

Unit retail price

pe

Unit carbon price

c

Unit production cost (not including low-carbon processing cost)



Propensity of consumers for the online channel



Environmental damage coefficient

em

Unit amount of carbon emission from production process before low-carbon processing

er

Unit amount of carbon emission in the offline shop

eo

Unit amount of carbon emission delivered from the distribution center to consumers

et

Unit amount of carbon emission that the consumers drive to the retail store



Demand expansion effectiveness coefficient of the manufacturer’s emission reduction rate



Demand expansion effectiveness coefficient of the retailer’s low-carbon promotion degree



Competition coefficient between the online and offline channels, and  [0,1 2]

k

Cost coefficient of manufacturer’s emission reduction

m

Cost coefficient of retailer’s low-carbon promotion

m

Unit carbon quota for the manufacturer

Em

Emission cap for the manufacturer

Fi

Threshold value, i  1,...,9

Hi

Threshold value, i  1,...,6

12

Li

Threshold value, i  1,...,6

k'

Threshold value

Decision variables w

Unit wholesale price



Unit marginal profit of the retailer,   p  w



Manufacturer’s emission reduction rate, and  [0,1]

s

Retailer’s low-carbon promotion degree in the offline shop

3.1. Assumptions

The following assumptions are provided to specify the scope of this research for further model formulation: Assumption 1. The relationship between the manufacturer and the retailer is modeled as a Stackelberg game, where the retailer is the leader and the manufacturer is the follower. Based on observations from current practice, we focus on a retailer’s O2O supply chain. The retailer who can develop his own O2O sales mode is always a retail giant. That is, the O2O retail supply chain arises in markets where the retailer’ sizes is large compared to his supplier. Today, large retailers like Wal-Mart and Suning, who are powerful in the market, have greater bargaining power in the supply chain and develop their O2O sales mode. They can maintain their margin on sales while squeezing profit from their suppliers (Lu et al., 2011). Therefore, a Stackelberg game is formulated to analyze firms’ operational decisions, in which the giant retailer acts as the game’s leader. The sequence of the firms’ decisions is as follows: First, the retailer declares a marginal profit and determines the low-carbon

promotion level. Then the manufacturer makes decision on the wholesale price and the emission reduction rate to maximize his profit. Assumption 2. The low-carbon investment cost is assumed to be a quadratic function of firms’ effort 13

level. In this paper, we use the quadratic function to describe the extra cost for producing low-carbon products or providing low-carbon promotion, which is commonly adopted in previous literature (Yao and Liu, 2005; Zhou et al., 2016). Thus, the abatement cost that the manufacturer should undertake is C ( )  k 2 2 , where the parameter k is understood as the cost effectiveness of emission reduction.

Here, the abatement cost is assumed as a disposable investment to improve the production process which turns raw material into product (Luo et al., 2016). Thus, the parameter k is assumed to be significantly large (Wang and Zhao, 2014). Similarly, the cost for the retailer to provide low-carbon promotion is C (s)  ms 2 2 , where the parameter m measures the cost effectiveness of the promotion. The smaller the

value of m , the more effective the cost. The low-carbon promotion cost is also a one-time investment and m is relatively large. In order to ensure that the profit functions in the three models are jointly concave on the decision variables, we assume that

k  2 ,

k    pe em  , 2

2m   2

and

a  2  pe em    c  . Similar assumptions can be found in Wang et al. (2016) and Ji et al. (2017).

As in Ghosh and Shah (2012) and Li et al. (2016), we also assume that manufacturers’ low-carbon investment does not affect his traditional marginal cost. That is, the unit production cost remains the same before and after the implementation of emission reduction technology. Assumption 3. The consumers are assumed to be of environmental consciousness and accordingly will note the emission reduction rate of products when shopping. According to the findings in the literature (like Kotchen, 2005; Motoshita et al., 2015), we assume that the consumers have preference for low-carbon products. Thus, the emission sensitive demand function is used in our paper. For simplicity but without loss of generality, we suppose that consumers are sensitive to manufacturers’ emission reduction rate just as counterpart assumptions addressed in 14

Wang et al. (2016) and Du et al. (2016b). The assumption is reasonable because consumers can gain some relevant information from low-carbon labels which are provided by the manufacturer.

3.2. Model Setup

Before proceeding with the analysis, we need to first delineate the firm’s demand function. In pursuit of social welfare maximization, the government should balance a tradeoff between economic performance and environmental performance. Thus, this section also presents the environmental damage function and social welfare function. 3.2.1. Demand function Considering the impact of manufacturer’s emission reduction and the retailer’s low-carbon promotion on the demand, the demand functions in the online channel and the offline channels are formulated as follows: d1   a  p     s .

(1)

d2  1    a  p     s .

(2)

The linear demand functions, which are used by Ghosh and Shah (2012) and Carrillo et al. (2014), are inherited in this paper. The parameter  represents the consumer’s propensity to buy from the online channel. In our model, we capture consumers’ low-carbon preference chiefly through the parameter  , which is understood as the demand expansion effectiveness coefficient of emission reduction by the manufacturer. In the offline shop, consumers have the possibility of examining the products and receiving more detailed environmental information of the products, whereas the service is provided by the retailer. However, the same product, purchased from an online channel, can only be virtually inspected through website and cannot be immediately owned. In the O2O retail supply chain

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with consistent pricing strategy, some consumers would like to use online channel to search information then switch to offline shop to complete the purchase. Here, as long as consumers visit the offline shop and buy the product finally (either purchase the product immediately or order the product through the online channel), the sales volume is calculated into the demand of offline channel. Consequently, we assume that the demand in the offline channel is upward sloping in retailer’s low-carbon promotion degree; while the demand in the online channel is downward sloping in retailer’s low-carbon promotion degree. The parameter  measures the efficacy of low-carbon promotion in stimulating the demand. The parameter  is denoted as the competition between the online and offline channels, also describes the shift from online channel to offline channel with regards to the retailer’s service. Here, 0    1 2 indicates that the positive effect of retailer’s low-carbon promotion on the offline channel is greater than the negative effect on the online channel. That is, the incremental sales volume in the offline channel due to the retailer’s service is greater than the volume transferred from the online channel.

3.2.2. Environmental damage function In this paper, we use an environmental damage function U  T 2 to describe the environmental pollution from the carbon emission of the supply chain (Wang and Zhao, 2014). The parameter  is denoted as the environmental damage coefficient and T is the total emissions in the supply chain. To calculate the total emissions in the supply chain, it is necessary to identify emissions in different activities. Carbon emissions occur along the whole life cycle of the product. Especially, most of them are produced in the production, inventory and transportation processes. In this work, we assume that the manufacturer outsources his logistics to a third-party logistics enterprise, which is common in practice. For the sake of simplicity, this paper just considers the carbon footprints mainly from three aspects: production, inventory and the last mile delivery processes. 16

(1) Production process In our model, we capture manufacturers’ low-carbon behaviors chiefly through the decision variable

 , which is denoted as    em  em  em . Obviously,  is in the range of [0,1] . Here, em is understood as the unit amount of carbon emission from production process before low-carbon processing, and em is the unit amount of carbon emission from production process after low-carbon processing. Therefore, in the production process, unit amount of carbon emissions after low-carbon processing is em (1   ) . (2) Inventory process The offline shop provides a place for the retailer to exhibit products, which will absolutely produce carbon emissions. The unit amount of carbon emission in the offline shop is expressed by er , which is understood as the unit carbon emission from the inventory process. (3) Last mile delivery process This article explores two last mile delivery modes: attended home delivery (AHD) and collection-and-delivery points (CDPs). Here, the AHD mode means that the retailer provides consumers with home-delivery service; and the CDPs mode indicates that the consumers pick-up the cargo from the offline shop by themselves. In the O2O retail supply chain, consumers have to decide which channel to buy from. When consumers choose online shopping, the retailer will provide them with home-delivery service. In this paper, we assume that the retailer uses the principle of proximity in the distribution. The unit amount of carbon emission delivered from the distribution center to consumers is denoted by eo . The following introduces the situation when consumers choose offline shopping. In order to evaluate the product physically, consumers have to drive to the offline shop, which produce carbon emission et per unit. In the offline shop, consumers can also choose to pick-up the cargo by themselves or ask the retailer to provide home-delivery service. We use the parameter  to represent the proportion that consumers 17

ask for home-delivery service in the offline shop. Furthermore, we adopt the similar way as in Du et al. (2013) and Yang et al. (2014) to assume that the total carbon emissions are proportional to production quantity. Consequently, the total amount of carbon emissions in the supply chain is as follows: T  em 1    d1  d2   eo  d1   d2    er  et  d2 .

