Pricing decisions of green supply chain considering products’ green degree and sales efforts under government subsidy

Cao, Xiaogang; Liu, Jie; Huang, Kai

doi:10.1108/MSCRA-08-2024-0033

Purpose

For the green supply chain composed of a green product manufacturer and a green product retailer, this paper studies the equilibrium decisions under three scenarios: (1) the government provides green degree subsidy for the manufacturer; (2) the government subsidizes the R&D and innovation cost of the manufacturer; (3) the government subsidizes the sales effort cost of the retailer.

Design/methodology/approach

In view of the green preference awareness of end consumers, we analyze the changes of product green degree, green sales effort, product pricing decision, the manufacturer’s and the retailer’s profit and social welfare. The results show that government subsidies will encourage the manufacturer to produce greener products, while subsidizing the manufacturer are more effective than subsidizing the retailer; sales effort cost subsidies can directly motivate the retailer to pay more sales effort and thereby increase the green product sales.

Findings

With the same government subsidies, green R&D and innovation cost subsidies are more favorable for the retailer, and the subsidies for green degrees are more favorable for the manufacturer. No matter what kind of subsidy strategy, it can effectively improve the green degree of products, and compared with subsidizing the retailer, subsidizing the manufacturer can improve the green degree effect better.

Originality/value

Government subsidies can effectively improve social welfare, so the government can promote the improvement of social welfare through subsidy distribution. Under the same government subsidy expenditure, the social welfare under the subsidized the retailer is higher than subsidizing the manufacturer.

1. Introduction

With the increasing scarcity of global resources and increasingly severe environmental problems, sustainable development has been deeply embedded in today’s social and economic development philosophy. Since the manufacturing industry is one of the main sources of environmental pollution, in recent years, the manufacturing industry has incorporated efforts on sustainable development into the core value and mission of enterprises, and constantly tried to reduce the negative impact of manufacturing activities on the environment through technological innovation and strategy adjustment. Recycling and remanufacturing of waste products is one of the important measures. Remanufacturing refers to the process of processing and transforming waste and waste items, so that they have new use value and functions, and then reselling them to the market.

In this context, a green supply chain management model considering resource consumption and environmental impact has become the focus of academic and business circles. Under the dual drivers of frequent introduction of green environmental protection policies and consumers' increasing awareness of green protection, green products are increasingly favored by consumers. Manufacturing enterprises develop and produce green products, which can not only improve their environmental image, but also gain competitive advantages in the market. For example, Tesla, an electric vehicle manufacturer, utilizes a variety of green subsidy policies globally. In the U.S. market, Tesla consumers are eligible for federal government tax credits, a policy designed to encourage consumers to purchase electric vehicles and reduce their dependence on fossil fuels. Tesla models such as the Model S and Model X have received thousands of dollars in subsidies as a result. IKEA, the world’s leading furniture retailer, has adopted a green sales strategy through its line of “sustainable products”, such as furniture made from recycled materials. To encourage consumers to buy these products, IKEA offers price discounts and additional subsidies through its “recycling program”. IKEA’s green sales efforts not only enhanced the environmental image of its products, but also increased consumer demand for sustainable products through price concessions and subsidies. This strategy not only boosts IKEA’s sales, but also contributes to a broader societal awareness of environmental issues and influences consumer purchasing behavior in a more environmentally friendly direction.

With the continuous improvement of consumers’ environmental awareness, the concept of green consumption has been gradually established, and more consumers tend to buy products with higher green degree. The greening of the product refers to the friendliness of the product to human and nature, such as the content of harmful substances, energy consumption level, recyclability, etc., which has become an important factor affecting consumers’ purchase decisions. Product green degree is an important factor affecting the market demand, the improvement of the green degree is not only conducive to stimulating the demand of consumers, but also can reduce the waste of resources and environmental pollution, establish a good corporate image, and improve the competitiveness of enterprises; at the same time, the promotion of environmental awareness has changed consumers’ behavior. According to the report, 51% of American consumers are willing to pay more for high green products, namely environmental premium (environmental premium), 67% of consumers think the environmental performance is very important in the purchase process. In OECD countries, 27% of consumers are green consumers, who have a strong environmental awareness and are willing to pay for green products, so many companies respond to such market changes by improving the greening of their products.

Investments in advertising, sales personnel demonstrations, and other corporate sales efforts are significant factors influencing market demand. Sales efforts serve as a crucial mechanism for enhancing customer satisfaction and expanding market share, and they have been widely adopted by numerous retailers. Such efforts can boost product demand and capture market share. In many instances, retailers’ sales efforts can indeed influence demand, such as through strategic product placement, salesperson training, and increased advertising investments. The heightened demand generated by these sales efforts not only benefits retailers but also suppliers. For suppliers, a higher level of sales effort is generally preferable; however, if retailers shoulder the entire cost of these efforts, they might opt for a level that is most advantageous for themselves rather than the most optimal for the supply chain as a whole. In the context of a green supply chain, sales efforts essentially aim to promote green products, which are a key strategy within such supply chains. The perspectives and intensity of these sales efforts will vary. If the government were to provide a certain percentage of sales subsidies, it could alter both the supply chain strategy and the benefits accrued by each member. This intervention might lead to a more efficient and equitable distribution of costs and benefits across the supply chain.

In the green supply chain, manufacturers responsible for producing green products and retailers making green sales efforts are often faced with shortage of funds or technology; with the majority of small and medium-sized manufacturing enterprises in China, green production will increase production costs, including learning green technology and purchasing green equipment, thus reducing the enthusiasm of manufacturing enterprises to conduct green production. In order to cope with the development obstacles of green production and promote the benign development of green supply chain, the government’s financial subsidies are indispensable. To this end, the government will develop corresponding subsidy policies aimed at supporting the primary entities within the green supply chain—namely, manufacturers and retailers. These subsidies will focus on two key areas: funding manufacturers’ technological research and development of green products and the procurement of environmentally friendly components, as well as incentivizing retailers’ green sales efforts. For the government, it should formulate reasonable and effective financial subsidies to more effectively encourage manufacturers to develop and produce more green products and to encourage retailers to make more sales efforts to increase market demand. However, different leading modes of the supply chain, different subsidy objects and different modes of subsidy will all affect the optimal decision of the green supply chain. Analyzing the effect of these subsidy policies is an important research problem. This article aims to explore the following questions:

What are the impacts of different government subsidy strategies on the manufacturer’s wholesale price, the green degree of products, the retailer’s sales price and green sales effort level?
What are the impacts of the consumer sensitivity coefficient to the green degree and the sensitivity coefficient to the green sales efforts on the effect of government subsidies and the pricing decision of the supply chain?
How is the subsidy effect under different government subsidy strategies?

The major contributions of this paper:

This paper considers the impact of greenness and the retailer’s sales efforts on product demand in the green supply chain, studies the impact of greenness and sales efforts on the decision of supply chain members.
This paper considers the different subsidy objects and subsidy behaviors of the government, including the greenness and innovation cost subsidies for the manufacturer and the sales effort cost subsidy for the retailer, studies the influence of different subsidy objects and subsidy behaviors on the decision of supply chain members.
This paper makes a comprehensive comparative analysis of the optimal decision results of different subsidy objects and subsidy behaviors, explores the comprehensive selection of subsidy objects and subsidy strategies according to different subsidy objectives.

2. Literature review

2.1 Research on supply chain decision-making based on government subsidies

Cohen et al. (2016) consider external influences from the government and find that government subsidies directly provided to consumers can influence suppliers' production and pricing decisions. Li et al. (2018) consider the impact of government consumption subsidies for environmental products and alternative subsidies for environmentally friendly products on dual-channel supply chain decision-making. Wen et al. (2018) find that the change of government subsidy coefficient does not affect the greening of products and the ranking of manufacturers’ profits, but has an impact on the ranking of retailers’ profits. Sun et al. (2019) show that setting the government subsidy value within the relevant range can reduce the free hiking of suppliers or manufacturers in the market. He et al. (2019) find that the government can motivate manufacturers by setting appropriate levels of subsidies that would always benefit consumers and the entire supply chain, but not always benefit the environment. Liu et al. (2019a, b) believe that a certain range of government subsidies can promote the supply chain members to undertake the CSR, and improve the overall performance and social welfare of the supply chain. Jung and Feng (2020) study the government subsidies for the development of green technology in enterprises and the impact of subsidies on environmental and social welfare. Wu and Hu (2020) focus on the impact of the synergistic effect between external government subsidies and internal redundancy on green technology innovation. Yang et al. (2021) find that government subsidies can be used as an effective way to alleviate the prisoner’s dilemma, promoting technological progress by reducing the financial burden of enterprises, which is conducive to expanding the market for green products and improving social welfare. Yang et al. (2021) find that in the context of COVID-19, the government could obtain the maximum level of quarantine efforts and social welfare through cost-sharing subsidies to manufacturers. Kang et al. (2021) find that reasonable government subsidies can promote the effectiveness of market resource allocation, eliminate market failures, improve corporate social responsibility (CSR), increase the output of agricultural products, and increase the profits of farmers and core enterprises. Wang et al. (2021) examine the value of information sharing to GSC decisions in the context of government subsidies to consumers, and the two-part tariff contract is applicable to coordinate GSC, which is conducive to improving the green degree of products. In order to ease the financial pressure on manufacturers to recycle and remanufacturing, some governments implement production and recycling subsidies, while retailers provide revenue-sharing and cost-sharing contracts. Therefore, Zhang et al. (2021) mainly study the incentive design of governments and retailers and the impact of these incentives on the closed-loop supply chain. To address the supply chain emission reduction dilemma caused by the wholesale price constraint, Ren and Hu (2024) reveal the key role of the Nash bargaining and cooperation mechanism in coordinating the profit distribution and emission reduction incentives by constructing a competition and cooperation game model, and propose a dynamic optimization scheme of government subsidies to crack the interactive effects of policy and market constraints.

