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Since the tax of carbon emission is popular and consumers are exhibiting low-carbon preference, the green manufactures have to spend more extra cost on investing carbon emission reduction (CER) technology to decrease the carbon emission. To encourage the manufacture’s CER investment efforts, this paper explores the impact of carbon tax, CER cost, and consumers’ low-carbon preference on low-carbon decision-making and designs a revenue-sharing contract (RS) by constructing Stackelberg models. Based on the theoretical and numerical analysis, this paper finds that the supply chain would benefit from the increment of consumer’s environmental awareness but be depressed by the increase of the CER investment cost factor. Additionally, there exists a unique optimal carbon tax to make CER degree the maximum. Furthermore, RS can effectively promote manufacturers to reduce carbon emissions and also improve the supply chain efficiency.

With the rapid development of the economy, global carbon dioxide emission has sharply increased in the past few decades, which significantly resulted in serious climate and global warming [

The extant findings have shown that coordination contracts or carbon tax as the mechanism are used to compensate and counterbalance the CER cost, resulting in motiving the manufacture to employ CER investments [

To answer the above questions, this paper considers a low-carbon supply chain, where the manufacturer makes CER investment to produce low-carbon products and sell them through a single retailer. In modeling and analysis, this paper finds the equilibrium strategies of the supply chain under centralized and decentralized decision-making and discusses the impacts of low-carbon awareness, CER cost factor, and carbon tax on the supply chain in detail. Furthermore, a revenue-sharing contract (RS) is adopted to stimulate the manufacturer to improve CER degree and coordinate the supply chain. The results indicate that the supply chain is better off exhibiting low-carbon preference and will suffer a loss from the increase CER cost factor when the carbon tax is low. Moreover, the paper finds that there exists a unique optimal carbon tax to make CER degree the maximum. And RS can encourage the manufacturer’s CER investments but fails to coordinate the supply chain, and the manufacturer and the retailer prefer to implement RS when the RS coefficient is in a certain threshold. This research makes three contributions to the literature. First, this paper integrates consumers’ low-carbon awareness, CER cost factor, and carbon tax into supply chain models and explores how these factors affect the CER degree and firms’ profit. Second, this paper finds that the government should impose different optimal carbon taxes to inspire the manufacturer to make the best efforts on CER investments in different scenarios. Finally, this paper designs RS to incentive the manufacture to improve CER degree and also enhance the supply chain efficiency.

The remainder of this paper is organized as follows. Section

With the transition to the sustainable supply chain, there is a growing interest in the decision-making problems and the design of coordination/incentive contracts. Research on low-carbon supply chain decisions mainly focuses on price [

Authors’ contribution.

Authors | CER cost | Carbon tax | Consumers’ low-carbon preference | Coordination/incentive contract |
---|---|---|---|---|

Mishra et al. [ | ✓ | |||

Chen and Hu [ | ✓ | |||

Wang et al. [ | ✓ | |||

Yang and Chen [ | ✓ | ✓ | ✓ | |

Li et al. [ | ✓ | ✓ | ✓ | |

This paper | ✓ | ✓ | ✓ | ✓ |

Environmental issues are new hotspots in supply chain research. Currently, low-carbon decision-making of the supply chain is mainly studied from three factors: low-carbon preference, CER cost factor, and carbon tax.

In the view of carbon tax, Mishra et al. [

Li et al. [

Based on the extant literature studies, many authors analyzed the impact of various factors on the low-carbon operation decision-making of enterprises. However, the aforementioned research studies have incomprehensively considered the impact of CER cost factor, carbon tax, and consumers’ low-carbon awareness on the low-carbon decisions and RS. Our paper aims to fill the gap by introducing CER cost factor, consumers’ low-carbon preference, and carbon tax into the analytical framework. Thus, the incentive effect of carbon tax and RS can be studied more accurately and realistically. The conclusion will help the firms make decisions and design incentive contract in a low-carbon supply chain, as well as provide insights for the government to formulate the optimal carbon tax policy.

This paper focuses on a low-carbon supply chain comprising one manufacturer and one retailer where consumers are exhibiting low-carbon preference. The manufacturer produces low-carbon products and sells them to the retailer in the wholesale price. The manufacturer is dominant in the supply chain, who decides the CER degree and the wholesale price. The retailer decides the retail price and sells to consumers. The government imposes carbon tax on carbon emission. Due to the need of the research problem, the following variables and parameters are defined in Table

Notation and parameters.

Notation | Interpretation |
---|---|

Decision variables | |

Wholesale price | |

Retail price | |

Carbon emission reduction degree | |

Parameters | |

The carbon emission of unit low-carbon product after the manufacturer’s CER efforts | |

The initial carbon emission of unit traditional product | |

Market demand | |

The base market potential | |

Consumers’ low-carbon preference coefficient | |

A carbon tax for each unit emission | |

CER cost factor | |

CER cost | |

Unit manufacturing cost | |

RS coefficient/share of retailer’s revenue with the manufacturer, | |

The whole supply chain profit | |

The manufacturer’s profit | |

The retailer’s profit | |

The supply chain efficiency |

For the purposes of discussion and without loss of generality, this paper makes the following basic assumptions.