(3)

3.2.3. Social welfare function From the perspective of social welfare, we consider the economic and environmental performance. It is widely accepted that carbon emissions can induce the increase of social cost, which damages the social welfare (Xu et al., 2016b). Thus, in our model, the total social welfare includes the supply chain’s profit and the environmental performance. It is denoted that  m is the manufacturer’s profit and  r is the retailer’s profit. According to Krass et al. (2013), the social welfare function can be modeled as follows:    m   r U .

(4)

4. Model solutions and discussions This section derives the equilibrium solutions for the supply chain members in three different models: without cap-and-trade regulation, cap-and-trade regulation based on grandfathering mechanism and cap-and-trade regulation based on benchmarking mechanism. We use superscripts i ( i  a, b, c ) to distinguish the three models above respectively. Further, we compare the optimal decisions, profits and social welfare among the three models.

4.1. Model a: Without cap-and-trade regulation

As a benchmark, we first consider a low-carbon supply chain without cap-and-trade regulation. 18

Based on the demand functions in Section 3, the profits of the manufacturer, the retailer and the supply chain can be modeled as follows: 1 2

(5)

 ra   p  w d1  d 2   ms 2 .

1 2

(6)

 a   ma   ra .

(7)

 ma   w  c  d1  d 2   k 2 .

Lemma 1. For Model a, there exist equilibrium solutions only when 0  H 2  H1 , where  a* 

2m  a  2c   k   2 

8m  k   2   k  1    

2

, s a* 

 k  a  2c 1   

8m  k   2   k  1   

2

,

2 mk  a  6c   c 8m 2  k 2 1     2m  a  2c    ,  a*  . w  2 2 2 8m k   2  k  1     8m  k     k  1     a*





Note that the emission reduction rate must satisfy 0   a*  1 . Thus we can conclude that only when 0  H 2  H1 the feasible solutions exist. Here we can understand this condition in the following way.

Firstly, the condition 0  H 2  H1 holds when k is significantly large. As discussed in Assumption 2, manufacturer’s abatement cost is a one-action investment. Thus, it is reasonable to assume that the parameter k is large enough to meet the condition. Secondly, if the condition is not satisfied, the profit functions’ concavity cannot be guaranteed. In accord with the fact that the manufacturer and the retailer both have positive profit margin, we need to set this condition. Thirdly, when k is too small, implying that manufacturer’s abatement cost is low. Under this circumstance, the manufacturer’s optimal choice is to reduce his carbon emissions infinitely, owing to the fact that manufacturer’s high emission reduction rate will actually boost his sales volume. That is, the higher the emission reduction rate, the more profit the manufacturer can obtain. In fact, the emission reduction rate must in the range of [0,1] as is defined in Section 3.2.2. Conclusively, the condition is necessary to ensure the exactness of the model and the efficiency of the result. The following propositions and theorems are derived based on such condition. 19

Interestingly, it is found that without cap-and-trade regulation, manufacturer’ optimal solution is not influenced by his carbon emissions. Without cap-and-trade regulation, the manufacturer will not reduce his carbon emissions actively for lack of motivation and pressure. It also explains why a lot of manufacturing enterprises in pursuit of profit maximization for enterprise management goal and ignores the corporate social responsibilities without any government pressure or restrictions. Under the equilibrium decisions, the market demands are: d1a* 

F1  2mkc

8m  k  

2

  k  1   

2

, d 2a* 

2mk  a  c   F1

8m  k   2   k  1    

2

.

Substituting the optimal solution into Equation (5) and (6), we can obtain the manufacturer’s and the retailer’s optimal profits: 2m2 k  a  2c   k   2 

mk  a  2c 

2

 ma* 



8m  k   2   k  1    



2 2

,  ra* 

2

16m  k   2   2k  1    

2

.

We can also see that without cap-and-trade regulation, the initial carbon emission has no impact on manufacturer’s optimal profit. That is because without external restriction, the manufacturer doesn’t take carbon emission into consideration when he makes decisions. In the following paper, H i ( i  1, 2,..., 6 ), Fi ( i  1, 2,...,9 ), Li ( i  1, 2,..., 6 ) and k  are the threshold values and given in Appendix A.9. Under the

equilibrium decisions, the total carbon emissions in the supply chain is as follows: T a*  F2 H1  F3 H12 . Thus the social performance is  a*   ma*   ra*   F2 H1  F3  H14 . 2

4.2. Model b: Cap-and-trade regulation based on grandfathering mechanism

Under the cap-and-trade regulation, firms will receive free emission quotas from government, and the carbon quotas can be traded through carbon trading market. Here, the carbon price is determined by the carbon trading market. With carbon quota allocation based on grandfathering mechanism, firms get carbon quotas after carbon verification according to their historical emission data (Sadegheih, 2011). The 20

cap-and-trade system uses the total “cap” to attain environmental goals and allows “trade” to achieve the effective scheduling through market regulation (Du et al., 2016a). The carbon credits of the manufacturer come from the following ways: carbon quotas allocated by the government, the emission savings from the implementation of carbon emission reduction technology, and carbon quotas bought from the carbon trading market. The manufacturer’s and retailer’s profit function are: 1 2

 mb   w  c  d1  d 2   em 1    d1  d 2   Em  pe  k 2 .

(8)

1 2

 rb   p  w d1  d 2   ms 2 .

(9)

Lemma 2. For model b, there exist equilibrium solutions only when 0  H 4  H3 , where 2m  a  2  pe em  c    k     pe em    k  a  2  pe em  c   1       , s b*  , 2 2 2 2 8m  k     pe em    k  1     8m  k     pe em    k  1         2



b*

wb* 

ma  k  2 pe em    pe em   H 5  pe em  c  8m  k     pe em    k  1       2

2

,  b* 

2m  a  2  pe em  c      pe em  2 2 8m  k     pe em    k  1     

.

With 0   b*  1 , we can get 0  H 4  H3 . The condition exists when k is significantly large. Similar discussion can refer to Lemma 1. The following propositions and theorems are derived based on such condition. Compared with Model a, we can observe that under the cap-and-trade regulation based on grandfathering mechanism, both the manufacturer’s and the retailer’s decisions will be affected by the manufacturer’s initial carbon emission. It illustrates that government’s low carbon constraint has some effects on firms’ decisions. The supply chain members must incorporate environmental considerations into their decisions under cap-and-trade regulation. However, it is apparent that the government is unable to change firms’ decisions through adjusting the total cap. Under the equilibrium decisions in Lemma 2, the market demands are: d1b* 

F4  2mk  pe em  c  8m  k     pe em    k  1       2

2

, d 2b* 

2mk  a   pe em  c    F4 2 2 8m  k     pe em    k  1      

.

Substituting the optimal solution into Equation (8) and (9), we can obtain the manufacturer’s and the 21

retailer’s optimal profits: 

b* m

2 2 2 2m2 k  a  2  pe em  c   k     pe em   mk  a  2  pe em  c      E p , b* .    m e r 2 2 2 2 2 16m  k     pe em    2k  1    8m  k     pe em    k  1        





Under the equilibrium decisions, the total carbon emissions in the supply chain is as follows: b* b* b* T b*  F5 H3  F6 H32 . Thus the social performance is    m   r    F5 H3  F6 

Proposition 1. (1)

2

H 34 .

s b* s b*  b*  b*  b*  b* 0,  0 ; (2)  0,  0 ; (3) 0, 0.      

