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Article

Optimal Strategies in Green Supply Chains When Considering Consumers’ Green Preferences and Government Subsidies

1
School of Economics and Management, Nanjing Tech University, Nanjing 211816, China
2
School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(13), 2209; https://doi.org/10.3390/math13132209
Submission received: 31 May 2025 / Revised: 24 June 2025 / Accepted: 5 July 2025 / Published: 7 July 2025

Abstract

Green and low-carbon development of supply chains represents a practical approach to addressing climate change and enhancing corporate competitiveness. From the perspective of the relationship between policy subsidies and channel power structures, this paper constructs Stackelberg game models under four different scenarios to conduct theoretical analyses of the optimal strategies, supported by numerical simulations. The research findings reveal the following. (1) Under the product subsidy policy, the enhancement of consumers’ green preference will lead to a green premium, and in the case of the technology subsidy policy, consumers’ green preference will inhibit wholesale prices and retail prices. However, there is a threshold in the manufacturer-led case, and a “green premium” is also claimed when this threshold is exceeded. (2) The effects of the product subsidy policy and the green technology level subsidy policy on prices are opposite, where an increase in the product subsidy will increase the wholesale price and retail price, while an increase in the green technology level subsidy will reduce the wholesale price. The technology subsidy policy has a more significant effect on the promotion of green technology. (3) The power of supply chain channels will directly affect corporate profits, and the leader of the supply chain often has higher profits. Compared with product subsidies, technology subsidies can inhibit the channel power of retailers.

1. Introduction

As global climate change and resource constraints become increasingly severe, the green and low-carbon transition has emerged as a core agenda for economic and social development worldwide. Against this backdrop, green and low-carbon development in supply chains serves not only as a key lever for addressing climate change but also as a strategic choice for enterprises seeking to build sustainable competitiveness [1,2,3]. However, interventions from multiple external factors, such as consumers’ green preferences and policy uncertainty, significantly increase the complexity of decision-making in green supply chains. Concurrently, internal supply chain factors, including channel power structures and sales effort levels, further intensify the decision-making challenges faced by green supply chain enterprises. Therefore, systematically examining the optimal strategies for green supply chains under the interaction of consumers’ green preferences, policy uncertainties, and supply chain power structures holds significant practical importance for resolving the “green premium” dilemma and achieving synergy between economic and environmental performance.
In recent years, the research on the impact of external factors on green supply chains can be categorized into three aspects. First, the influence of consumer green preference [4,5,6,7]. For instance, Meng et al. (2021) [5] proposed a dual-channel green supply chain model that considers both consumers’ green preferences and channel preferences. Second, the impact of government subsidy policies [8,9,10]. For example, Liang et al. (2025) [10] explored pricing strategies under different financing modes and investigated how subsidies affect green transformation, value creation, and financing equilibrium in supply chains. Third, the effect of environmental policies [11,12,13]. Gao et al. (2020) [11] addressed dual-channel green supply chain management challenges under eco-labeling policies. By designing contracts that enable supply chain members to make informed decisions, they achieved increased profitability while greening the supply chain, revealing how eco-labeling policies impact both economic and environmental performance. Internal factors within green supply chains also significantly influence corporate decision-making. Existing research unfolds across three dimension. First, the product greenness level in supply chains [14,15,16]. Miyamoto (2023) [16] constructed a two-stage Stackelberg model where suppliers produce marginally cost-intensive green products, comparing the green product diffusion and social surplus across supply chain networks with and without environmental product standards. Second, the supply chain channel power [17,18,19]. Lou et al. (2020) [17] modeled a supplier–manufacturer system using game theoretic approaches to examine how different power structures affect green practices in supply chains. Third, the internal supply chain competition [20,21,22]. Peng et al. (2022) [22] investigated competitive and cooperative strategies in dual-channel supply chain pricing and green marketing, considering customer satisfaction. In Model 1, two retailers cooperate with the manufacturer while competing, while in Model 2, Retailer 1 cooperates with the manufacturer and competes with Retailer 2. Existing research primarily focuses on individual external factors such as consumers’ green preferences and government subsidies, with insufficient exploration of optimal decision-making in green supply chains under the impact of multiple factors. This paper incorporates external consumers’ green preferences, sales effort sensitivities, and internal product green technology levels and retailer sales efforts into a multi-factor-driven analytical framework, providing a better understanding of how factors such as consumers’ green preferences and government subsidies influence optimal decisions in green supply chains.
In summary, in order to explore how consumers’ green preferences, external factors of government subsidies and channel power structures affect the optimal decision-making in green supply chains, this study employs Stackelberg game models to construct green supply chain decision-making models under four scenarios, considering government subsidies and channel power structures from different perspectives. Theoretical analysis is conducted of the optimal decisions for manufacturers and retailers, complemented by numerical simulations that examine the impact of consumers’ green preferences and government subsidy levels on optimal strategies. The innovation of this research is as follows. (1) Expanding the existing demand function to only consider the price factor and the degree of sales effort, taking into account the green preferences of consumers and the level of green technology of products, constructing a unified analytical framework driven by multi-dimensional factors, and revealing the decision-making mechanism of green supply chains under the interaction of multiple factors. (2) Overcoming the limitations of existing studies that separate consumers’ green preferences, government subsidy policies, and the internal structure of the supply chain, based on the perspective of channel power structure and government subsidy association, a dynamic game model under four scenarios (PM/PR/TM/TR model) is constructed, which accurately depicts the non-cooperative equilibrium state of manufacturers and retailers in pricing decisions, green technology input decisions, and sales effort input decisions, which is helpful in understanding supply chain decisions under different policies and market demands. (3) This study yields some novel and practically significant conclusions: under the technology subsidy policy, wholesale and retail prices are suppressed, whereas the product subsidy policy leads to a “green premium.” When consumers’ green preferences are powerful, even a manufacturer-led scenario will charge a “green premium.” Furthermore, supply chain channel power has a direct impact on corporate profits, with the supply chain leader earning higher profits.
The rest of this article is organized as follows. Section 2 is the problem description and model assumptions. Section 3 is the model building and model solving. Section 4 analyzes the impact of consumers’ green preference and government subsidies on optimal decision-making. Section 5 is the simulation analysis. Section 6 is the conclusions and discussion.