Song and Wang (2022) find that government subsidies have a positive impact on the progress of green technology in the supply chain, but the incomplete use of government subsidies under information asymmetry may reduce the policy efficiency. Xiao et al. (2022) discuss the impact of AP (altruistic preference) and government subsidies (ecological design subsidies and recycling subsidies) on ecological design and manufacturing recycling systems. Zhou et al. (2022) examine the impact of government subsidies on enterprise technological innovation in the presence of two forms of government subsidies (production subsidy per unit or innovation subsidy). Chen et al. (2022) examine the optimal production and subsidy rate of the supply chain when considering that consumer environmental awareness (CEA) is dynamic. Chen et al. (2019) find that if the product green degree, retailer profit and manufacturer profit are the evaluation criteria of the government subsidy mechanism, the corresponding optimal strategies are R&D input cost subsidy, production cost subsidy and green degree subsidy respectively. The study of Xu et al. (2024) analyzes the impact of government subsidies on manufacturers and retailers by constructing a Stackelberg game model of a manufacturer-dominated dual-channel green supply chain, and finds that subsidies to manufacturers are more effective in improving the green quality of products and the overall efficiency of the supply chain when the direct sales channel is dominated, and there is a difference in the impact of consumer channel preferences on green quality in terms of the target of the subsidies.

Han et al. (2022) find that when government subsidies exist, products were more green, manufacturers and retailers have higher profits, and can also coordinate the impact of retailers’ fair concerns on product pricing and green decisions. Ling et al. (2022) show that government subsidies can lower sales prices and increase market share, and that higher subsidy rates may not always benefit both the environment, social welfare and social profits. Liu et al. (2022a, b) discuss the impact of remanufacturing process innovation on the closed-loop supply chain from the perspective of government subsidies, and find that government subsidies will damage the profits of retailers, but improve the overall social welfare and have little impact on the environment. Pan and Ma (2024) discuss the green technology selection and product pricing decision of control and control enterprises under different government subsidy methods (unit product subsidy and green technology cost subsidy). Song and Yan (2023) find that government subsidies can bring higher social welfare when manufacturers have a partnership when considering the impact of government subsidies, consumer green preferences and green information trust, but the optimal choice of subsidies (for research and development costs or product production costs) depends on the level of competition and the difficulty of research and development. Wang et al. (2021) analyze the optimal operation decision of green supply chain in two modes of government subsidy for manufacturer R&D cost and production cost of green products. Barman et al. (2023) show that government subsidies can reduce the cost of green products and benefit both manufacturers and suppliers. The study by Sadrabadi et al. (2024) proposes a Stackelberg model-based framework for optimizing automotive battery recycling pricing strategies under government subsidies, demonstrating through an Iranian case analysis that centralized supply chain decision-making yields higher profitability than decentralized approaches while emphasizing policy coordination to enhance industry sustainability.

2.2 Research on the greening degree of products in the supply chain

Liu and Yi (2017) analyze the changing trend of price with the green degree and targeted advertising investment level, and show that the optimal retail price and wholesale price were negatively correlated with the green degree and targeted advertising investment level. Hong and Guo (2019a, b) study the cooperation contract in the green product supply chain, and find that the cooperation between partners can help the supply chain to achieve environmental improvement. Jafar et al. (2019) study the optimal coordinated decision-making of three-level two-channel green supply chain under the condition of manufacturers producing any green level commodities. Amin and Jafar (2019) study the pricing, product greening and coordination of dual-channel supply chains under channel interruption. Liu et al. (2019a, b) discuss the closed-loop supply chain optimal decision composed of leading manufacturers, retailers and third-party recyclers in terms of product greening and recycling competition. Liu et al. (2020) study which contracts are more effective to motivate companies to improve and benefit their products under different power structures. Wei et al. (2021) consider green supply chains with asymmetric heterogeneity preferences, where manufacturers do not know whether the type of retailer behavior is self-interest or altruistic. Liang and Sun (2022) design two fee contracts to coordinate the dual-channel green supply chain, enabling a win-win situation for both manufacturers and retailers. Cheng et al. (2022) study how retailers' overconfidence affects the green level of fashion products in a competitive environment. Cao and Mei (2022) find when the demand meets certain conditions and the manufacturer has favorable and fair concerns, the manufacturer’s risk aversion will lead to the decline of product green level, and the manufacturers’ fair concern will affect the investment of green products and improve the green level of products. Shuai et al. (2023) discuss how the adoption of block chain affects the duopoly game between green products and non-green products. Bai and Wang (2022) construct the wholesale price contract, cost-sharing contract and two-part contract model, and discuss the impact of three contracts on supply chain decisions by using optimization theory and method. Zhang et al. (2023a, b) examine which kind of cooperation contract (wholesale price contract or cost sharing contract) can more effectively improve the greening of products and promote market demand when considering the consumer reference price effect under different power structures.Cai et al. (2023a, b) show that suppliers always prefer mandatory disclosure of demand information, while retailer’ preference for disclosure depends on the combined impact of wholesale price and green degree level on demand. Cheng et al. (2023) show that manufacturers should increase their green investment within their financial capacity to improve the sustainable operation of their supply chains. Xiao et al. (2024) employs a Stackelberg game to model optimal pricing in a dual-channel green supply chain, demonstrating that government subsidies fail to counteract the impacts of manufacturers’ fairness concerns and risk aversion on pricing, yet R&D and green degree subsidies enhance product greenness and overall profitability.

2.3 Research on green sales effort in the supply chain

Amit et al. (2019) express demand as a linear function of sales price, green quality level and sales effort level, and study the dual-channel pricing strategy and coordination mechanism. Hong and Guo (2019a, b) take into account the impact of wholesale price contracts, cost sharing and two tariff contracts on the optimal decision of green supply chain under the green efforts of manufacturers and retailers. Li et al. (2021) examine the factors that affect demand when a risk-averse ordering company determines its pricing and sales efforts. Duan et al. (2021) study the impact of sales effort on the supply chain and found that sales effort and payment methods had a significant impact on balanced decisions and profits. Pal and Sarkar (2021) state the optimal strategy for the supply chain, achieving a higher level of green innovation and promotion efforts to always increase all profits. Cai et al. (2022) find that when introducing cost-sharing contracts, conditions exist that both suppliers and retailers are willing to actively make sales efforts. Cai et al. (2023a, b) study the imitation mechanism of suppliers, considering the conflicting impact of retail price and sales effort. Hu et al. (2023) show that sales efforts can always increase the profits of the OEM and the entire closed-loop supply chain, and only when the retailers' sales efforts costs are much lower than the OEM. Shan et al. (2023) study a problem for a retailer that can decide on promotional efforts on delivery to address the risk of supplier disruption. Zhang et al. (2023a, b) design two pricing contracts to study the decision-making issues of product pricing, carbon emission reduction and sales efforts. Yang et al. (2023) combine the pre-sale model with the fair concerns of retailers to propose a green supply chain composed of manufacturers making investments to improve the green level of their products and retailers making regular promotion efforts.

In conclusion, despite extensive scholarly examination of government subsidy strategies' impact on enterprise or supply chain decisions, much of the research has concentrated on singular subsidy approaches. These studies often overlook the nuanced effects of varied government subsidies on the supply chain as a whole. Moreover, existing research predominantly provides subsidies to manufacturers and consumers while neglecting the role of retailer-led green sales efforts. This oversight fails to account for how retailers' promotional activities influence the overall sustainability of the supply chain. Therefore, if the government were to implement a certain percentage of sales subsidies targeted at retailers, it could potentially alter the strategic decisions within the supply chain and affect the profitability of its various stakeholders.

Based on this, this paper considers the green supply chain composed of the government, green product manufacturers and green product retailers, in which the manufacturer is the leader and the retailer is the follower. In order to encourage the development of green supply chain, the government will subsidize the green degree of the manufacturer, the green R&D innovation cost and the green sales effort cost of the retailer, and analyze the impact of government subsidies on supply chain pricing decisions, member profits and social welfare.

3. Model description and assumptions

3.1 Model description

We consider a green supply chain model consisting of the government, a green product manufacturer and a green product retailer, in which the manufacturer and the retailer play a Stackelberg game, with the manufacturer being the leader and the retailer as the follower.

The decision order of the supply chain is as follows: the government first chooses the subsidy model and the subsidy level, the manufacturer then determines the wholesale price $w$ and green degree of the product $g$ according to the government’s decision, and the retailer finally determines the retail price $p$ and green sales effort level of the product $e$ according to the manufacturer’s decision. In order to encourage the development of green supply chain, the government will subsidize the manufacturer’s greening degree of their products, the cost of green R&D and innovation and the cost of green sales efforts of the retailers in order to analyze the impacts of government subsidies to the manufacturer (green degree subsidy and green R&D innovation cost subsidy) and subsidies to the retailer (green sales effort cost subsidy) on supply chain pricing decisions, member profits and social welfare.

3.2 Assumptions

Assumption 1.

Referring to Hong and Guo (2019a, b), the market demand decreases with the retail price $p$ ⁠, with the increase of green degree $g (g > 0)$ ⁠, the level of sales effort $e (e > 0)$ increases, and the market demand function is $D = a - b p + k g + q e$ ⁠, where $a - b p > 0$ indicates that no matter how much the price is, there are always consumers willing to buy the product; $a (a > 0)$ denotes the potential market size, $b (0 < b < 1)$ is the price elasticity coefficient of the product, $k (0 < k < 1)$ denotes the sensitivity coefficient for consumers to green degree, and $q (0 < q < 1)$ denotes the sensitivity coefficient for consumers to green sales efforts.

Assumption 2.

The production cost of unit product of the manufacturer is $c_{m}$ ⁠, and the sales cost of unit product of the retailer is $c_{r}$ ⁠. In order to simplify the calculation, we assume that it is always 0.

Assumption 3.

Following Chen et al. (2019), the additional cost for the manufacturer to conduct green R&D and innovation by introducing new equipment and technologies is $\frac{1}{2} z g^{2}$ ⁠, where $z (z > 0)$ denotes the cost factor for green R&D innovation; the cost of the retailer’s sales efforts $e$ to increase the product sales and profit is $\frac{1}{2} h e^{2}$ ⁠, where $h (h > 0)$ denotes green sales effort cost coefficient.