Proposition 1(1) and (2) indicates that retailer’s optimal low-carbon promotion degree and manufacturer’s optimal emission reduction rate increase as  (or  ) increases, which is conform to our common sense. A larger  means that consumers are more sensitive to low-carbon products. It will provide a strong incentive for both the manufacturer and the retailer to increase the low-carbon investment. A larger  indicates that retailer’s low-carbon promotion can more effectively stimulate the actual purchase behavior of consumers. Motivated by this, both the manufacturer and the retailer invest more money in low-carbon innovation. A high emission reduction rate will lead to a high cost. Naturally, the retailer will increase his marginal profit so as to pass the cost on to consumers, which is shown in Proposition 1(3).

 

 

d b*   0 if   k 1  1     3  5      1 d 2b* d1b* d 2b* Proposition 2. (1)   0,  0,     d1b*   0 if   k 1  1     3  5   

12

 pe em

12

 pe em

;

(2)

 mb*  rb*  mb*  mb*  rb*  rb*  0 ; (3)  0.  0,  0,  0,  0,      

Proposition 2(1) shows that both the online demand and offline demand increase as  increases. Obviously, the increasing of the emission reduction rate and the low-carbon promotion degree result in the rising of the supply chain sales volume. Furthermore, the rate of the offline demand is greater than that of online demand. If the manufacturer increases  by one unit, the increase in offline demand is more than the increase in online demand. The increase of  contributes more to the offline demand. It 22

indicates that consumers’ preference for low-carbon products has a greater influence on the offline demand than that on the online demand. In addition, the offline demand increase as  increases. When  increase, consumers are more sensitive to retailers’ low-carbon promotion or some other low-carbon

exhibition. In the offline shop, consumers can evaluate products directly and obtain more detailed environmental information of products. Naturally, more consumers who drive to the offline shop will be attracted to buy the low-carbon products. Proposition 2(1) also implies that the increase of  has a positive effect on the online demand when   k 1  1     3  5   pe em . The inequality holds 12

when  is relatively larger. In this case, consumers are product oriented rather than service oriented. That is, the consumers pay more attention to the product’s low-carbon level. Thus, the channel competition has a small influence on the online demand. Conversely, when  is small, the consumers are more easily attracted by retailer’s low-carbon promotion. Thus, more consumers will transfer from the online channel to the offline channel, which brings a negative impact on the online demand. Proposition 2(2) and (3) show that both the manufacturer’s and the retailer’s optimal profits increase as  (or  ) increases and decrease as  increases. The demand expansion makes both the manufacturer’s and the retailer’s profit rise up. It indicates that consumers’ low-carbon preference can help the supply chain boost its profit. In this case, the manufacturer and the retailer can together enjoy the premium of the supply chain profit created by consumers’ low-carbon preference. As  or  increases, both the manufacturer and the retailer will invest more money in low-carbon processing. However, the profit increment coming from the demand expansion is larger than the profit decrement coming from the low-carbon investment. Therefore, the increase of the two parameters is always profitable for the supply chain members. A larger  means that channel conflict is fiercer. It is no doubt that the fiercer channel conflict will be detrimental to the profit of the supply chain members. 23

Consequently, the retailer who owns both online and offline shops is expected to strengthen the cooperation between two channels. In conclusion, under the dual-channel retailing environment, consumers can easily buy products through different channels. In the offline shop, consumers can also choose to order products through the APP or website. After evaluating the products, consumers can decide whether to buy products or not and which method to buy from. Such consumption pattern will also help reduce return rates. It is beneficial for the retailer to attract consumers from online to offline. This conclusion is reasonable because consumers are more easily to be motivated to buy low-carbon products in the offline shop, which results in a higher demand and allows the retailer to earn more profits.

4.3. Model c: Cap-and-trade regulation based on benchmarking mechanism The benchmarking methodology has been established on the basis of the principle of ‘one product = one benchmark’⑤. A benchmark does neither represent an emission limit nor even an emission reduction target, but merely a value used to calculate free allocation per installation. Compared with grandfathering methodology, benchmarking mechanism has a higher requirement for data and is more difficult to implement. We denote that the low-carbon-emission firms are those when em   m , and the high-carbon-emission firms are those when em   m . Under the cap-and-trade regulation based on benchmarking mechanism, the profit functions of the manufacturer and the retailer are as follows: 1 2

 mc   w  c  d1  d 2   em 1      m   d1  d 2  pe  k 2 . 1 2

 rc   p  w d1  d 2   ms 2 .

(11)

Lemma 3. For model c, there exist equilibrium solutions only when 0  H 6  H3 , where

⑤

(10)

http://ec.europa.eu/clima/policies/ets/cap/allocation/index_en.htm

24

2 2m  a  2  pe em  pe m  c   k     pe em    k  a  2  pe em  pe m  c   1        , s c*  , 2 2 2 2 8m  k     pe em    k  1     8m  k     pe em    k  1         c*

wc* 

ma  k  2 pe em    pe em    H 5  pe em  pe m  c  8m  k     pe em    k  1       2

2

,  c* 

2m  a  2  pe em  pe m  c      pe em  2 2 8m  k     pe em    k  1      

.

In Lemma 3, the condition 0  H 6  H 3 holds when k is significantly large. The discussion is similar to that of Lemma 1, thus we omit it. Under cap-and-trade regulation based on benchmarking mechanism, firms’ optimal decisions are affected by the manufacturer’s initial carbon emission as well as the unit carbon quota. More importantly, through adjusting the unit carbon quota, the government can motivate the manufacturer to increase the emission reduction rate and encourage the retailer to improve the low-carbon promotion degree. It indicates that the government’s unit carbon quota has an instructive effect on firms’ decisions. Under the equilibrium decisions that presented in Lemma 3, the market demands are: d1c* 

F4  kpe m 2 1   2   2mk  pe em  pe m  c  2 2 8m  k     pe em    k  1     

, d 2c* 

2mk  a   pe em  pe m  c    kpe m 2 1   2   F4 2 2 8m  k     pe em    k  1      

.

Substituting the optimal solution into Equation (10) and (11), we can obtain the manufacturer’s and the retailer’s optimal profits: 

c* m

2 2 2 2m2 k  a  2  pe em  pe m  c   k     pe em   mk  a  2  pe em  pe m  c     , c*  . r  2 2 2 2 2   16 m k    p e  2 k  1           e m 8m k     pe em   k  1          





Under the equilibrium decisions, the total carbon emissions in the supply chain is as follows: c* c* c* T c*  F7 H3  F8 H32 . Thus the social performance is    m   r   F7 H3  F8 

2

H 34 .

5. Comparative analysis This section presents the analysis of the results described in Section 4. To obtain some managerial insights, this section compares the optimal decisions, profits and social welfare among the three cases. The specific aim of the following theorems and corollaries is to evaluate the impact of the two allocation 25

methods, so as to find which one is beneficial to the supply chain members and environment. First, we mainly compare the optimal decisions among the three models, including the emission reduction rate, low-carbon promotion degree and pricing decisions. Three theorems are provided below. Theorem 1. The emission reduction rate of the manufacturer in the three models satisfy  a*   b*   c* . Theorem 1 indicates that the implementation of cap-and-trade policy will absolutely induce the manufacturer to increase the emission reduction rate. As a carbon trading system covered enterprise, the manufacturer is forced to reduce carbon emissions. Thus, the cap-and-trade regulation is an effective mechanism to push the manufacturer to choose environmental friendly production pattern. The result is consistent with the earlier research. Furthermore, though a strict cap can influence the decisions of supply chain members, it cannot reflect in the decisions directly. By contrast, governments can effectively influence firms’ decisions through the unit carbon quota  m , which guide the manufacturers to make efficiency investments in reducing emissions, meaning that the manufacturer produce products with a higher emission reduction rate. Thus we can conclude that compared with grandfathering mechanism, the benchmarking methodology can more effectively push the manufacturer to produce low-carbon products and take actions to curb emissions. We can understand the result from the following aspects. Firstly, the grandfathering mechanism is based on historical emissions. It provides no reward for high efficiency and low emission firms. In other words, it is unfair to cleaner enterprises. In addition, the grandfathering mechanism controls carbon emissions from the total amount level. It provides an opportunity for firms to comply with the cap-and-trade policy through reducing production rather than through implementing low-carbon technologies. Secondly, the benchmarking mechanism rewards more efficient and lower-emitting firms. It controls carbon emissions from the unit level and all the firms have the same 26

baseline. Thus, the high emission firms have to reduce the unit carbon emission through technical innovation. In summary, the benchmarking mechanism is relatively fair and has higher efficiency. Denote that d i*  d1i*  d2i* , i  a, b, c . And d i* represents the total demands in the supply chain. a* b* c* a* b* c*  s  s  s , d  d  d b* a* c* b* a* c*  s  s  s , d  d  d