2. Problem Description and Model Assumptions

This study constructs a green supply chain composed of a manufacturer and a retailer. The manufacturer produces green products using green technology, wholesaling them at a manufacturing cost that is passed on to the retailer as the price w . The retailer then sells the products to end customers at the retail price p (the retail price is higher than the wholesale price, p > w ). Government subsidies serve as a crucial instrument for enhancing the greenness of products and promoting environmentally friendly products. The research incorporates two subsidy policies: a product subsidy targeting end consumers and a green technology subsidy targeting manufacturers. Considering different channel power structures, we develop Stackelberg game models under four scenarios (as shown in Figure 1). For analytical clarity, the following assumptions are made:
Assumption 1.
The manufacturer is responsible for producing green products with a green technology level of e . Referring to [23,24,25], the relationship between the technological R&D cost and the technology level is given by  C r = 1 2 k e 2  , where  k  denotes the green technology R&D cost coefficient. The fixed cost for manufacturing green products is  c .
Assumption 2.
The retailer orders green products from the manufacturer according to market demand, ensuring that all the green products are fully cleared. To enhance the green product sales, the retailer engages in sales effort behavior, incurring a sales effort cost. Referring to [26,27], the relationship between the sales effort cost and the sales effort level is given by the following function: C s = 1 2 η θ 2 , where  η  denotes the sales effort cost coefficient, and  θ  represents the retailer’s sales effort level.
Assumption 3.
The product price is a critical factor influencing market demand. With continuously increasing consumer environmental awareness, the level of product greenness and the retailer’s sales effort also impact market demand. Referring to [28,29,30], the market demand q for the product is expressed as a linear function of the retail price  p  and green technology level  e  , that is,  q = a p + λ e + b θ  , where  a  denotes the potential market size,  λ  represents the consumer green preference coefficient, and  b  indicates consumer sensitivity to sales effort level. In order to facilitate the subsequent solution, p = w + m , m represents the retailer’s profit margin.
Assumption 4.
To accelerate the green product penetration, the government implements subsidy policies to enhance the product greenness and stimulate end consumer purchases. Two subsidy schemes are considered. The first is a per-unit product subsidy, that is, providing subsidies to consumers who purchase green products. This subsidy directly reduces the effective retail price, with a subsidy amount t . Referring to [6,31], the actual consumer purchase price becomes  p t  , and the demand function is  q = a ( p t ) + λ e + b θ  . The second is a green technology subsidy, that is, subsidizing manufacturers’ technological R&D costs by granting a per-unit subsidy based on the product’s greenness level  μ e  .
Assumption 5.
The production and consumption of green products contribute to carbon emission reduction, generating environmental benefits. Referring to [32,33,34], the emission reduction per product at different technology levels is assumed to be h e , where  h  denotes the manufacturer’s emission reduction efficiency coefficient.The environmental benefit per unit of emission reduction is  s  . Consequently, the total environmental benefit derived from selling all the green products is  Π E N = h e × q × s  .
The relevant symbols and their meanings are shown in Table 1.