Assumption 4.

Following Guo et al. (2022) the government subsidizes the green degree of the manufacturer, green R&D and innovation cost and the cost of green sales efforts of the retailer. Its decision goal is to maximize social welfare. Total social welfare (⁠ $S W$ ⁠) is jointly determined by the consumer surplus (⁠ $C S$ ⁠), the profit of the manufacturer (⁠ $\prod_{m}$ ⁠), the profit of the retailer (⁠ $\prod_{r}$ ⁠) and government subsidy (⁠ $G S$ ⁠), i.e. $S W = \prod_{m} + \prod_{r} + C S - G S$ ⁠. The manufacturer and retailer are both “completely rational economic people” and risk-neutral, each seeking to maximize their own interests.

Assumption 5.

According to the definition of Panda et al. (2017), consumer surplus is an important indicator to weigh consumer welfare, i.e. the difference between the highest price that consumers are willing to pay for a certain number of products, which can be expressed as $C S = \int_{p}^{p_{\max}} D d p = \frac{D^{2}}{2 b}$ ⁠, where $p_{\max}$ represents the price when the demand is 0, that is, the actual price of the product. Letting $D = 0$ we obtain $p_{\max} = \frac{a + k g + q e}{b}$ ⁠,where $p$ denotes the actual price of the product.

Assumption 6.

There are three government subsidy strategies: ① subsidizing the manufacturer according to the green level of the product. If denoting the green degree subsidy coefficient as $θ$ ⁠, then the total government subsidy expenditure is $θ g$ ⁠. ② Subsidizing the manufacturer according to the cost of green R&D and innovation. We denote $ε (0 < ε < 1)$ as the government subsidy coefficient based on R&D cost, then the government subsidy expenditure is $\frac{1}{2} ε z g^{2}$ ⁠. ③ Subsidizing the retailer based on the cost of green sales effort. We use $τ (0 < τ < 1)$ to denote the subsidy coefficient based on the cost of green sales efforts, then the government subsidy expenditure is $\frac{1}{2} τ h e^{2}$ ⁠.

Assumption 7.

The sublabel $m$ denotes the manufacturer, and the sublabel $r$ denotes the retailer. The above label $M_{1}, M_{2}, R$ indicate the government subsidizes the manufacturer the green degree subsidy, the green R&D and innovation cost subsidy and the green sales effort cost subsidy for the retailer, respectively.

The notation is shown in Table 1.

Table 1

Notation

Decision variables	Meanings
$w$	Wholesale price
$g$	Green degree
$p$	Retail price
$e$	Green sales effort level
$θ$	Green degree subsidy coefficient
$ε$	R&D cost subsidy coefficient
$τ$	Sales effort cost subsidy coefficient

Parameters	Meanings
$a$	Potential market size
$b$	Price elasticity coefficient
$k$	The sensitivity coefficient of consumers to the green degree
$q$	Consumer sensitivity factor to green sales efforts
$c_{m}$	Manufacturer’s production cost per unit product
$c_{r}$	ales cost per unit product for the retailer
$z$	The cost coefficient of green R&D innovation for the manufacturer
$h$	Retailer’s green sales effort cost coefficient

Parameters	Meanings
$a$	Potential market size
$b$	Price elasticity coefficient
$k$	The sensitivity coefficient of consumers to the green degree
$q$	Consumer sensitivity factor to green sales efforts
$c_{m}$	Manufacturer’s production cost per unit product
$c_{r}$	ales cost per unit product for the retailer
$z$	The cost coefficient of green R&D innovation for the manufacturer
$h$	Retailer’s green sales effort cost coefficient

Other symbols	Meanings
$S W$	Social welfare
$\prod_{m}$	Manufacturer’s profit
$\prod_{r}$	Retailer’s profit

Source(s): Authors’ own work

The game decision order is as follows: in the first stage, the government takes social welfare maximization as the goal to decide the subsidy coefficient based on the green degree, the subsidy coefficient based on the research and development cost, and the subsidy coefficient based on the cost of green sales effort; in the second stage, the manufacturer decides the wholesale price and the product green degree according to the government decision; in the third stage, the retailer decides the retail price and the green sales effort level according to the decision of the manufacturer in the previous stage.

4. Model analysis

4.1 Green degree subsidy(Strategy $M_{1}$ ⁠)

In order to encourage the manufacturer to produce greener products and promote energy conservation and emission reduction work, the government often gives direct subsidies to products whose green degree exceeds a certain standard. In reality, the amount of government subsidies for products is often related to the green degree. The supply chain structure diagram under Strategy $M_{1}$ is shown in Figure 1.

Figure 1

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The supply chain structure diagram under strategy $M_{1}$ ⁠. Source: Authors’ own work

Then the optimization problems of the manufacturer, retailer profit and government are as follows, respectively.

Max {\underset{w, g}{\prod_{m}}}^{M_{1}} = w (a - b p + k g + q e) + θ g - \frac{1}{2} z g^{2}

(1)

Max {\underset{p, e}{\prod_{r}}}^{M_{1}} = (p - w) (a - b p + k g + q e) - \frac{1}{2} h e^{2}

(2)

Max {\underset{θ}{S W}}^{M_{1}} = {\prod_{m}}^{M_{1}} + {\prod_{r}}^{M_{1}} + C S^{M_{1}} - G S^{M_{1}}

(3)

After calculation, the equilibrium solutions and profit functions under this model are shown in Table 2.

Table 2

Equilibrium solutions and profits under the strategy $M_{1}$

Symbols	Results
$w^{M_{1}}$	$w^{M_{1}} = \frac{(2 b h - q^{2}) (a z + k θ)}{b (- h k^{2} + 4 b h z - 2 q^{2} z)}$
$g^{M_{1}}$	$g^{M_{1}} = \frac{a h k + 4 b h θ - 2 q^{2} θ}{- h k^{2} + 4 b h z - 2 q^{2} z}$
$p^{M_{1}}$	$p^{M_{1}} = \frac{(3 b h - q^{2}) (a z + k θ)}{b (- h k^{2} + 4 b h z - 2 q^{2} z)}$
$e^{M_{1}}$	$e^{M_{1}} = \frac{q (a z + k θ)}{- h k^{2} + 4 b h z - 2 q^{2} z}$
$θ^{M_{1}}$	$θ^{M 1} = - \frac{a h k (3 b h - q^{2}) z}{7 b h^{2} k^{2} - 3 h k^{2} q^{2} - 16 b^{2} h^{2} z + 16 b h q^{2} z - 4 q^{4} z}$
${\prod_{m}}^{M_{1}}$	${\prod_{m}}^{M_{1}} = \frac{a h^{2} z + 2 a h k θ + 2 (2 b h - q^{2}) θ^{2}}{- 2 h k^{2} + 8 b h z - 4 q^{2} z}$
${\prod_{r}}^{M_{1}}$	${\prod_{r}}^{M_{1}} = \frac{h (2 b h - q^{2}) {(a z + k θ)}^{2}}{2 {(2 q^{2} z + h (k^{2} - 4 b z))}^{2}}$
$S W^{M_{1}}$	$S W^{M_{1}} = \frac{a^{2} h (7 b h - 3 q^{2}) z}{2 h k^{2} (- 7 b h + 3 q^{2}) + 8 {(- 2 b h + q^{2})}^{2} z}$

Source(s): Authors’ own work

The specific proof process is shown in Appendix.

4.2 Green R&D innovation cost subsidy(Strategy $M_{2}$ ⁠)

Green R&D and innovation cost subsidy is a subsidy for the manufacturer who needs to increase R&D investment in producing green products, and it is the most direct and effective subsidy strategy to improve the enthusiasm of the manufacturer in producing green products (see Figure 2).

Figure 2

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Supply chain structure diagram under strategy $M_{2}$ ⁠. Source: Authors’ own work

The optimization problems of the manufacturer, retailer and the government are as follows, respectively.

Max {\underset{w, g}{\prod_{m}}}^{M_{2}} = w (a - b p + k g + q e) - \frac{1}{2} (1 - ε) z g^{2}

(4)

Max {\underset{p, e}{\prod_{r}}}^{M_{2}} = (p - w) (a - b p + k g + q e) - \frac{1}{2} h e^{2}

(5)

Max {\underset{ε}{S W}}^{M_{2}} = {\prod_{m}}^{M_{2}} + {\prod_{r}}^{M_{2}} + C S^{M_{2}} - G S^{M_{2}}

(6)

After calculation, the equilibrium solutions and profit functions under this model are shown in Table 3.

Table 3

Equilibrium solutions and profits under strategy $M_{2}$

Symbols	Results
$w^{M_{2}}$	$w^{M_{2}} = \frac{a (2 b h - q^{2}) (- z + z ε)}{b (h k^{2} - 4 b h z + 2 q^{2} z + 4 b h z ε - 2 q^{2} z ε)}$
$g^{M_{2}}$	$g^{M_{2}} = - \frac{a h k}{h k^{2} - 4 b h z + 2 q^{2} z + 4 b h z ε - 2 q^{2} z ε}$
$p^{M_{2}}$	$p^{M_{2}} = \frac{a z (3 b h - q^{2}) (- 1 + ε)}{b (h (k^{2} + 4 b z (- 1 + ε)) - 2 q^{2} z (- 1 + ε))}$
$e^{M_{2}}$	$e^{M_{2}} = \frac{a q z (- 1 + ε)}{h (k^{2} + 4 b z (- 1 + ε)) - 2 q^{2} z (- 1 + ε)}$
$ε^{M_{2}}$	$ε^{M_{2}} = \frac{3 b h - q^{2}}{7 b h - 3 q^{2}}$
${\prod_{m}}^{M_{2}}$	${\prod_{m}}^{M_{2}} = \frac{a^{2} h z (- 1 + ε)}{2 h (k^{2} + 4 b z (- 1 + ε)) - 4 q^{2} z (- 1 + ε)}$
${\prod_{r}}^{M_{2}}$	${\prod_{r}}^{M_{2}} = \frac{a^{2} h (2 b h - q^{2}) z^{2} {(- 1 + ε)}^{2}}{2 {(h (k^{2} + 4 b z (- 1 + ε)) - 2 q^{2} z (- 1 + ε))}^{2}}$
$S W^{M_{2}}$	$S W^{M_{2}} = \frac{a^{2} h (7 b h - 3 q^{2}) z}{2 h k^{2} (- 7 b h + 3 q^{2}) + 8 {(- 2 b h + q^{2})}^{2} z}$

Source(s): Authors’ own work

The proof process is similar to that under the green degree subsidy strategy in 4.1 and is omitted here.