Theorem 2. (1) If em   m , then 

 s a *  s b*  s c * , d a *  d b*  d c *  (2) If em   m , then  sb*  s a*  s c* , d b*  d a*  d c*  b* c* a* b* c* a* s  s  s , d  d  d

if L1  k  L2 if k  L2

;

if L1  k  L2 if L2  k  L3 . if k  L3

Theorem 2 compares the retailer’s low-carbon promotion degree and the total demands in the three models. We can conclude that sb*  sc* and d b*  d c* always holds. Therefore, compared with the grandfathering mechanism, the benchmarking methodology can more effectively motivate the retailer to promote low-carbon products. Naturally, the cap-and-trade regulation with benchmarking mechanism is more beneficial to increase the sales volume of low-carbon products and thus improve the market coverage of low-carbon products. Theorem 2 also shows that the variation trend of the market demand is consistent with that of the retailer’s low-carbon promotion degree. With Theorem 2(1) we can know that when em   m , that is, the initial unit carbon emission of the manufacturer is not larger than the unit carbon quota, then retailer’s low-carbon promotion degree in Model c is always the highest. Under the rule of benchmarking, the cooperation with low-carbon-emission manufacturer will motivate the retailer to invest more in low-carbon promotion. As a result, the market coverage of low-carbon products will improve, which is beneficial for sustainable development. If em   m and k  L2 , that is, the low-carbon-emission manufacturers should pay more extra cost for his emission reduction behavior, then the retailer’s low-carbon promotion degree in Model b is the lowest. Under such circumstance, the implementation of cap-and-trade regulation with grandfathering mechanism is not conducive to the promotion of low 27

carbon products. When em   m , that is, the initial unit carbon emission of the manufacturer is lower than the unit carbon quota, then retailer’s low-carbon promotion degree in Model c is the highest only when k  L3 . When k  L3 , the adoption of cap-and-trade regulation will lower the retailer’s promotion enthusiasm. For high-carbon-emission firms, if the emission reduction cost is too high, they will prefer to buy carbon quotas in carbon trading market when they lake quotas rather than invest in low-carbon technology. In this case, the products cannot be treated as low-carbon ones. Therefore, the retailer will lower his promotion effort. In summary, the cap-and-trade regulation with benchmarking mechanism is effective to increase the market share of low-carbon products when the retailer cooperates with a low-carbon-emission manufacturer or a manufacturer who has lower emission reduction cost. Theorem 3. (1)  b*   c* ; (2) If H 5  0 , then wb*  wc* ; If H 5  0 , then wb*  wc* ; (3) d1b*  d1c* , d2b*  d2c* .

Theorem 3 compares the pricing decisions of the supply chain members and the market demands between Model b and Model c. Combined with Lemma 2 and Lemma 3, we can know that when  m  0 , the optimal decisions and market demands in Model b is the same as that in Model c. Theorem 3 indicates that when H 5  0 , both the wholesale price and retailer’s marginal profit are higher in Model c than that in Model b. In this case, the retail price will be higher under the rule of benchmarking. With Theorem 1 and Theorem 2 we can know that both the manufacturer and the retailer will invest more money in the low-carbon products. A higher cost of low-carbon products results in a higher price. Through increasing the price, the manufacturer and the retailer transfer the extra cost to consumers. Though consumers have to pay more for the low-carbon product, they contribute to a higher demand. We 28

can also see that both the online and offline demands under the benchmarking mechanism are higher than that under the grandfathering mechanism. The profit of the supply chain members, which measures the economic performance, is worth considering when analyzing the chain members’ behaviors. Thus, we have the following theorems and corollary.  a*   rb*   rc*  Theorem 4. (1) If em   m , then  rb* a* c*   r   r   r  ra*   rb*   rc*  (2) If em   m , then  rb*   ra*   rc*  b* c* a*  r   r   r

if L1  k  L4 if k  L4

;

if L1  k  L4 if L4  k  L5 . if k  L5

Theorem 4 is provided to show the comparisons of the retailer’s profits among the three models. Compared with the grandfathering mechanism, the adoption of benchmarking mechanism is always profitable for the retailer. Though the retailer invests more in low-carbon promotion under the benchmarking mechanism, he can gain higher profits. It is reasonable because the manufacturer produces greener products and consumers are willing to pay more for environmentally friendly products, so the increase in earnings is more than the increase in cost. Improving the low-carbon degree of the product allows the retailer to earn more profit. If the retailer cooperates with a low-carbon-emission manufacturer, the cap-and-trade regulation with benchmarking mechanism always allows him to earn more profit. Compared with the non-low-carbon policy case, the cap-and-trade regulation allows the retailer to earn more profit when L1  k  L4 . As the increase of k , the retailer’s profit in Model b will become the lowest among the three

models. When em   m and k  L5 , the retailer can gain the highest profit in Model a. In this case, the cap-and-trade regulation fails to demonstrate its effectiveness in enhancing the retailer’s profit. That is, the implementation of low-carbon policy is detrimental to the retailer. Therefore, in order to gain more 29

profit, the retailer is willing to cooperate with low-carbon-emission firms. In reality, Suning has declared that he prefers to cooperate with low-carbon-emission manufacturers and advertises for low-carbon products. Such behavior will result in a higher coverage rate of low-carbon products. Conclusively, in the context of low-carbon environment, it is better for the retailer to cooperate with the partner whose emission reduction cost is lower. In addition, the benchmarking mechanism is in favor of the retailer. Theorem 5. For the manufacturer: if 0  Em  F9 H32 , then  mb*   mc* ; if Em  F9 H32 , then  mb*   mc* . For the manufacturer, the grandfathering mechanism is less profitable only when Em  F9 H32 . When the emission cap (the maximal amount of carbon quotas) for the manufacturer is lower than the threshold, the manufacturer prefers the benchmarking mechanism to the grandfathering mechanism. If the emission cap is higher than the threshold, the manufacturer can gain more profit in the grandfathering mechanism than the benchmarking mechanism can. This is because a high emission cap provides an opportunity for the manufacturer to sell more carbon quotas in the carbon trading market.  mb*   mc* if Em  min  F9 H 32 ,  m d c*  Corollary 1. (1)  b* ; c* 2 c*   m   m

if Em  max  F9 H 3 ,  m d



(2) When k  k  and F9 H32  Em  m d c* , then  mb*   mc* ; (3) When k  k  and  m d c*  Em  F9 H32 , then  mb*   mc* . In Corollary 1, Em is the emission cap for the manufacturer under the grandfathering mechanism, while  m d c* can be regarded as the total carbon quotas for the manufacturer under the benchmarking mechanism. When k  k  and F9 H32  Em  m d c* , the total quotas under grandfathering mechanism are lower than that under benchmarking mechanism. However, the grandfathering mechanism allows the manufacturer who has a higher emission reduction cost to gain more profit. Thus, from the perspective of improving the effectiveness of carbon quota allocation, the government can use grandfathering 30