3. Model Construction and Solution

In the green supply chain, the manufacturer decides the wholesale price and green technology level of the product, while the retailer determines the retail price and sales effort level. Both parties aim to maximize their profits. From the perspectives of supply chain channel power and policy subsidies, Stackelberg game models are developed under four scenarios. The models are then solved using the backward induction method.

3.1. Manufacturer-Led Model with Product Subsidies (PM)

In this scenario, the manufacturer holds the dominant position in the green supply chain. The manufacturer first decides the wholesale price and the product’s green technology level. Upon observing the manufacturer’s decisions, the retailer then determines the product’s retail price and the sales effort level. In this scenario, government subsidies are provided directly to end consumers. The objective functions for the manufacturer and retailer at this stage are:
Π M P M = ( w c ) ( a ( p t ) + λ e + b θ ) 1 2 k e 2
Π R P M = ( p w ) ( a ( p t ) + λ e + b θ ) 1 2 η θ 2
Using the backward induction method to solve this, let p = w + m , where m represents the retailer’s profit margin. Substituting p = w + m into Equations (1) and (2), and setting the first-order derivatives to zero, yields the retailer’s optimal response function for the profit margin and sales effort level:
m P M = η a + t w + e λ 2 η b 2
θ P M = b a + t w + e λ 2 η b 2
Substituting Equations (3) and (4) into Equation (1), for Equation (1) to achieve a maximum, the Hessian matrix k η λ 2 η b 2 η λ 2 η b 2 2 η b 2 2 η must be negative definite, satisfying 2 η b 2 > 0 and 4 k n n λ 2 2 k b 2 > 0 . At this point, setting the first-order derivatives to zero and solving simultaneously yields the manufacturer’s optimal decisions for the wholesale price and green technology level as follows:
w P M * = k a + c + t b 2 2 η + c η λ 2 2 b 2 k + η 4 k + λ 2
e P M * = a + c t η λ 2 b 2 k 4 k η + η λ 2
Substituting Equations (5) and (6) into Equations (3) and (4) and solving yields the retailer’s optimal decisions for the profit margin and sales effort level as follows:
m P M * = k a c + t η 2 b 2 k + 4 k η η λ 2
θ P M * = b k a c + t 2 b 2 k + η 4 k + λ 2
Summing Equations (5) and (7) yields the retail price of the green product:
p P M * = b 2 k a + c + t k 3 a + c + 3 t η + c η λ 2 2 b 2 k + η 4 k + λ 2
q P M * = k a c + t η 2 b 2 k + 4 k η η λ 2
Substituting Equations (5)–(9) into the profit functions of the manufacturer, the retailer, and the environmental performance function, the manufacturer’s profit, the retailer’s profit, and the environmental performance at this stage are, respectively,
Π M P M * = k a c + t 2 η 4 b 2 k + 2 η 4 k + λ 2
Π R P M * = k 2 a c + t 2 b 2 2 η η 2 2 b 2 k + η 4 k + λ 2 2
Π E N P M * = h k s a c + t 2 η 2 λ 2 b 2 k + η 4 k + λ 2 2