4.3 Green sales effort cost subsidies(Strategy $R$ ⁠)

The green sales effort cost subsidy is the government subsidy for the cost of green sales effort for the retailer (see Figure 3).

Figure 3

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Supply chain structure diagram under strategy $R$ ⁠. Source: Authors’ own work

The optimization problems of the manufacturer, retailer and the government are as follows, respectively.

Max {\underset{w, g}{\prod_{m}}}^{R} = w (a - b p + k g + q e) - \frac{1}{2} z g^{2}

(7)

Max {\underset{p, e}{\prod_{r}}}^{R} = (p - w) (a - b p + k g + q e) - \frac{1}{2} (1 - τ) h e^{2}

(8)

Max {\underset{τ}{S W}}^{R} = {\prod_{m}}^{R} + {\prod_{r}}^{R} + C S^{R} - G S^{R}

(9)

After calculation, the equilibrium solutions and profit functions under this model are shown in Table 4.

Table 4

Equilibrium solutions and profits under strategy $R$

Symbols	Results
$w^{R}$	$w^{R} = \frac{a z (- 2 b h + q^{2} + 2 b h τ)}{b (h k^{2} - 4 b h z + 2 q^{2} z - h k^{2} τ + 4 b h z τ)}$
$g^{R}$	$g^{R} = \frac{a k (- h + h τ)}{h k^{2} - 4 b h z + 2 q^{2} z - h k^{2} τ + 4 b h z τ}$
$p^{R}$	$p^{R} = \frac{a z (q^{2} + 3 b h (- 1 + τ))}{b (2 q^{2} z - h (k^{2} - 4 b z) (- 1 + τ))}$
$e^{R}$	$e^{R} = - \frac{a q z}{2 q^{2} z - h (k^{2} - 4 b z) (- 1 + τ)}$
$τ^{R}$	$τ^{R} = \frac{2 z (3 b h - q^{2})}{h (10 b z - k^{2})}$
${\prod_{m}}^{R}$	${\prod_{m}}^{R} = \frac{a^{2} h z (- 1 + τ)}{4 q^{2} z - 2 h (k^{2} - 4 b z) (- 1 + τ)}$
${\prod_{r}}^{R}$	${\prod_{r}}^{R} = \frac{a^{2} h z^{2} (q^{2} + 2 b h (- 1 + τ)) (- 1 + τ)}{2 {(- 2 q^{2} z + h (k^{2} - 4 b z) (- 1 + τ))}^{2}}$
$S W^{R}$	$S W^{R} = \frac{a^{2} z (- h k^{2} + 7 b h z + q^{2} z)}{- 24 b q^{2} z^{2} + 2 h {(k^{2} - 4 b z)}^{2}}$

Source(s): Authors’ own work

The proof process is similar to that under the green degree subsidy strategy in 4.1 and is omitted here.

5. Equilibrium analysis

Proposition 1.

$\frac{\partial w^{M_{1}}}{\partial θ} > 0, \frac{\partial g^{M_{1}}}{\partial θ} > 0, \frac{\partial p^{M_{1}}}{\partial θ} > 0, \frac{\partial e^{M_{1}}}{\partial θ} > 0, \frac{\partial {\prod_{m}}^{M_{1}}}{\partial θ} > 0, \frac{\partial {\prod_{r}}^{M_{1}}}{\partial θ} > 0$ ⁠.

Proposition 1 shows that when the government subsidizes the manufacturer according to the green degree of products, the wholesale price, green price, retail price, sales effort level of green, and the profits of the manufacturer and retailer all increase with the green degree subsidy coefficient. When the government subsidizes the manufacturer on the standard of green degree, the higher the green level of the product, the more subsidies the manufacturer gets. In fact, the high green degree means better quality, high quality products need the manufacturer to pay more cost and resources, so that the manufacturer needs to purchase green raw materials and introduce advanced green technologies. These measures will inevitably increase the input cost and reduce the enthusiasm of manufacturers in production.

In order to improve its enthusiasm, the government subsidizes its green degree. Government subsidies can mobilize the enthusiasm of the manufacturer to a certain extent, increase the wholesale price and the greening of products, thus raising the retail price, and further promoting the level of green sales efforts of the retailer. For consumers with green consumption awareness, they pay more attention to the greening of products and have a certain psychological price affordability. They will not reduce the purchase of green products due to the price rise, but stimulate the market demand and benefit both the manufacturer and retailer. At the same time, when the government gives the manufacturer green subsidies, even if the manufacturer is in the dominant position and enjoys the subsidies, the retailer’s income will increase with the government subsidies, which also shows the possibility of cooperation among members in the green supply chain.

The specific proof process is shown in Appendix.

Proposition 2.

(1). $\frac{\partial w^{M_{1}}}{\partial k} > 0$ ⁠, $\frac{\partial g^{M_{1}}}{\partial k} > 0$ ⁠, $\frac{\partial θ^{M_{1}}}{\partial k} > 0$ ⁠, $\frac{\partial {\prod_{m}}^{M_{1}}}{\partial k} > 0$ ⁠;

${\begin{cases} 0 < \frac{- a h z + \sqrt{h z (a^{2} h z - 4 b h θ^{2} + 2 q^{2} θ^{2})}}{h θ} < 1, \\ {\begin{cases} 0 < k < \frac{- a h z + \sqrt{h z (a^{2} h z - 4 b h θ^{2} + 2 q^{2} θ^{2})}}{h θ}, \frac{\partial p^{M_{1}}}{\partial k} < 0, \frac{\partial e^{M_{1}}}{\partial k} < 0, \frac{\partial {\prod_{r}}^{M_{1}}}{\partial k} < 0 \\ \frac{- a h z + \sqrt{h z (a^{2} h z - 4 b h θ^{2} + 2 q^{2} θ^{2})}}{h θ} < k < 1, \frac{\partial p^{M_{1}}}{\partial k} > 0, \frac{\partial e^{M_{1}}}{\partial k} > 0, \frac{\partial {\prod_{r}}^{M_{1}}}{\partial k} > 0 \end{cases} \\ \frac{- a h z + \sqrt{h z (a^{2} h z - 4 b h θ^{2} + 2 q^{2} θ^{2})}}{h θ} > 1, \frac{\partial p^{M_{1}}}{\partial k} < 0, \frac{\partial e^{M_{1}}}{\partial k} < 0, \frac{\partial {\prod_{r}}^{M_{1}}}{\partial k} < 0 \end{cases}$ ⁠.

Proposition 2 shows that when the government subsidizes the manufacturer according to the green degree, the wholesale price, the product green degree, the green degree subsidy coefficient and the manufacturer’s profit all increase with the consumers’ sensitivity coefficient to the green degree; when $0 < \frac{- a h z + \sqrt{h z (a^{2} h z - 4 b h θ^{2} + 2 q^{2} θ^{2})}}{h θ} < 1$ ⁠, the sensitivity coefficient of consumers to green is small, and the retail price, green sales effort level and retailer profit all decrease with the green sensitivity coefficient; otherwise, they all increase with the green degree sensitivity coefficient; when $\frac{- a h z + \sqrt{h z (a^{2} h z - 4 b h θ^{2} + 2 q^{2} θ^{2})}}{h θ} > 1$ ⁠,they all decrease with the green degree sensitivity coefficient. Government subsidies the manufacturer help to arouse the enthusiasm of the production of green products, which means that the manufacturer will invest more resources and energy to produce high green degree products, make efforts to improve their brand image and consumer trust, thus to promote consumer purchase demand, which is conducive to promote green concept, advocate green life. The more sensitive consumers are to the green degree, the higher the green degree and the level of sales efforts, which contains the basic fact that “a rising tide lifts all boats”. The more sensitive consumers are to the green degree, the more the manufacturer will try to improve the green degree of their products. Even if the manufacturer is dominant and subsidized, the retailer is still likely to make profits, demonstrating the possibility of members in the supply chain to promote a green supply chain and the importance of government subsidies for the implementation of green strategies. But who enjoys the subsidy does not mean that it has an absolute advantage. For example, when manufacturers receive greenness subsidies(⁠ $\frac{- a h z + \sqrt{h z (a^{2} h z - 4 b h θ^{2} + 2 q^{2} θ^{2})}}{h θ} < k < 1$ ⁠), the retailer still has a chance to make profits when consumers are more sensitive to greenness. Therefore, in the green supply chain, the government should give certain financial subsidies to stimulate the manufacturer to take consumers as an important influencing factor, and pay close attention to the sensitivity of consumers to the green degree.

The specific proof process is shown in Appendix.

Proposition 3.

(1). $\frac{\partial w^{M_{1}}}{\partial q} > 0, \frac{\partial g^{M_{1}}}{\partial q} > 0, \frac{\partial p^{M_{1}}}{\partial q} > 0, \frac{\partial e^{M_{1}}}{\partial q} > 0, \frac{\partial {\prod_{m}}^{M_{1}}}{\partial q} > 0, \frac{\partial {\prod_{r}}^{M_{1}}}{\partial q} > 0$ ⁠;

${\begin{cases} 0 < \sqrt{\frac{2 (8 b^{2} h^{2} z - 6 b h q^{2} z + q^{4} z)}{b h^{2}}} < 1, {\begin{cases} 0 < k < \sqrt{\frac{2 (8 b^{2} h^{2} z - 6 b h q^{2} z + q^{4} z)}{b h^{2}}}, \frac{\partial θ^{M_{1}}}{\partial q} > 0 \\ \sqrt{\frac{2 (8 b^{2} h^{2} z - 6 b h q^{2} z + q^{4} z)}{b h^{2}}} < k < 1, \frac{\partial θ^{M_{1}}}{\partial q} < 0 \end{cases} \\ \sqrt{\frac{2 (8 b^{2} h^{2} z - 6 b h q^{2} z + q^{4} z)}{b h^{2}}} > 1, \frac{\partial θ^{M_{1}}}{\partial q} > 0 \end{cases}$ ⁠.