mechanism and set the emission cap which falls in the range of F9 H32  Em  m d c* , so as to motivate the manufacturer who has a higher emission reduction cost to reduce carbon emission. Such setting can reduce the allocation of free quotas, as well as increase the manufacturer’s profit. Here, one boundary of the cap depends on the benchmarking mechanism. The unit carbon quota  m can be regarded as industry averages based the carbon calculation. That is, the government can set the suitable range for the cap according to sector characteristics. In addition, when k  k  and  m d c*  Em  F9 H32 , then the benchmarking mechanism allows the manufacturer to gain more profit though with lower carbon quotas. It is effective for the government to adopt the benchmarking mechanism to the manufacturer who has a lower emission reduction cost, and set the emission cap which falls in the range of  m d c*  Em . In this case, the benchmarking mechanism helps the government reduce the allocation of free quotas. Here, the upper bound for the constraint can be obtained from firms’ historical carbon emissions. Generally speaking, low-carbon-emission firms usually have a higher cost coefficient of emission reduction. The technological improvements are more and more difficult as the initial carbon emission reduces. Therefore, in order to maximize carbon quota utilization, it is effective to use grandfathering mechanism for the low-carbon-emission firms and set the emission cap in a suitable range showed above; and use benchmarking mechanism for the high-carbon-emission firms and set the benchmark  m d c*  Em . For the low-carbon-emission firms, the benchmarking mechanism allows them to sell more carbon quotas when they produce more products. That is because the unit carbon quota is usually at the average position in a particular industry. Thus, the grandfathering mechanism may be more effective. In addition, for the high-carbon-emission firms, the grandfathering mechanism allows them to reduce production so as to conform to the regulations. As a result, the benchmarking mechanism can more effectively compel the high-carbon-emission firms to reduce carbon emission through green innovation. 31

In reality, discriminated low-carbon policy exists. That is, the government adopts different policies to different industries. On the one hand, Shanghai adopts different carbon quota allocation methods for different sectors⑥. The benchmarking mechanism is applied in the electric power enterprises, thermal power enterprises and automobile glass production enterprises. For non-industrial sectors such as air transport, ports, airports, hotels and shopping malls, as well as some complex industrial sectors, the grandfathering mechanism is adopted. On the other hand, discriminated carbon tax is adopted by many countries. For example, Sweden imposes 50% of carbon tax on manufacturing enterprises while nothing on electricity industry. For specific industry, carbon abatement cost is determined by some endogenous factors such as technology, energy mix, energy price, energy efficiency, etc. Through simulation analysis, Wu et al. (2016) showed that the abatement costs of air transport and oil refinery & coking sectors would be relatively high, whereas iron & steel sector has a low mitigation cost. For iron & steel and chemicals sectors, it is easier to cut emissions through adoption of efficient technologies. As a result, its carbon abatement cost tends to be relatively low. Thus, based on reality and the findings in Corollary 1, we provide the recommendation that the government can adopt discriminated policies to different manufacturers according to their emission reduction cost and industrial characteristics. The adoption of discriminated low-carbon policy can improve the effectiveness of quota allocation. From the above analyses, we see that the total amount of carbon emissions in the supply chain is an important factor to measure the environmental performance. Denote that T  T b*  T c* , which represents the supply chain carbon emission increment/decrement between the grandfathering method and the benchmarking method. Furthermore, we have the following theorem. T b*  T c* if 0    min  L6 , 1 Theorem 6. (1) T   0 ; (2)  b* . c*  T

⑥

T

if max  0, L6     1

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Theorem 6 is provided to show the comparisons of total carbon emissions in the supply chain between Model b and Model c. Theorem 6(1) indicates that T decreases as  increases, where  represents the proportion that consumers ask for home-delivery service in the offline hypostatic store. When  is relatively small ( 0    min  L6 , 1 ), implying that the total carbon emissions of the supply chain under the grandfathering mechanism is relatively large. With the increase of  , the advantages of the benchmarking method weakens. When  falls in the range of max  0, L6     1 , the total carbon emissions of the supply chain under the benchmarking mechanism is relatively large. For the supply chain which has a lower  , the benchmarking mechanism is more beneficial. However, the adoption of the benchmarking mechanism in the supply chain that has a high  will result in high carbon emissions. From the perspective of reducing carbon emissions, the consumers who drive to the offline shop should give a thought to pick-up the cargo by themselves. Next, we compare the two allocation methods from the perspective of social welfare. The theorem below provides the conditions where the benchmarking allocation method would be more suitable for sustainable development. Theorem 7. When 0  Em  F9 H32 and 0    min  L6 , 1 , then  mb*   mc* ,  rb*   rc* , b*  c* . Theorem 7 derives the condition under which the benchmarking mechanism is superior to that of the grandfathering mechanism. If the emission cap is lower than a threshold F9 H 32 and  is relatively low, then the benchmarking mechanism allows both the manufacture and the retailer to earn more profit, more importantly, it contributes to a higher social welfare. In this case, both the economic and environmental performances can be achieved. With Theorem 1 and Theorem 2, such case will also increase the low-carbon level of the product, as well as improve the market coverage of low-carbon products, which is beneficial for sustainable development. 33

Conclusively, the benchmarking allocation method would be more suitable for sustainable development under certain conditions. Such circumstance can be obtained through the cooperation between the government and the supply chain members: as the policy-maker, the government is expected to set the rational unit carbon quota for the benchmarking mechanism, which satisfies Em  F9 H32 ; as the cap-and-trade regulation covered enterprises, the manufacture should reduce his carbon emissions according to the regulation; as the leader in the supply chain, in order to maximize the profit while giving due consideration to social welfare, the retailer should be responsible for encouraging the consumers to pick-up the cargo by themselves in his offline shop. In fact, compared with the benchmarking mechanism, the grandfathering mechanism is more widely adopted now. But more and more academics and practitioners are advising the government to use the benchmarking mechanism. Liao et al. (2016) stated that the grandfathering mechanism is acceptable at the beginning of the experimental state and the government should adopt benchmarking mechanism as soon as possible to promote carbon trading. In terms of the pilot carbon emission trading system in China, some practitioners declared that the benchmarking mechanism is worth considering in the unified carbon emissions trading market mechanism⑦. That is because the benchmarks are based on the advanced industrial emission level, which can help eliminate some backward production capacity and achieve industrial upgrading. The results of this paper are consistent with the above ideas. The government should establish rational benchmarks for the purpose of improving the low-carbon level of the products and achieving the sustainable development of our society.

6. Numerical analysis In this section, we analyze the above three models with numerical analysis. Since it is hard to obtain ⑦

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34

the data from the enterprises, we turn to design the parameters to verify our results. The parameter values used in this section are as follows:   0.45 , a  80 , m  40 , pe  1 ,   1 ,   0.1 , c  8 ,  =1.2 , Em  12 , eo  0.8 , et  1.2 ,   0.12 ,   0.5 , er  0.3 .

6.1. Impact of em on the total carbon emissions and the social welfare

This subsection considers the impact of manufacturer’s initial carbon emissions on the supply chain’s carbon emissions and the social welfare. In this subsection we suppose that k  50 .

Fig. 1 is about here Fig.1. The total carbon emissions as function of em .

Fig.1 depicts the curves of the optimal total amount of carbon emissions in different model with respect to em . Obviously, with the increasing of em , the carbon emissions increases linearly in Model a. However, under the cap-and-trade regulation, the curves increase first and then decrease. When the initial carbon emission from production process is higher than a threshold, the cap-and-trade regulation has advantages in curbing carbon emission of the supply chain. The figure also shows that when the initial carbon emission from production process is relatively low, the total supply chain carbon emissions in benchmarking mechanism are larger than that in grandfathering mechanism. However, as the initial carbon emission increases, the total emissions in grandfathering mechanism will be larger than that in benchmarking mechanism. It indicates that the grandfathering mechanism is beneficial to control the total supply chain emissions, where the supply chain contains low-carbon-emission firms. That is because the unit carbon quota is usually at the average position in a particular industry. For the low-carbon-emission firms, the benchmarking mechanism allows them to sell more carbon quotas when 35

they produce more products. Therefore, the grandfathering mechanism will be more effective. On the contrary, adopting benchmarking mechanism to restrict high-carbon-emission firms is more effective. The conclusion is reasonable because the benchmarking mechanism forces the high-carbon-emission firms to reduce unit carbon emissions through technical improvement.