3.2. Retailer-Led Model with Product Subsidies (PR)

In this scenario, the retailer holds the dominant position in the green supply chain. The retailer first decides the retail price and sales effort level of the green product. Upon observing the retailer’s decisions, the manufacturer then makes its decisions. In this scenario, government subsidies are also provided directly to end consumers. The objective functions for the manufacturer and retailer at this stage are:
Π M P R = ( w c ) ( a ( p t ) + λ e + b θ ) 1 2 k e 2
Π R P R = ( p w ) ( a ( p t ) + λ e + b θ ) 1 2 η θ 2
Using backward induction, let p = w + m , and substitute into Equations (14) and (15) to obtain the manufacturer’s optimal response function for the wholesale price and green technology level:
w P R = k a + c m + t + b θ c λ 2 2 k λ 2
e P R = a c m + t + b θ λ 2 k + λ 2
Substituting Equations (16) and (17) into Equation (15), for the Hessian matrix 2 k λ 2 2 k b k 2 k λ 2 b k 2 k λ 2 η to be negative definite at this stage, the conditions 2 n ( 2 k λ 2 ) k b 2 > 0 and 2 k λ 2 > 0 must hold. Setting the first-order derivatives to zero and solving simultaneously yields the retailer’s decisions for the retail price and sales effort level:
m P R * = a c + t η 2 k λ 2 b 2 k + 4 k η 2 η λ 2
θ P R * = b k a c + t b 2 k 4 k η + 2 η λ 2
Substituting Equations (18) and (19) into Equations (16) and (17) yields the manufacturer’s optimal decisions:
w P R * = c + k a c + t η b 2 k + 4 k η 2 η λ 2
e P R * = a c + t η λ b 2 k + 2 η 2 k + λ 2
Solving further yields the optimal retail price and optimal sales volume for this scenario. The manufacturer’s optimal profit, retailer’s optimal profit, and environmental performance at this stage are, respectively, as follows:
p P R * = c + a c + t η 3 k λ 2 b 2 k + 4 k η 2 η λ 2
q P R * = k a c + t η b 2 k + 4 k η 2 η λ 2
Π M P R * = k a c + t 2 η 2 2 k λ 2 2 b 2 k + 2 η 2 k + λ 2 2
Π R P R * = k a c + t 2 η 2 b 2 k + 4 η 2 k + λ 2
Π E N P R * = h k s a c + t 2 η 2 λ b 2 k + 2 η 2 k + λ 2 2