Proposition 3 shows that when the government subsidizes the manufacturer according to the green degree, the wholesale price, product green degree, retail price, green sales effort level, and the profits of the manufacturer and retailer all increase with the sensitivity coefficient of consumers to green sales efforts; when $0 < \sqrt{\frac{2 (8 b^{2} h^{2} z - 6 b h q^{2} z + q^{4} z)}{b h^{2}}} < 1$ ⁠,if the sensitivity coefficient of consumers to green degree is small, the subsidy coefficient of green degree increases with the sensitivity coefficient of consumers to green sales efforts, while it decreases with the sensitivity coefficient of consumers to green sales efforts; when $\sqrt{\frac{2 (8 b^{2} h^{2} z - 6 b h q^{2} z + q^{4} z)}{b h^{2}}} > 1$ ⁠,it increases with the sensitivity coefficient of consumers to green sales efforts. Similar to Proposition 2, the more consumers are affected by the retailer’s green sales efforts, the more the retailer will try to enhance their sales efforts to influence consumers’ decisions. That is to say, the improvement of consumers’ environmental awareness is conducive to the implementation of the green supply chain strategy. Even if the government subsidizes the manufacturer, the behavior of the manufacturer giving profits to the retailer remains, which increases the benefits of both the manufacturer and retailer. In addition, it can be seen from (2) that the government’s subsidy coefficient of green degree is affected by the sensitivity coefficient of consumers to green sales efforts, which is related to the size relationship of $\sqrt{\frac{2 (8 b^{2} h^{2} z - 6 b h q^{2} z + q^{4} z)}{b h^{2}}}$ and 1, and the sensitivity coefficient of consumers to green degree.

The specific proof process is shown in Appendix.

Proposition 4.

(1). $\frac{\partial w^{M_{2}}}{\partial ε} > 0$ ⁠, $\frac{\partial g^{M_{2}}}{\partial ε} > 0$ ⁠, $\frac{\partial p^{M_{2}}}{\partial ε} > 0$ ⁠, $\frac{\partial e^{M_{2}}}{\partial ε} > 0$ ⁠, $\frac{\partial {\prod_{m}}^{M_{2}}}{\partial ε} > 0$ ⁠;

${\begin{cases} 2 z (2 b h - q^{2}) < h k^{2}, \frac{\partial {\prod_{r}}^{M_{2}}}{\partial ε} < 0 \\ 2 z (2 b h - q^{2}) > h k^{2}, {\begin{cases} 0 < ε < \frac{2 z (2 b h - q^{2}) - h k^{2}}{2 z (2 b h - q^{2})} < 1, \frac{\partial {\prod_{r}}^{M_{2}}}{\partial ε} > 0 \\ \frac{2 z (2 b h - q^{2}) - h k^{2}}{2 z (2 b h - q^{2})} < ε < 1, \frac{\partial {\prod_{r}}^{M_{2}}}{\partial ε} < 0 \end{cases} \end{cases}$ ⁠.

Proposition 4 shows that when the government subsidies the manufacturer according to the green R&D innovation cost, the wholesale price, product green degree, retail price, green sales effort level and manufacturer’s profit all increase with the R&D cost subsidy coefficient; when $2 z (2 b h - q^{2}) < h k^{2}$ ⁠,the retailer’ profit decreases with the R&D cost subsidy coefficient; when $2 z (2 b h - q^{2}) > h k^{2}$ ⁠, when the subsidy coefficient is small, the retailer’s profit increases with the subsidy coefficient; when the subsidy coefficient is large, the retailer’s profit decreases with the subsidy coefficient. The government will subsidize manufacturers for the cost of research and innovation. After receiving the subsidies, the manufacturer will increase green investment to improve the greening of products, prompting the manufacturer to raise wholesale price and benefit the manufacturer. The improvement of product green level will encourage the retailer to raise the retail price and sales efforts, and also stimulate the increased purchasing power of consumers with green consumption awareness, thus leading to an increase in market demand. Furthermore, when $2 z (2 b h - q^{2}) > h k^{2}$ ⁠, appropriate government subsidies for (⁠ $0 < ε < \frac{2 z (2 b h - q^{2}) - h k^{2}}{2 z (2 b h - q^{2})} < 1$ ⁠) are more conducive to improving the economic benefit of the retailer, otherwise, it is not conducive to improving the economic benefit of the retailer. An interesting phenomenon is observed: even when the government does not subsidize the retailer, the retailer’s income still tends to increase as the government subsidies to the manufacturer grow. This phenomenon is known as “free-rider” behavior, which can compress the manufacturer’s income and lead to an imbalance in the economic income distribution among supply chain members. Consequently, the government can implement certain corrective measures to balance the economic benefits of its members, such as imposing additional taxes on retailers at a certain percentage. The specific proof process is shown in Appendix.

Proposition 5.

(1). ${\begin{cases} 0 < \sqrt{\frac{2 z (2 b h - q^{2}) (- 1 + ε)}{h^{2}}} < 1, {\begin{cases} 0 < k < \sqrt{\frac{2 z (2 b h - q^{2}) (- 1 + ε)}{h^{2}}}, \frac{\partial g^{M 2}}{\partial k} < 0 \\ \sqrt{\frac{2 z (2 b h - q^{2}) (- 1 + ε)}{h^{2}}} < k < 1, \frac{\partial g^{M 2}}{\partial k} > 0 \end{cases} \\ \sqrt{\frac{2 z (2 b h - q^{2}) (- 1 + ε)}{h^{2}}} > 1, \frac{\partial g^{M 2}}{\partial k} < 0 \end{cases}$ ⁠;

$\frac{\partial w^{M 2}}{\partial k} > 0, \frac{\partial p^{M 2}}{\partial k} > 0, \frac{\partial e^{M 2}}{\partial k} > 0, \frac{\partial {\prod_{m}}^{M 2}}{\partial k} > 0$ ⁠;
${\begin{cases} 2 z (2 b h - q^{2}) < h k^{2}, \frac{\partial {\prod_{r}}^{M 2}}{\partial k} < 0 \\ 2 z (2 b h - q^{2}) > h k^{2}, {\begin{cases} 0 < ε < \frac{2 z (2 b h - q^{2}) - h k^{2}}{2 z (2 b h - q^{2})} < 1, \frac{\partial {\prod_{r}}^{M 2}}{\partial k} > 0 \\ \frac{2 z (2 b h - q^{2}) - h k^{2}}{2 z (2 b h - q^{2})} < ε < 1, \frac{\partial {\prod_{r}}^{M 2}}{\partial k} < 0 \end{cases} \end{cases}$

Proposition 5 shows that when the government subsidies the manufacturer based on the cost of innovation. Proposition 5 shows that when the government subsidies manufacturers based on the cost of innovation, when $0 < \sqrt{\frac{2 z (2 b h - q^{2}) (- 1 + ε)}{h^{2}}} < 1$ ⁠, if the sensitive coefficient of consumers to the green degree is small, the green degree decreases with the green sensitive coefficient, and increases with the green sensitive coefficient when the sensitive coefficient is large; when $\sqrt{\frac{2 z (2 b h - q^{2}) (- 1 + ε)}{h^{2}}} > 1$ ⁠, it decreases with the green degree sensitivity coefficient; and the wholesale price, retail price, green sales effort levels and the manufacturer’s profit all increase with the consumers’ sensitivity to the green degree. When $2 z (2 b h - q^{2}) > h k^{2}$ ⁠, appropriate government subsidies (⁠ $0 < ε < \frac{2 z (2 b h - q^{2}) - h k^{2}}{2 z (2 b h - q^{2})} < 1$ ⁠) are more conducive to improving the economic benefit of the retailer, otherwise, it is not conducive to improving the economic benefit of the retailer. The government provides subsidies to the manufacturer based on the costs associated with research and development (R&D) and innovation. When consumers are not sensitive to the greenness of products, the manufacturer has less incentive to enhance the green attributes of their products. Only when consumers become more sensitive to the greenness of products will the manufacturer be motivated to improve the environmental quality of their offerings, thereby stimulating consumer purchasing behavior. This indicates that the greater consumer preference for green products, the more conducive it is to promoting green production and sales. Consequently, product prices may also increase as a result. At the same time, the enhancement of consumers' green awareness can improve the green demand and promote the retailer to raise the retail price to increase their own profits. The level of sales effort increases with the sensitivity of consumers to green, the more the manufacturer can be encouraged to improve the greening of products, and the retailer will invest more sales efforts to increase the product sales. Therefore, in order to achieve the optimization of social benefits, the government should adjust the subsidy proportion appropriately according to the differences of the subsidy objects in different industries when formulating subsidy policies, so as to ensure the optimal social benefits of the whole supply chain.

The specific proof process is shown in Appendix.

Proposition 6.

(1). $\frac{\partial w^{M 2}}{\partial q} > 0, \frac{\partial g^{M 2}}{\partial q} > 0, \frac{\partial p^{M 2}}{\partial q} > 0, \frac{\partial ε^{M 2}}{\partial q} > 0$ ⁠;

${\begin{cases} \frac{\sqrt{- h k^{2} + 4 b h z (1 - ε)}}{\sqrt{2 z (- 1 + ε)}} < 1, {\begin{cases} 0 < q < \frac{\sqrt{- h k^{2} + 4 b h z (1 - ε)}}{\sqrt{2 z (- 1 + ε)}}, \frac{\partial e^{M 2}}{\partial q} > 0 \\ \frac{\sqrt{- h k^{2} + 4 b h z (1 - ε)}}{\sqrt{2 z (- 1 + ε)}} < q < 1, \frac{\partial e^{M 2}}{\partial q} < 0 \end{cases} \\ \frac{\sqrt{- h k^{2} + 4 b h z (1 - ε)}}{\sqrt{2 z (- 1 + ε)}} > 1, \frac{\partial e^{M 2}}{\partial q} > 0 \end{cases}$ ⁠.