Fig. 2 is about here Fig.2. The social welfare as function of em .

Fig.2 demonstrates the optimal social welfare in different model under different level of em . It is clear that in the case without cap-and-trade regulation, the social welfare decreases as em increases. By contrast, under the cap-and-trade regulation, the curves decrease first and then increase. It indicates that the cap-and-trade regulation contributes more social welfare when it covers the high-carbon-emission firms. The higher carbon emission level the manufacturer has, the more necessary to adopt cap-and-trade regulation. At the present stage, some high-emission industries are included in the cap-and-trade regulation in our country, which is beneficial to the improvement of the social welfare. 6.2. Impact of k and  m on the total carbon emissions and the social welfare

As is discussed above, the value of the manufacturer’s emission reduction cost coefficient and the unit carbon quota play crucial roles for the supply chain. Thus this subsection we highlight the impact of manufacturer’s emission reduction cost coefficient k and the unit carbon quota  m on the supply chain members’ decisions, profit and social welfare. In this subsection we suppose that em  0.6 .

Fig. 3 is about here Fig.3 The manufacturer’s emission reduction rate as function of k .

36

Fig. 4(1) is about here (1) k  60

Fig. 4(2) is about here (2) k  250 Fig.4 The manufacturer’s emission reduction rate under different levels of  m .

Fig.3 exhibits the impact of the emission reduction cost coefficient on the manufacturer’s emission reduction behavior. The manufacturer’s emission reduction rate decreases in k , which is due to the high abatement cost. It can be seen that the values of the emission reduction rate without low-carbon regulation are the lowest. Fig.4 is given to illustrate the impact of the unit carbon quota  m in the interval [0,1] on the manufacturer’s emission reduction rate. Fig.4(1) shows the situation when the manufacturer has a relatively low emission reduction cost ( k  60 ). We can observe that with the increase of the unit carbon quota, the manufacturer’s emission reduction rate in Model c also increases. A low unit carbon quota fits well with situation where the government imposes a tight control on firm’s carbon emissions under the benchmarking mechanism. On the other hand, a large unit carbon quota might hold for the situation where the government relaxes the cap-and-trade regulation based on the benchmarking mechanism. As the unit carbon quota increases, the carbon control regulation becomes looser. It seems that the manufacturer does not need to reduce so much emission. However, our result shows that the manufacturer will still improve his emission reduction rate. This conclusion seems different from our common sense, but it is reasonable because the existence of carbon trading market changes firms’ cost constitution and profit pattern. The loose control provides the manufacturer with important opportunity to sell more carbon quotas. The profit increment coming from the excessive carbon quotas surpasses the increase of emission reduction cost, which motivates the manufacturer to increase his emission reduction 37

rate. To further validate our conclusions, we provides another situation when the manufacturer has a relatively high emission reduction cost ( k  250 ), which is shown in Fig.4(2). In this case, the relationship between the emission reduction rate and the unit carbon quota is still valid. As is shown in Fig.4, the increase of  m will enlarge the difference between  b* and  c* . With Lemma 3 we can know that the manufacturer’s emission reduction rate in Model c depends on the value of  m . When  m  0 , we can get  b*   c* . Incorporating Fig.3 and Fig.4, we can conclude that the values of the emission reduction rate under benchmarking mechanism are slightly higher than those under grandfathering mechanism. Consequently, the cap-and-trade regulation can effectively push the manufacturer to increase his emission reduction rate. In addition, the benchmarking mechanism is superior to the grandfathering mechanism. These observations are consistent with the results in Theorem 1.

Fig. 5 is about here Fig.5 The retailer’s promotion degree as function of k .

Fig. 6 is about here Fig.6 The supply chain’s demand as function of k .

Fig.5 and Fig.6 illustrate the impact of the cost coefficient of manufacturer’s emission reduction k on the retailer’s promotion degree and the supply chain’s demand. As is shown, it can be seen that both the retailer’s promotion degree and the supply chain’s demand decrease in k . In addition, the variation trend of the total demand in the supply chain is consistent with that of the retailer’s promotion degree. With Lemma 2 and Lemma 3 we can easily know that when  m  0 , then sb*  s c* and d b*  d c* . Thus, according to Fig.5 and Fig.6, we can conclude that sb*  sc* and d b*  d c* , which illustrates that the 38

benchmarking mechanism can more effectively push the retailer to promote low-carbon products and motivate consumers to buy low-carbon products. Comparing Model a with Model b, we can see that when k  97.69 , then s a*  sb* and d a*  d b* ; otherwise, s a*  sb* and d a*  d b* hold. When  m is relatively high (  m  0.8  em ), the values of the promotion degree under benchmarking mechanism are the highest among the above presented models. With Fig.4, a higher unit carbon quota results in a higher emission reduction rate, which allows the products to be greener. Consequently, a loose carbon policy is beneficial to increase the market share of low-carbon products. However, too much carbon quotas can’t help realize the environmental goal. Therefore, the carbon quotas should be controlled into a rational range. On the contrary, when  m is relatively low (  m  0.3  em ), the values of the promotion degree under benchmarking mechanism are the highest among the above presented models only when k  193.93 . In this case, if k  193.93 , the implementation of cap-and-trade regulation will lower the

retailer’s low-carbon promotion degree. Therefore, the government should guide retailers to cooperate with the manufacturer who has lower emission reduction cost. These observations are consistent with the results in Theorem 2.

Fig. 7 is about here Fig.7 The manufacturer’s profit as function of k .

Fig.7 depicts the curves of the optimal profit of the manufacturer in different model with respect to k . Naturally, the increase of the emission reduction cost will shrink the manufacturer’s profit. It can be

observed that the cap-and-trade regulation based on grandfathering mechanism can help the manufacturer expand his profit. From the analysis in Section 4.2 we can know that the manufacturer’s profit in Model b depends on the value of Em . The increasing of the total carbon quotas results in the rising of the 39

manufacturer’s profit. Here, we analyze the above models with numerical analysis under specific values, where k  150 and  m  0.8 . Plugging the values of the parameters into Model b, we have d b*  16.09 , and  mb*  138.62 . In Model c, we have d c*  16.50 and  mc*  133.15 . In this case, the total amount of carbon quotas in Model c is  m d c*  13.2  Em . It indicates that the grandfathering mechanism allows the manufacturer to gain more profit with lower carbon quotas. Compare Model a with Model b, we can see that when  m is relatively high (  m  em ), the values of the manufacturer’s profit under Model c are higher than those in Model a. On the other hand, when  m is relatively low (  m  0.3  em ) and k is relatively high ( k  98.39 ), the values of the manufacturer’s

profit under Model a will be higher than those in Model c. The results state that a tight low-carbon regulation will be detrimental to the manufacturer who has a high emission reduction cost. Meanwhile, the manufacturer who has a low emission reduction cost will benefit from the implementation of cap-and-trade regulation. Fig.8 exhibits the impact of the cost coefficient of manufacturer’s emission reduction k on the retailer’s profit. Obviously, compared with the grandfathering mechanism, the benchmarking mechanism allows the retailer to gain more profit. Incorporating Fig.5, Fig.6 and Fig.8, we can conclude that the increasing of profit coming from the demand expansion surpasses the increase of the low-carbon promotion cost, which makes the profit of the retailer rise up. In the following we focus on the situation when  m  0.3 . As is shown in Fig.8, when k  98.14 , then  ra*   rc*   rb* . It indicates that the retailer should cooperate with the manufacturer who has a low emission reduction cost so as to reduce the detrimental effect coming from the cap-and-trade policy. In particular, under the grandfathering mechanism, the cooperation situation will be more demanding. From Fig.8 we can also see that a loose cap-and-trade regulation based on benchmarking mechanism is profitable for the retailer. Conclusively, 40

the retailer will prefer the benchmarking mechanism while the manufacturer will prefer the grandfathering mechanism.

Fig. 8 is about here Fig.8 The retailer’s profit as function of k .