3.3. Manufacturer-Led Model with Technology Subsidies (TM)

In this scenario, the manufacturer holds the dominant position in the green supply chain. Unlike the PM model, this scenario considers government subsidies provided to the manufacturer to encourage the product’s green level. The objective functions for the manufacturer and retailer at this stage are:
Π M T M = ( w c + μ e ) ( a p + λ e + b θ ) 1 2 k e 2
Π R T M = ( p w ) ( a p + λ e + b θ ) 1 2 η θ 2
Here, backward induction is also applied. Let p = w + m , substitute into Equations (27) and (28), and set the first-order derivative of Equation (28) to zero. This yields the retailer’s response function for the profit margin and sales effort level:
m T M = η a w + e λ b 2 + 2 η
θ T M = b a w + e λ b 2 2 η
Substituting the above Equations (29) and (30) into the manufacturer’s profit function, achieving a maximum requires 2 η b 2 2 η η ( μ λ ) b 2 2 η η ( μ λ ) b 2 2 η k 2 η μ λ b 2 2 η satisfying 2 η b 2 > 0 and 4 k η 2 k b 2 η ( λ + μ ) 2 > 0 . The optimal wholesale price and green technology level under this scenario are:
w T M * = c b 2 k 2 k η + η λ λ + μ + a b 2 k 2 k η + η μ λ + μ 2 b 2 k + η 4 k + λ + μ 2
e T M * = a c η λ + μ 2 b 2 k + η 4 k + λ + μ 2
Substituting Equations (31) and (32) into Equations (29) and (30) yields the retailer’s decisions for the profit margin and sales effort level:
m T M * = a c k η 2 b 2 k + η 4 k λ + μ 2
θ T M * = b a + c k 2 b 2 k + η 4 k + λ + μ 2
Summing Equations (31) and (33) yields the retail price of the green product:
p T M * = c b 2 k k η + η λ λ + μ + a b 2 k 3 k η + η μ λ + μ 2 b 2 k + η 4 k + λ + μ 2
Substituting Equations (31)–(35) and solving further yields the optimal sales volume, optimal profits, and environmental performance:
q T M * = a + c k η 2 b 2 k + η 4 k + λ + μ 2
Π M T M * = a c 2 k η 4 b 2 k + 2 η 4 k + λ + μ 2
Π R T M * = a c 2 k 2 b 2 2 η η 2 2 b 2 k + η 4 k + λ + μ 2 2
Π E N T M * = a c 2 h k s η 2 λ + μ 2 b 2 k + η 4 k + λ + μ 2 2

3.4. Retailer-Led Model with Technology Subsidies (TR)

In this scenario, the retailer holds the dominant position in the green supply chain. As in the TM scenario, government subsidies are granted to the manufacturer based on the product’s green level. The objective functions for the manufacturer and retailer at this stage are:
Π M T R = ( w c + μ e ) ( a p + λ e + b θ ) 1 2 k e 2
Π R T R = ( p w ) ( a p + λ e + b θ ) 1 2 η θ 2
Solve via backward induction. Let p = w + m , substitute into Equations (40) and (41), and set the first-order derivative of Equation (40) to zero. This yields the manufacturer’s response function for the wholesale price and green technology level:
w T R = c k λ λ + μ + a k μ λ + μ m b θ k μ λ + μ 2 k λ + μ 2
e T R = a c m + b θ λ + μ 2 k λ + μ 2
Substituting the response function into the retailer’s profit function, the requirement for a negative definite Hessian matrix 2 k 2 k λ + μ 2 b k 2 k λ + μ 2 b k 2 k λ + μ 2 η necessitates satisfying 2 η ( 2 k ( λ + μ ) 2 ) k b 2 > 0 and 2 k ( λ + μ ) 2 > 0 . Solving the system simultaneously yields the optimal profit margin and sales effort level as follows:
m T R * = a c η 2 k λ + μ 2 b 2 k + 2 η 2 k + λ + μ 2
θ T R * = b a + c k b 2 k + 2 η 2 k + λ + μ 2
Substituting Equations (44) and (45) into Equations (42) and (43) and solving yields the manufacturer’s optimal wholesale price and green technology level as follows:
w T R * = b 2 c k + η a k 3 c k + a μ λ + μ + c λ + μ 2 λ + μ b 2 k + 2 η 2 k + λ + μ 2
e T R * = a c η λ + μ b 2 k + 2 η 2 k + λ + μ 2
Solving further yields the retailer’s retail price and the sales volume of the green product as follows:
p T R * = b 2 c k + η 3 a k c k + c λ λ + μ + a λ + μ λ + 2 μ b 2 k + 2 η 2 k + λ + μ 2
q T R * = a + c k η b 2 k + 2 η 2 k + λ + μ 2
The manufacturer’s profit, retailer’s profit, and environmental performance at this stage are:
Π M T R * = a c 2 k η 2 2 k λ + μ 2 2 b 2 k + 2 η 2 k + λ + μ 2 2
Π R T R * = a c 2 k η 2 b 2 k + 4 η 2 k + λ + μ 2
Π E N T R * = a c 2 h k s η 2 λ + μ b 2 k + 2 η 2 k + λ + μ 2 2