Proposition 6 shows that when the government subsidies the manufacturer according to the R&D innovation cost, the wholesale price, product green degree, retail price and R&D innovation cost subsidy coefficient all increase with the sensitivity coefficient of consumers to green sales efforts; when $\frac{\sqrt{- h k^{2} + 4 b h z (1 - ε)}}{\sqrt{2 z (- 1 + ε)}} < 1$ ⁠, i.e. the sensitivity coefficient of consumers to green sales efforts is small, the level of sales efforts shows a trend of increasing, and when the sensitivity coefficient is large, i.e. $\frac{\sqrt{- h k^{2} + 4 b h z (1 - ε)}}{\sqrt{2 z (- 1 + ε)}} > 1$ ⁠, it also shows an increasing trend. As consumers become more sensitive to green sales efforts, the government will increase the level of subsidies for the manufacturer’s research and development and innovation costs, thus prompting the manufacturer to increase green product research and development to improve the greening of products, and further stimulate the retailer to increase green sales efforts to expand market demand. Appropriate consumer sales effort sensitivity (⁠ $0 < q < \frac{\sqrt{- h k^{2} + 4 b h z (1 - ε)}}{\sqrt{2 z (- 1 + ε)}}$ ⁠) will encourage the retailer to improve green sales effort levels, if it (⁠ $\frac{\sqrt{- h k^{2} + 4 b h z (1 - ε)}}{\sqrt{2 z (- 1 + ε)}} < q < 1$ ⁠) is too sensitive, as long as the retailer slightly increases the sales efforts, consumers will follow suit and increase their purchasing power of green products, which may put the retailers in short supply, leading to less consumer satisfaction with the retailers' services. At this point, the retailer will choose to reduce the level of sales efforts to ensure their own earnings and ensure the long-term and stable development of the supply chain.

The specific proof process is shown in Appendix.

Proposition 7.

(1). $\frac{\partial w^{R}}{\partial τ} > 0$ ⁠, $\frac{\partial g^{R}}{\partial τ} > 0$ ⁠, $\frac{\partial p^{R}}{\partial τ} > 0$ ⁠, $\frac{\partial e^{R}}{\partial τ} < 0$ ⁠;

$\frac{\partial w^{R}}{\partial q} > 0, \frac{\partial g^{R}}{\partial q} > 0, \frac{\partial p^{R}}{\partial q} > 0, \frac{\partial τ^{M 2}}{\partial q} > 0, \frac{\partial e^{R}}{\partial q} > 0$ ⁠.

Proposition 7 shows that when the government subsidizes the retailer according to the green sales efforts cost, the wholesale price, product green degree, retail price and green sales effort level all increase with the subsidy coefficient of sales efforts cost and consumers' sensitivity coefficient to green sales efforts, and the subsidy coefficient of government subsidy to green sales efforts also increases with the sensitivity coefficient of consumers to sales efforts. The government subsidizes the cost of the retailer’s green sales efforts, which increases the retailer’s sales efforts, and then increases the demand for products, and the demand exceeds the supply. Consequently, the manufacturer’s wholesale price increases, leading the retailer to further elevate the retail price. When the government subsidizes the retailer based on their green sales efforts, it stimulates the retailer’s enthusiasm for conducting green sales to some extent. However, as the subsidy coefficient increases, the level of optimal sales efforts by the retailers exhibits a decreasing trend. The more sensitive consumers are to green sales efforts, the more they can encourage the retailer to pay more efforts to sell green products, and then the retailer will raise the retail price to expand their market share, and the manufacturer will use this effect to raise the wholesale price and green degree of products to build a green image.

The specific proof process is shown in Appendix.

Proposition 8.

(1). ${\begin{cases} 0 < \sqrt{2 b h (1 - τ)} < 1, {\begin{cases} 0 < q < \sqrt{2 b h (1 - τ)}, \frac{\partial w^{R}}{\partial k} > 0 \\ \sqrt{2 b h (1 - τ)} < q < 1, \frac{\partial w^{R}}{\partial k} < 0 \end{cases} \\ \sqrt{2 b h (1 - τ)} > 1, \frac{\partial w^{R}}{\partial k} > 0 \end{cases}$ ⁠;

${\begin{cases} \frac{2 q^{2} z}{(k^{2} + 4 b z) (1 - τ)} < 1, {\begin{cases} 0 < h < \frac{2 q^{2} z}{(k^{2} + 4 b z) (1 - τ)}, \frac{\partial g^{R}}{\partial k} < 0 \\ \frac{2 q^{2} z}{(k^{2} + 4 b z) (1 - τ)} < h < 1, \frac{\partial g^{R}}{\partial k} > 0 \end{cases} \\ \frac{2 q^{2} z}{(k^{2} + 4 b z) (1 - τ)} > 1, \frac{\partial g^{R}}{\partial k} < 0 \end{cases}$ ⁠;
${\begin{cases} 0 < \sqrt{3 b h (1 - τ)} < 1, {\begin{cases} 0 < q < \sqrt{3 b h (1 - τ)}, \frac{\partial p^{R}}{\partial k} > 0 \\ \sqrt{3 b h (1 - τ)} < q < 1, \frac{\partial p^{R}}{\partial k} < 0 \end{cases} \\ \sqrt{3 b h (1 - τ)} > 1, \frac{\partial p^{R}}{\partial k} > 0 \end{cases}$ ⁠;
$\frac{\partial e^{R}}{\partial k} > 0$ ⁠, $\frac{\partial τ^{M 2}}{\partial k} > 0$ ⁠, $\frac{\partial {\prod_{m}}^{R}}{\partial k} > 0$ ⁠, $\frac{\partial {\prod_{r}}^{R}}{\partial k} > 0$

Proposition 8 shows that when the government subsidizes the retailer according to the cost of green sales efforts, if $0 < \sqrt{2 b h (1 - τ)} < 1$ (⁠ $0 < \sqrt{3 b h (1 - τ)} < 1$ ⁠), consumers have less sensitive coefficient to green sales efforts, the wholesale price (retail price) increase with the green sensitivity coefficient; when the sensitivity coefficient to green sales efforts is large, it decreases with the green sensitivity coefficient. When $\sqrt{2 b h (1 - τ)} > 1$ (⁠ $\sqrt{3 b h (1 - τ)} > 1$ ⁠), the wholesale price (retail price) increases with the green sensitivity coefficient. When $\frac{2 q^{2} z}{(k^{2} + 4 b z) (1 - τ)} < 1$ and the cost coefficient of green sales efforts is small, the greening degree of the product decreases with the green sensitivity coefficient, and the greening degree of the product increases with the green sensitivity coefficient when the cost coefficient of green sales efforts is larger; when $\frac{2 q^{2} z}{(k^{2} + 4 b z) (1 - τ)} > 1$ ⁠,the greening degree of the product decreases with the green sensitivity coefficient. The level of green sales efforts, the cost of sales efforts and the profits of the manufacturer and retailer all increase with the green sensitivity coefficient. Under the strategy of subsidizing the retailer for green sales efforts, the increase in the consumer sensitivity coefficient to the green degree can not only increase the government’s cost subsidy coefficient for green sales efforts, but also encourage the retailer to raise his green sales efforts, increasing profits for both the manufacturer and retailer and for the entire supply chain, which indicates that the change of wholesale price, product green degree and retail price on the sensitivity coefficient of consumers to green degree is related to the sensitivity coefficient of consumers to green sales efforts and the cost coefficient of retailers' green sales efforts.

The specific proof process is shown in Appendix.

6. Comparison analysis

For consumers, they still want to buy high-green products at the lowest possible price. Based on this, we refer to the research of DAI et al., (2017) to introduce the evaluation index-performance price ratio to measure the impact of government subsidies on consumers. Performance-to-price ratio $R = \frac{g}{p}$ is defined as-ratio of green degree to selling price. The larger the ratio $R$ ⁠, the higher the cost performance of green products, and the more willing consumers are to buy them. The government adopts three subsidy strategies to subsidize, and its performance-to-price ratio is as follows, respectively.

R (θ) = \frac{b (a h k + 4 b h θ - 2 q^{2} θ)}{(3 b h - q^{2}) (a z + k θ)}

R (ε) = \frac{b h k}{(3 b h - q^{2}) z (1 - ε)}

R (τ) = \frac{b h k (1 - τ)}{z (3 b h (1 - τ) - q^{2})}

Proposition 9.

(1). The government’s performance price ratio under the product green degree subsidy increases with the green degree subsidy coefficient(⁠ $\frac{\partial R (θ)}{\partial θ} > 0$ ⁠). (2). The performance price ratio of the government under the green R&D and innovation cost subsidy increases with the R&D cost subsidy coefficient $ε$ (⁠ $\frac{\partial R (ε)}{\partial ε} > 0$ ⁠). (3). The performance price ratio of the government under the green R&D and innovation cost subsidy increases with the sales effort cost subsidy coefficient $τ$ (⁠ $\frac{\partial R (τ)}{\partial τ} > 0$ ⁠).

The specific proof process is shown in Appendix.

Proposition 9 shows that the government’s different subsidy strategies to the manufacturer and retailer are beneficial to consumers, and with the greater the government subsidies, the higher the performance price ratio of the product, the more consumers benefit, and the greater the satisfaction of consumers.

In order to compare the effects of the 3 subsidy strategies, the comparability issue needs to be addressed first. We compare the subsidy effects of different strategies on the condition of the same government subsidy expenditure. The government subsidy expenditure corresponding to the three subsidy strategies are as follows, respectively.