Fig. 9 is about here Fig.9 The total amount of carbon emissions in the supply chain as function of k .

Fig.9 depicts the curves of the optimal total amount of carbon emissions in different model with respect to k . It can be observed that the total carbon emissions increase in k and  m . If the manufacturer has a higher emission cost, he will choose to buy carbon quotas through the carbon trading market rather than implement low-carbon innovation. As a result, the total carbon emissions will be higher. We can see that without cap-and-trade regulation, the total amount of carbon emissions are the highest among the three cases when k  222.18 . But the gap between the case with cap-and-trade regulation and the case without cap-and-trade regulation narrows as k increases. It implies that the effectiveness of the cap-and-trade regulation weakens for the firm who has a high emission reduction cost. It is interesting that with the increase of  m , the total amount of carbon emissions in Model c will be higher. In particular, when  m  0.8 and k  222.18 , T c* will be the highest. With Fig.4 we can know that  c* increases as the increase of  m . In other words, the unit carbon emissions of the product decrease. Thus, the increase of total carbon emissions in the supply chain comes from the demand expansion.

Fig. 10 is about here Fig.10 The total welfare as function of k . 41

Fig.10 depicts the curves of the optimal social welfare in different model with respect to k . It can be seen that the social welfare decreases in k while increases in  m . What is working for the social welfare is the carbon emission reduction cost, demand increase and the carbon quotas. A higher k results in a lower social welfare. We can see that the change trend of the social welfare with k under the grandfathering mechanism is similar to that under the benchmarking mechanism. Whether the social welfare under benchmarking mechanism is higher than that under grandfathering mechanism depends on the relationship between Em and  m . For the manufacturer who has a lower emission reduction cost, the adoption of cap-and-trade regulation can more effectively improve social welfare. It can also be observed that the increasing unit carbon quota  m remains beneficial for the social welfare. Though a loose carbon policy results in higher carbon emissions in the supply chain, it brings higher social welfare. Under such circumstance, more consumers will be attracted to buy low-carbon products, which is beneficial to the sustainable development of our society.

7. Conclusions Under the low-carbon environment, this paper examines an O2O retail supply chain consisting of one manufacturer and one retailer with the cap-and-trade regulation. A giant retailer who has access to both online and offline shops and adopt consistent pricing strategy is considered. In our model, the manufacturer’s low-carbon innovation and the retailer’s low-carbon promotion are both taken into account. Further, the consumers are assumed to be of environmental consciousness. Three decision models are constructed and analyzed: without cap-and-trade regulation, cap-and-trade regulation based on grandfathering mechanism, and cap-and-trade regulation based on benchmarking mechanism. The main findings of this paper are summarized as follows. (1) It is found that consumers’ preference for low-carbon products can push both the manufacturer and the retailer to increase 42

low-carbon investment. Furthermore, the results imply that consumers’ low-carbon preference is profitable for the supply chain. Thus, it is necessary for the government and the supply chain members to build low-carbon environment and make more citizens care about the low-carbon level of the products. (2) By analyzing both the grandfathering mechanism and the benchmarking methodology, this work discovers that though a strict cap can influence the decisions of supply chain members, it cannot reflect in the decisions directly. Compared with the grandfathering mechanism, the benchmarking mechanism can more effectively push the manufacturers, especially the high-emissions ones, to produce low-carbon products and take actions to curb emissions. Simultaneously, the benchmarking mechanism can also motivate the retailer to promote low-carbon products. In other words, the benchmarking mechanism can more effectively push the supply chain members to turn to greener production and operation patterns. Thus, the cap-and-trade regulation with benchmarking mechanism is beneficial to improve the market coverage of low-carbon products. (3) From the social welfare perspective, it is more effective for the government to use grandfathering mechanism for low-carbon-emission firms and use benchmarking mechanism for high-carbon-emission firms. Furthermore, under certain circumstances, the benchmarking allocation method would be more suitable for sustainable development. The government is expected to establish the benchmarks in a certain interval and the retailer should encourage consumers to pick-up the cargo by themselves in the offline shop. The cooperation between the government and the supply chain members can help attain the economic and environmental goals. (4) Numerical analysis indicates that the cap-and-trade regulation contributes more social welfare when it covers the high-carbon-emission firms. In addition, the effectiveness of the cap-and-trade regulation weakens for the firm who has a high emission reduction cost. Furthermore, a loose carbon policy results in higher carbon emissions in the supply chain while brings higher social welfare. 43

This research can be extended in several directions in future work. First, we in this work consider a retailer-dominated O2O supply chain. We can further discuss a manufacturer-dominated O2O supply chain. Second, we suppose that the total carbon emissions are linear in production quantity. In practice, the calculation of carbon emissions is more complicated. Therefore, some other description should be considered in the future. Third, our research focuses on the operational decisions under symmetric information. In reality, the consciousness of carbon disclosure among enterprises is weak. Thus the carbon emission information may be asymmetric among enterprises. Therefore, an interesting extension is to consider the dual-channel supply chain under asymmetric carbon information.

Acknowledgments This work is partially supported by the National Natural Science Foundation of China (No. 71572058, 71101054), National Social Science Foundation (12BGL052) and the Fundamental Research Funds for the Central Universities, SCUT (No.2015ZZ057).

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Appendices A.1. Proof of Lemma 1 In order to obtain the Stackelberg equilibrium, the best response of the follower and in the second stage should be determined at first. The leader’s decision problem is solved based on the follower’s response. With Equation (5) we can get

 2 ma  2 ma  2 ma  2 ma , ,   4  0   2   k . Let H be a w w w2  2

Hessian of  ma ,  4 H  ma     2

2  .  k 

H is a negative definite because H11  0 , and det  H   4  k   2   0 . Hence,  ma is jointly

concave on the decision variables. Thus, there exists optimal solution of Equation (5). From the first-order conditions, the best response of manufacturer to retailer’s marginal profit and low-carbon promotion degree are given by 



2k  2 

 a  1    s  2    c  , w 

k  a  2   2c    sk 1     4 2 c 4k  2 

.

As the supply chain information is symmetric, together with Eq. (6), we can get  2 ra  2 ra  k 1    ,   s s 2  k   2 

8km  k   2    k 1    

 2 ra  m . s 2

 ra

Hence,

 2 ra 2k  0,  2 k  2

is jointly concave on  and s

2

4k  2 

 0 . Let  r   0 and  r s  0 , then we get  a* , s a* , wa* and  a* .

A.2. Proofs of Lemma 2 and Lemma 3 The proofs are similar to that of Lemma 1, thus, we omit them. A.3. Proof of Theorem 1   a*

b*

when

 



2 2 pe em m 8m  k   2   k 2 1      a  2  pe em    c   8 m  a  2c  2  pe em     0. 2 2 2 2 8m  k     k  1    8m k     pe em    k  1      





Combined with Lemma 2 and Lemma 3, we can know that    . Conclusively, we can get  a*   b*   c* . b*

c*

A.4. Proof of Theorem 2 Combined with Lemma 2 and Lemma 3, we can easily know that sb*  sc* . 49

With H1  8m  k   2   k  1     0 , we can get k 

8m 2

2

s s  a*

b*



8m   1    

 L1 .

2

,

2 pe em k 1    8m  k   2   k  1      4m  a  2c  2  pe em  2

8m  k     k  1    8m k    p e    k  1     2

2

2

2

e m

Thus when k 

s a*  s c* 

8m 2  4m  a  2c  2  pe em  8m   1   

2

 L2 , s a*  sb* ; otherwise, s a*  sb* .



2

,

If

em   m ,

2 pe k 1    8m  em   m   k   2   k  em   m   1      4mem  a  2c  2  pe em  2

8m  k     k  1    8m k    p e    k  1     2

2

2

e m

We k

can

conclude

that:

(1)

If

8m 2  em   m   4mem  a  2c  2  pe em 

 em   m  8m   1   

It

is

easily

2



to

em   m ,

then

s a*  s c* ;

(2)

when

 L3 , then s a*  s c* ; when k  L3 , then s a*  s c* .

prove

L1  L2

that

.