It is assumed the demand function is linearly decreasing in selling price and increasing in CER degree [

The manufacturer takes extra cost to invest CER technologies. It is common knowledge that the manufacturer makes initial changes in products and processes easily while the subsequent improvement being more difficult [

The manufacturer must pay the carbon tax for carbon emission in the production process. Every unit carbon emission should pay

In order to ensure all decision variables and profits are positive, we assume

Using the aforementioned notations and assumptions, this paper models the profits of the manufacturer, the retailer, and the total supply chain as follows. The manufacturer’s profit

As a benchmark, the manufacturer and the retailer jointly determine the CER degree

In a centralized supply chain, the optimal CER degree is

See Appendix.

In a centralized supply chain,

If

See Appendix.

Lemma

Lemma

In a decentralized supply chain, the relationship between the manufacturer and the retailer is modeled as a Stackelberg game, where the manufacturer is the leader and the retailer is the follower. In the first stage, the manufacturer decides the CER degree

In the decentralized supply chain, the optimal retail price is

See Appendix.

In the decentralized supply chain,

If

See Appendix.

Lemma

Lemma

According to the calculation and analysis in the above section, we compare the equilibrium outcomes in the centralized and the decentralized supply chain, which are shown in Theorem

If

See Appendix.

Theorem

In this section, we propose the RS contract in which the manufacturer offers the retailer a lower wholesale price, and the retailer shares revenue with the manufacturer with a fraction

The timeline is as follows. Firstly, the manufacturer makes CER efforts to reduce the emission of the products, which yields the CER degree

Under the RS contract, the optimal CER degree is

The proof is similar to that of Proposition

Under RS,

If

Lemma

Lemma

The proof is similar to that of Lemma

Under the RS contract,

See Appendix.

Theorem

From the aforementioned explanations, we are unable to obtain closed-form conditions for profit comparison considering various factors. So, we conduct a set of numerical experiments to study the factors how various factors, such as the CER cost factor

Effect of

Effect of

Effect of

Effect of

Effect of

Impact of RS on the supply chain efficiency.

Now, we explore how the CER cost factor

Figure

Now, we explore how the carbon tax

Now, we explore how the customers’ low-carbon preference

Figure

Now, we explore how RS affects the supply chain efficiency

Figure

This paper demonstrates some key and deliberate insights for managers and policy makers who need to consider the manufacturer’s CER cost factor, the government’s carbon tax, and consumers’ low-carbon preference. The managerial implication for managers and policy makers can be obtained as follows:

With the decrease in the CER cost factor, the CER degree and the supply chain members’ profits will increase. Therefore, the manufacturer should improve the CER degree with the decrease in the CER cost factor. Moreover, the manufacturer should set the highest CER degree in the centralized, medium under RS, and the lowest in the decentralized supply chain.

As consumers’ low-carbon preference increases, the retail price and the supply chain members’ profits increase significantly. Therefore, the retailer should improve the retail price with the increase in the consumers’ low-carbon preference. Moreover, the retailer should set the highest selling price in the decentralized, medium under RS, and the lowest in the centralized supply chain when

Carbon tax has a certain incentive effect on the manufacturer’s CER degree. The government should impose different carbon taxes in different scenarios, i.e., the highest carbon tax in the centralized supply chain, medium under RS, and the lowest in the decentralized supply chain. Based on the optimal carbon tax imposed by the government, the incentive mechanism can stimulate the manufacturer to increase their efforts towards CER investment for environmental and economic benefits.

RS cannot perfectly coordinate the supply chain but can improve the supply chain efficiency and encourage the manufacturer to increase CER investment.

In this study, some factors are taken into consideration such as the manufacturer’s CER cost factor, the government’s carbon tax, and consumers’ low-carbon preference to establish profit models of the low-carbon supply chain. Stackelberg game models are developed to address the centralized, decentralized, and RS scenarios between the manufacturer and the retailer. The models determine the optimal CER degree and price decisions, as well as the carbon tax imposed by the government. This paper finds that the supply chain would benefit from the increment of consumer’s environmental awareness but be depressed by the increase of CER cost. Additionally, there exists a unique optimal carbon tax to improve CER degree in different scenarios. Furthermore, this paper finds that RS is effective to inspire the manufacture to exert the best efforts to improve CER degree. Moreover, RS is a feasible incentive tool to the manufacturer and retailer when the RS coefficient is in a certain threshold value.

There are some limitations on this paper. The assumption is that the manufacturer is in the dominant position in the supply chain. And this paper adopts simulated data to verify the proposed model. A case study utilizing real industrial data is not inserted in this model. So, retailer-dominant or/and power-balanced scenarios should be discussed in the future. And a case study utilizing real industrial data should be extended. These extensions will help us come to a better understanding on the low-carbon supply chain operation in the future [

The Hessian matrix of

Solving the first-order conditions

Substituting

Taking the first derivative of

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Similarly,

Taking the first derivative of

Taking the first derivative of

Similarly,

Taking the second derivative of

Taking the second derivative of

Substituting (A

According to equation (A

Taking the first derivative of

Taking the first derivative of

Taking the first derivative of

Taking the first derivative of

Taking the first derivative of

Taking the first derivative of

Taking the second derivative of

If

If

If

If

If

The underlying data supporting the results of this study can be found in the manuscript.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by Academic Discipline Project of Shanghai Dianji University (Project no.16Ysxk03), Special Program for Humanities and Social Science of Shanghai Dianji University, and the National Social Science Fund of China, “Research on the Practical Orientation of Green Consumption in the New Era” (Project no. 20BKS079).