G S^{M 1} (θ) = \frac{θ (- a h k + 2 (q^{2} - 2 b h) θ)}{2 q^{2} z + h (k^{2} - 4 b z)}

G S^{M 2} (ε) = \frac{a^{2} h^{2} k^{2} z ε}{2 {(h (k^{2} + 4 b z (- 1 + ε)) - 2 q^{2} z (- 1 + ε))}^{2}}

G S^{R} (τ) = \frac{a^{2} h q^{2} z^{2} τ}{2 (- 2 q^{2} z + h (k^{2} - 4 b z) (- 1 + τ))}

It can be seen that with the increase of the subsidy coefficient $θ, ε$ ⁠, and $τ$ ⁠, the corresponding government subsidy expenditure increases. In order to get the same government subsidy expenditure, a certain amount of relationships should be satisfied among $θ, ε$ ⁠, and $τ$ when determining the subsidy coefficient. Suppose that the government first gives $θ$ ⁠, and then the values of $ε (θ)$ and $τ (θ)$ can be determined according to $G S^{M 1} (ε) = G S^{M 2} (θ)$ and $G S^{M 1} (τ) = G S^{M 2} (θ)$ ⁠, and the calculation formula is as follows, respectively.

ε (θ) = \frac{(2 q^{2} z + h (k^{2} - 4 b z)) (- a^{2} h^{2} k^{2} - 16 {(2 b h - q^{2})}^{2} θ^{2} + a h k (8 (q^{2} - 2 b h) θ + A_{1}))}{16 {(2 b h - q^{2})}^{2} z θ (a h k + 2 θ (2 b h - q^{2}))},

τ (θ) = \frac{(2 q^{2} z + h (k^{2} - 4 b z)) (- a^{2} q^{2} z^{2} + (a h k + 2 θ (2 b h - q^{2})) 4 (k^{2} - 4 b z) θ + a q z A_{2})}{4 h {(k^{2} - 4 b z)}^{2} θ (a h k + 2 θ (2 b h - q^{2}))},

Where $A_{1} = \sqrt{a^{2} h^{2} k^{2} + 16 a h k (2 b h - q^{2}) θ + 32 {(- 2 b h + q^{2})}^{2} θ^{2}}$ ⁠, $A_{2} = \sqrt{a^{2} q^{2} z^{2} - (a h k + 2 θ (2 b h - q^{2})) 8 (k^{2} - 4 b z) θ}$ ⁠.

One of the purposes of government subsidies for the manufacturer for producing green products is to improve the greening of products, and one of the purposes of subsidies for the retailer for selling green products is to improve the level of green sales efforts. Based on this, we mainly compare the subsidy effects of the three strategies with wholesale price, product green degree, retail price, green sales effort level, manufacturer and retailer profit, and social welfare as the evaluation criteria. Because the comparison results are relatively complex, we will analyze these in the numerical examples section.

7. Numerical analysis

In order to illustrate the validity of the model and the correctness of the verification conclusions and propositions, this study uses Matlab for numerical simulation to analyze the impact of three government subsidy strategies on the green supply chain. Based on the results of the derivation of the mathematical model within the range allowed by the parameters and referring to the corresponding literature (Meng et al., 2021), we assume that the relevant parameters in the model are valued as follows: $a = 50, b = 3, k = 1, q = 1, z = 10, h = 2, θ \in [0, 1]$ ⁠,then the calculated parameters satisfy the assumption of the relationship between parameters in all the above models.

The following results can be obtained here:

From Figure 4 we can see the impact of the government’s green degree subsidy coefficient for the manufacturer on the wholesale price of products under the three government subsidy strategies. We can conclude from Figure 4 that the relationship between the optimal wholesale prices of manufacturers in the three modes is $w^{M_{2}} > w^{M_{1}} > w^{R}$ , which indicates that the wholesale prices of manufacturers are highest in the M2 mode, followed by the M1 mode, and the lowest wholesale prices of manufacturers in the R mode. The wholesale price exhibits an increasing trend as the subsidy coefficient for greenness rises; however, the influence of the subsidy coefficient on the wholesale price is most pronounced for products receiving R&D cost subsidies, followed by those benefiting from greenness subsidies, with sales effort cost subsidies having the least impact. This shows that government subsidies will encourage the manufacturer to produce more green products. In order to get green income and make up for the extra cost of green quality improvement, the manufacturer will set higher wholesale prices. Compared with subsidies retailers, subsidies to the manufacturer to motivate the manufacturer to produce more green product effect will be better.

Figure 4

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The effect of government. Source: Authors’ own work

From Figure 5 we can see the influence of the government’s green degree subsidy coefficient to the manufacturer on the greening degree of products under the three government subsidy strategies. Through Figure 5, we can get the relationship between the greenness of the optimal product in the three modes as $g^{M_{2}} > g^{M_{1}} > g^{R}$ , which indicates that the greenness of the product is the highest in the M1 mode, followed by the M2 mode, and the greenness of the product is the lowest in the R mode. The product green degree also increases with the green degree subsidy coefficient, and the change of the subsidy coefficient of the R&D costs under the green degree of influence is higher than green degree subsidies, higher than sales cost subsidies, which indicates that no matter what kind of government subsidy strategy, all can really stimulate the supply chain manufacturer improve product green degree, and compared with subsidies to the retailer, subsidies to the manufacturer to promote product green degree effect better.

Figure 5

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The effect of government subsidy on wholesale prices on green degree. Source: Authors’ own work

From Figure 6 we can see the impact of the government’s green degree subsidy coefficient on the retail price under the three government subsidy strategies. From Figure 6, we can get that the relationship between the optimal retail prices of retailers under the three models is $p^{M_{2}} > p^{R} > p^{M_{1}}$ ⁠. Unlike Figure 4, Figure 5, at this time, the retailer under the M2 model has the highest wholesale price, while the M1 model has the lowest wholesale price. The retail price increases with the green degree subsidy coefficient, and the impact of the subsidy coefficient on the retail price under the R&D cost subsidy is higher than the sales effort cost subsidy and higher than the green degree subsidy. It can be seen that the retailer provides green investment and sales efforts under the cost subsidy of green sales efforts, and the retail price under this strategy is relatively high to make up the investment cost; secondly, the green degree subsidy for green product manufacturer can reduce the production cost of the manufacturer and the purchasing cost of the retailer, thus effectively reducing the retail price of green products and expanding the market demand for products.

Figure 6

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The effect of government. Source: Authors’ own work

As illustrated in Figure 7, the impact of the government’s green degree subsidy coefficient on the manufacturer’s sales effort level under three different subsidy strategies is evident. From Figure 7 we can get that the relationship between the optimal level of sales effort of the manufacturer in the three different modes is $e^{R} > e^{M_{1}} > e^{M_{2}}$ ⁠. At this time, the level of sales effort of the manufacturer is the highest in the R mode, while the level of sales effort of the manufacturer is the lowest in the M2 mode. The sales effort level increases with the green degree subsidy coefficient. Moreover, the change in the subsidy coefficient exerts a more substantial effect on the sales effort level under the sales effort cost subsidy compared to both the green degree subsidy and the R&D cost subsidy. This observation suggests that, relative to subsidizing the manufacturer directly, cost subsidies targeting green sales efforts can more effectively influence retailers, thereby encouraging greater green initiatives and boosting the sales of environmentally friendly products.

Figure 7

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The effect of government subsidy on retail prices on sales effort level. Source: Authors’ own work

This shows that the essence of green supply chain lies in the greening of manufacturing: when the market demand is sensitive to the wholesale price of products, subsidizing the manufacturer are more favorable; when the market demand is sensitive to the product green, retail price and green sales efforts, the sales efforts for green promotion are more valuable and subsidizing the retailer is prominent.

In Figures 8 and 9, we compare the size of profit of manufacturer and retailer in different modes, from the figure we can see that the relationship between the profit of manufacturer and retailer in different modes is $Π_{m}^{R} > Π_{m}^{M_{1}} > Π_{m}^{M_{2}}$ , $Π_{r}^{M_{2}} > Π_{r}^{R} > Π_{r}^{M_{1}}$ this shows that the profit of manufacturer and retailer is also different in three different modes. For the manufacturer the manufacturer’s profit is highest in the R model and for the retailer the retailer’s profit reaches its highest in the M2 model. As shown in Figure 8, the impact of the government’s green degree subsidy coefficient on the manufacturer’s profit under three different subsidy strategies is evident. The manufacturer’s profit increases as the green degree subsidy coefficient rises. Furthermore, the impact of the subsidy coefficient on the manufacturer’s profit is more pronounced under the sales effort cost subsidy compared to both the green degree subsidy and the R&D cost subsidy. This may be because of the low green demand in the market, and the government subsidizes the retailer’s green sales efforts, which can motivate them to invest more green sales efforts and expand the green demand in the market, and then the manufacturer will have higher profits. At the same time, under the same government financial subsidy expenditure, if only the subsidy is given to the manufacturer, the green degree subsidy is obviously more conducive to improving the economic benefits of manufacturers compared with the R&D and innovation cost subsidy.

Figure 8

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The effect of government subsidy on manufacturer’s profit. Source: Authors’ own work

Figure 9

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The effect of government subsidy on retailer’s profit. Source: Authors’ own work

As illustrated in Figure 9, the impact of the government’s green degree subsidy coefficient on the retailer’s profit under three different subsidy strategies is evident. The retailer’s profit increases with the green degree subsidy coefficient. However, when the subsidy coefficient is low, the impact on the retailer’s profit under the R&D cost subsidy is greater than that under the sales effort cost subsidy. Conversely, when the subsidy coefficient is high, the impact under the sales effort cost subsidy becomes greater than that under the R&D cost subsidy, and it consistently remains higher than the impact of the green degree subsidy. When the government subsidy coefficient is small, the retailer’s capital and technology are limited, leading to the lack of active green sales in the early stage, which cannot fully compensate the costs generated by their sales efforts, resulting in their lack of enthusiasm to sell green products, and makes their profit lower than the R&D cost subsidy strategy. When the subsidy coefficient is high, the retailer acquires sufficient funds and resources, enhancing their sales initiative and investing more capital and labor into selling green products, thereby increasing their economic benefits. At this point, their profit surpasses that of the R&D cost subsidy strategy. Additionally, under identical financial subsidy expenditures, if the subsidy is provided to the manufacturer, the retailer realizes higher economic benefits under the green R&D cost subsidy mechanism compared to the green degree subsidy.