In

addition,

2 L2 8m  em   m   4m  a  2c  2  pe em  em   m    1 , therefore, L2  L3 . Thus, L1  L2  L3 . L3 8m 2  em   m   4mem  a  2c  2  pe em 

Conclusively, (1) em   m  0 .

When k  L2 , sb*  s a*  sc* ; when L1  k  L2 , s a*  sb*  sc* . (2) em   m  0 . When k  L3 , sb*  sc*  s a* ; when L2  k  L3 , sb*  s a*  sc* ; when L1  k  L2 , s a*  sb*  sc* . The comparison of the total demands d i* in the supply chain is similar to that of the low-carbon promotion degree s i* above, thus, we omit it. A.5. Proof of Theorem 4 Combined with Lemma 2 and Lemma 3, we can easily know that  rb*   rc* .   a* r

b* r



 8m  k     k  1    8m k    p e    k  1    

,

2 2 2mkpe em  a   pe em  2c  8m  k   2   k 2 1      2m  a  2c   2  pe em    2

2

2

2

e m

2 L2 4m  a  2c  2  pe em  a   pe em  2c   8m a   pe em  2c    1 , thus L2  L4 . 2 L4 2m  a  2c   2  pe em   8m 2 a   pe em  2c  

8m 2  a   pe em  2c  L1   1 , thus L1  L4 . L1  L4  L2  L3 . L4 2m  a  2c 2  2  pe em   8m 2 a   pe em  2c 

50

2m  a  2c   2  pe em   8m 2 a   pe em  2c   2

k

When

   a* r

c* r

2mkpe

2  a   pe em  2c   8m   2 1      

e

m

 L4 ,

 ra*   rb* ; otherwise,  ra*   rb* .



2 2   m   a   pe em  pe m  2c   8m  k   2   k 2 1      2mem  a  2c   2  pe em    . 2 2 2 8m  k   2   k  1    8m  k     pe em    k  1     







If em   m  0 , then  ra*   rc* . 2mem  a  2c   2  pe em   8m 2  em   m  a   pe em  pe m  2c   2

em   m  0 , when

If

k

 em   m  a   pe em  pe m  2c  8m   2 1   

2

 

 L5 ,

 ra*   rc* ; otherwise,  ra*   rc* . We can prove that L3 L5  1 and L4 L5  1 , thus L4  L5  L3 .

Conclusively, (1) If em   m  0 .

When k  L4 ,  rb*   ra*   rc* ; when L1  k  L4 ,  ra*   rb*   rc* . (2) If em   m  0 . When k  L5 ,  rb*   rc*   ra* ; when L4  k  L5 ,  rb*   ra*   rc* ; when L1  k  L4 ,  ra*   rb*   rc* . A.6. Proof of Theorem 5 8m2 kpe m  k     pe em    a  2  pe em  c   pe m     Em pe  , 2 2 2 8m  k     pe em    k  1       2

  b* m

c* m





8m2 k m  k     pe em    a  2  pe em  c   pe m  F    92 ,  mb*   mc* . Then we can get when Em  2 2 2 H3 8m  k     pe em    k  1       2





A.7. Proof of Corollary 1 The total carbon quotas in Model c is  m d c* 



2mk m  a  2  pe em  pe m  c   2 2 8m  k     pe em    k  1      





,

2 2 2 2  a  2  peem  c  4m k     peem    k  1      2 pe m 6m k     peem    k  1     F9     c*   m d  2mk m 2 2 2 H 32 8m  k     peem    k  1      

When









,

then





,

k  k

, then

2 2 2 2 a  2  peem  c  4m k     peem    k  1     2 pe m 6m k     peem    k  1     0    

4m    peem  a  2  peem  c   3 pe m  k  k 2 2 2 2      a  2  peem  c  4m   1      2 pe m 6m   1     2

F9   m d c* . 2 H3

51

F9   m d c* ; 2 H3

when

, i.e.,

(1) If k  k  , we can conclude that: when Em   m d c* , then  mb*   mc* ; when  mb*   mc* ; when Em 

F9  Em   m d c* , then 2 H3

F9 , then  mb*   mc* ; H 32

(2) If k  k  , we can conclude that: when Em 

F9 F , then  mb*   mc* ; when  m d c*  Em  92 , then H3 H 32

 mb*   mc* ; when Em   m d c* , then  mb*   mc* ;

Thus we can obtain Corollary 1. A.8. Proof of Theorem 6 With T b*  F5 H3  F6 H32 and T c*  F7 H3  F8 H32 , we can get T  T b*  T c* 

F5 F7 F F F  F7 F6  F8   6  8  5  . H 3 H 3 H 32 H 32 H3 H 32

From the first-order condition, we can get

kpe m eo  2m   2 1   2   T   0 . Let T  0 , 2 2  8m  k     pe em    k  1      

then we can get 

16em m2    pe em   a  2  pe em  c   pe m   H 3  2m  2em  eo  er  et    2 1   2   eo  er  et   H 3eo  2m   2 1   2 

Note that 0    1 , we can conclude that (1) If L6  0 , then T  0 ; (2) If 0  L6  1 , then when 0    L6 , T  0 ; when L6    1 , T  0 ; (3) If L6  1 , then T  0 . Conclusively, When 0    min  L6 , 1 , then T b*  T c* ; When max  0, L6     1 , then T b*  T c* .

A.9. Threshold values H1  8m  k   2   k  1    , H 2  2m  a  2c  , 2

2 2 H 3  8m k     pe em    k  1    , H 4  2m a  2  pe em  c     pe em  ,  

H5  2m 3k  2    pe em  2  pe em   k  1    , 2

H 6  2m a  2  pe em  pe m  c     pe em  . F1  ma 4 2 1  2   k 8  3  k 2 1     a   a 1     1    c  , F2  2mak  em  er   eo  et   2cmk 2em  eo 1     er  et   1    eo  er  et  F1 ,

F3  4em m2  k  a  2c  , 2

52

 L6 .

2 F4  ma 4 1  2    pe em   k 8  3  k 2 1     a   a 1     1    pe em  c  .  

F5  2mak  em  er   eo  et   2mk  pe em  c  2em  er  1    eo  et   1    eo  er  et  F4 , F6  4em m2 k a  2  pe em  c     pe em  , 2





F7  F5  kpe m 2m 2em  eo 1     er  et    2 1   2  eo 1     er  et  , F8  4em m2 k a  2  pe em  pe m  c     pe em  , 2

2 F9  8m2 k m k     pe em   a  2  pe em  c   pe m  .  

L1 

L3 

8m 2 8m   1    

2

, L2 

8m 2  4m  a  2c  2  pe em  8m   1    

8m 2  em   m   4mem  a  2c  2  pe em 

 em   m  8m   1   

2



2

,

2m  a  2c   2  pe em   8m 2  a   pe em  2c   2

, L4 

2  a   pe em  2c  8m   2 1      

2mem  a  2c   2  pe em   8m 2  em   m  a   pe em  pe m  2c   2

L5 

L6 

 em   m  a   pe em  pe m  2c  8m   2 1   

 

,

16em m2    pe em   a  2  pe em  c   pe m   H 3  2m  2em  eo  er  et    2 1   2   eo  er  et   H 3eo  2m   2 1   2  

4m    peem  a  2  peem  c   3 pe m  2 2  a  2  peem  c  4m   2 1      2 pe m 6m   2 1         2

k 

2

53

.

,

,

Fig.1. The total carbon emissions as function of em .

Fig.2. The social welfare as function of em .

Fig.3 The manufacturer’s emission reduction rate as function of k .

(1) k  60 .

(2) k  250 . Fig.4 The manufacturer’s emission reduction rate under different levels of  m .

Fig.5 The retailer’s promotion degree as function of k .

Fig.6 The supply chain’s demand as function of k .

Fig.7 The manufacturer’s profit as function of k .

Fig.8 The retailer’s profit as function of k .

Fig.9 The total amount of carbon emissions in the supply chain as function of k .

Fig.10 The total welfare as function of k .