This shows that subsidizing the retailer is better when the supply chain pursues the interests of the manufacturer. When the supply chain pursues the benefit of the retailer and the subsidy coefficient is lower than a certain threshold, subsidizing the manufacturer is favorable. When the subsidy coefficient is greater than a certain threshold, it is more advantageous to subsidize the retailer directly. Second, if only considering subsidy to the manufacturer, then green R&D innovation cost subsidy is more favorable for the retailer; whereas for the manufacturer, the manufacturer prefers to green subsidy.

As can be seen from Figure 10, the influence of consumer sensitivity coefficient on social welfare under the three government subsidy strategies. Social welfare increases with the consumers’ sensitivity coefficient to green degree. The increase of consumers' sensitivity to green degree means that consumers are willing to pay higher prices to buy more green products, which also reflects the increasing awareness of environmental protection. The increase in social welfare indicates that consumers can achieve higher psychological satisfaction with increasing green preference. Therefore, in practice, measures should be taken to encourage consumers to actively improve their awareness of green preference and establish the concept of green consumption, which is very important for the government to improve social welfare. Moreover, the change of consumers 'sensitivity coefficient to green degree has the same impact on the social welfare under manufacturers' green subsidy and R&D cost subsidy, which is always lower than the retailer’s green sales effort cost subsidy for the retailer. Consumers' green sensitivity coefficients affect social welfare, and the two subsidy mechanisms converge in their incentive effects on greenness in equilibrium, leading to a consistency in the impact of changes in consumers' green sensitivity coefficients on social welfare This shows that government subsidies can effectively improve social welfare, and the government can promote social welfare through subsidy distribution. At the same time, direct subsidies to the retailer are more conducive to the development of green industries. In order to improve social welfare, the government must implement subsidies for green products.

Figure 10

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The effect of government subsidy on social welfare. Source: Authors’ own work

Under the same government subsidy expenditure, the social welfare under subsidizing the retailer will be higher compared with the subsidy to the manufacturer, that is, the government is more inclined to subsidize the green sales effort cost for the retailer.

It can be seen that under the condition of the same government subsidies, The ranking of supply chain index values (wholesale price, product green degree, retail price, sales effort level, manufacturer profit, retailer profit, social welfare) corresponding to the three government subsidy strategies is not exactly the same. This ranking is also the ranking of the merits and disadvantages of the three government subsidy strategies under different supply chain indicators. The government can comprehensively choose the subsidy strategy according to different subsidy objectives, and consider from many aspects, so as to be more conducive to maintaining the sustainable development of the supply chain members.

8. Concluding remarks and future research directions

This paper considers the green supply chain game model composed of the government, a green product manufacturer and a green product retailer, with the manufacturer as the leader and the retailer as the follower. In order to encourage the development of green supply chain, the government will subsidize the manufacturer’s green degree of products, the green R&D innovation cost, and the green sales effort cost of the retailer. We analyze the impact of government subsidy to the manufacturer (green degree subsidy and green R&D innovation cost subsidy) and subsidy to the retailer(green sales effort cost subsidy) on supply chain pricing decisions, member profits and social welfare, thus we can obtain the following conclusions:

Government subsidies will encourage the manufacturer to produce greener product. Encouraging the manufacturer to produce greener products is better than subsidizing the retailer. Compared with subsidy to the manufacturer, cost subsidies for the retailer’s green sales efforts can directly act on the retailer to encourage them to pay more green sales efforts and increase the sales volume of green products.
With the same government subsidies, considering only the manufacturer, the benefits of the supply chain members benefit the green innovation cost subsidy for the retailer; the subsidy strategy can stimulate the supply chain manufacturer to increase the green level of the products and improve the green level of the products than subsidizing the retailer. Under the same government subsidy expenditure, if only consider subsidy to the manufacturer, green R&D innovation cost subsidies are more favorable for the retailer; for the manufacturer, the green degree of subsidy is more favorable. Either kind of subsidy strategy can effectively stimulate the supply chain manufacturer to improve the green degree of their products, and the subsidy to the manufacturer is more effective in promoting the green degree of their products than subsidizing the retailer.
Government subsidies can effectively improve social welfare, and the government can promote the improvement of social welfare through the distribution of subsidies. At the same time, direct subsidy to the retailer is more conducive to the development of green industries. Under the same government subsidy expenditure, the social welfare under the subsidy to the retailer is higher than that under the subsidy to the manufacturer, that is, the government is more inclined to subsidize the green sales effort cost to the retailer.

9. Management implications

This article has the following management implications: In the green supply chain, the more sensitive consumers are to the green sales efforts of products, the more the retailer can be encouraged to pay more sales efforts to sell green products and expand their market share. The manufacturer can use this effect to increase the wholesale price and the greening of products to build a green image.

In fact, the government should take measures to encourage consumers to actively improve their awareness of green preference and establish the concept of green consumption, which is crucial for the government to improve social welfare. The government should give certain financial subsidies to encourage the manufacturer to take consumers as an important influencing factor, pay close attention to consumers’ sensitivity to the green degree of products, and promote the improvement of consumers’ awareness of environmental protection, which is conducive to the implementation of green supply chain.

When the government subsidy to the manufacturer is small, even if the government does not subsidize the retailer, the retailer’s income increases with government subsidies, thus “free rider” behavior, it will compress the manufacturer’s earnings, which leads to members of the supply chain income distribution imbalance, at this point, the government can take certain punitive measures to balance the economic benefits between members, such as to impose a certain proportion of additional taxes on the retailer, etc. In order to make the social benefits optimal, the government should adjust the subsidy proportion according to the differences of the subsidy objects in different industries, comprehensively select the subsidy strategies according to different subsidy objectives, and consider the subsidy strategies from various aspects to maintain the sustainable development of the supply chain.

The government subsidy strategy analyzed in this study is for the manufacturer and retailer, and in fact, the government will also subsidize green consumers. This study is conducted under the condition of supply chain information symmetry. When the manufacturer’s green R&D innovation cost information or the retailer’s green sales effort cost information is private information, the government subsidy decision problem when unilateral or bilateral information asymmetry deserves further study. The comparative analysis of the three government subsidy strategies in this study is that the government subsidy expenditure is the same, and other government goals can also be selected, such as the maximum government net income, which are all possible research directions in the future.

To sum up, the research emphasizes the key role of government subsidies in promoting the development of green supply chain. Enterprises should pay close attention to the government’s subsidy policies and actively apply for relevant subsidies to reduce their own cost of green transformation. Members of the supply chain should strengthen communication and cooperation, and jointly develop green supply chain strategies to maximize the overall benefits. Consumers 'awareness of environmental protection is increasing, and the market demand for green products is increasing. Enterprises should pay attention to improving the greening of products to meet consumers' demand for environmental protection products. At the same time, they should enhance consumers' awareness and acceptance of green products through marketing and other means. Just like Volkswagen, it has been committed to producing environmentally friendly products and actively building a green supply chain. In the production process, the enterprise pays attention to resource conservation and environmental protection, cooperates with upstream and downstream enterprises in the supply chain, and jointly promotes the green transformation through the incentive effect of government subsidies, achieving a win-win situation of environmental benefits and economic benefits, and making contributions to the sustainable development of the society.

Combine environmental economics with supply chain management, further explore how the principle of environmental economics can be applied to supply chain management to optimize resource utilization and reduce environmental impact; and integrate the integration of sustainable development theory into green supply chain management to ensure the coordinated development of economic, social and environmental dimensions of supply chain. The future research direction can be based on the deepening of theoretical basis, technological innovation and application, policies and regulations, which will help to promote the in-depth development of green supply chain and achieve the sustainable development goal.

This work was supported by the Major Research Project of Philosophy and Social Science in Hubei Province (Preliminary Funding Project of Provincial Social Science Fund) (No: 22ZD086) and the Major Research Project of Philosophy and Social Science in Hubei Province (Preliminary Funding Project of Provincial Social Science Fund) (No: 22ZD086).

Data availability statement: All the data within this manuscript will be provided upon request.

Conflict of interest statement: We state that there is no conflict of interest within this manuscript.

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Pricing decisions of green supply chain considering products’ green degree and sales efforts under government subsidy

1. Introduction

2. Literature review

2.1 Research on supply chain decision-making based on government subsidies

2.2 Research on the greening degree of products in the supply chain

2.3 Research on green sales effort in the supply chain

3. Model description and assumptions

3.1 Model description

3.2 Assumptions

4. Model analysis

4.1 Green degree subsidy(Strategy $M_{1}$ ⁠)

4.2 Green R&D innovation cost subsidy(Strategy $M_{2}$ ⁠)

4.3 Green sales effort cost subsidies(Strategy $R$ ⁠)

5. Equilibrium analysis

6. Comparison analysis

7. Numerical analysis

8. Concluding remarks and future research directions

9. Management implications

References

Further reading

Supplementary data

Email Alerts

Cited By

Pricing decisions of green supply chain considering products’ green degree and sales efforts under government subsidy Open Access

1. Introduction

2. Literature review

2.1 Research on supply chain decision-making based on government subsidies

2.2 Research on the greening degree of products in the supply chain

2.3 Research on green sales effort in the supply chain

3. Model description and assumptions

3.1 Model description

3.2 Assumptions

4. Model analysis

4.1 Green degree subsidy(Strategy M1⁠)

4.2 Green R&D innovation cost subsidy(Strategy M2⁠)

4.3 Green sales effort cost subsidies(Strategy R⁠)

5. Equilibrium analysis

6. Comparison analysis

7. Numerical analysis

8. Concluding remarks and future research directions

9. Management implications

References

Further reading

Supplementary data

Email Alerts

Suggested Reading

Related Chapters

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Cited By

Pricing decisions of green supply chain considering products’ green degree and sales efforts under government subsidy

4.1 Green degree subsidy(Strategy $M_{1}$ ⁠)

4.2 Green R&D innovation cost subsidy(Strategy $M_{2}$ ⁠)

4.3 Green sales effort cost subsidies(Strategy $R$ ⁠)