4. Analysis of the Impact of Consumers’ Green Preferences and Government Subsidies on Optimal Decisions

4.1. Impact on Optimal Decisions Under the PM Scenario

Proposition 1.
w P M * λ > 0  ,  p P M * λ > 0  ,  e P M * λ > 0  ,  θ P M * λ > 0  ,  w P M * t > 0  ,  p P M * t > 0  ,  e P M * t > 0  ,  θ P M * t > 0  .
Proposition 1 shows that in the case of PM, the wholesale price, retail price, green technology level, sales effort and consumer green preference are positively correlated, and the wholesale price, retail price, green technology level, sales effort and government subsidy are also positively correlated.
The proof is in Appendix A.

4.2. Impact on Optimal Decisions Under the PR Scenario

Proposition 2.
w P R * λ > 0  ,  p P R * λ > 0  ,  e P R * λ > 0  ,  θ P R * λ > 0  ,  w P R * t > 0  ,  p P R * t > 0  ,  e P R * t > 0  ,  θ P R * t > 0  .
Proposition 2 indicates that under the PR scenario, the wholesale price, retail price, green technology level, and sales effort level exhibit positive correlations with the consumer green preference and government subsidy level.
The proof is in Appendix A.

4.3. Impact on Optimal Decisions Under the TM Scenario

Proposition 3.
k > η μ λ + μ 2 ( 4 η λ 2 b 2 λ )  ,  w T M * λ > 0  ,  k < η μ λ + μ 2 ( 4 η λ 2 b 2 λ )  ,  w T M * λ < 0  ,  p T M * λ > 0  ,  e T M * λ > 0  ,  θ T M * λ > 0  ,  η λ λ + μ 2 + 2 k η λ μ + b 2 μ > 0  ,  w T M * μ > 0  ,  η λ λ + μ 2 + 2 k η λ μ + b 2 μ < 0  ,  w T M * μ < 0  ,  η > 2 k ( η μ b 2 μ ) λ ( λ + μ 2 + 2 k )  ,  p T M * μ > 0  ,  η < 2 k ( η μ b 2 μ ) λ ( λ + μ 2 + 2 k )  ,  p T M * μ < 0  ,  e T M * μ > 0  ,  θ T M * μ > 0  .
Proposition 3 indicates that under the TM scenario, the green technology level and sales effort level exhibit positive correlations with the consumer green preference and government subsidy level. When k > η μ λ + μ 2 ( 4 η λ 2 b 2 λ ) , the wholesale price increases with rising consumer green preference; otherwise, it decreases. The retail price exhibits a positive correlation with the consumer green preference. When η λ λ + μ 2 + 2 k η λ μ + b 2 μ > 0 is satisfied, the wholesale price increases monotonically with a rising government subsidy level; otherwise, it decreases. When η > 2 k ( η μ b 2 μ ) λ ( λ + μ 2 + 2 k ) , the retail price increases with a rising government subsidy level.
The proof is in Appendix A.

4.4. Impact on Optimal Decisions Under the TR Scenario

Proposition 4.
k > 2 η μ λ + μ 2 ( 4 η λ + b 2 μ )  ,  w T R * λ > 0  ,  k < 2 η μ λ + μ 2 ( 4 η λ + b 2 μ )  ,  w T R * λ < 0  ,  k > 2 η μ λ + μ 2 4 η λ + 2 b 2 λ + 3 b 2 μ  ,  p T R * λ > 0  ,  k < 2 η μ λ + μ 2 4 η λ + 2 b 2 λ + 3 b 2 μ  ,  p T R * λ < 0  ,  e T R * λ > 0  ,  θ T R * λ > 0  ,  b 2 k λ + 2 μ + 2 η 2 k μ + λ λ + μ 2 > 0  ,  w T R * μ > 0  ,  b 2 k λ + 2 μ + 2 η 2 k μ + λ λ + μ 2 < 0  ,  w T R * μ < 0  ,  b 2 k 3 λ + 4 μ + 2 η 2 k μ + λ λ + μ 2 > 0  ,  p T R * μ > 0  ,  b 2 k 3 λ + 4 μ + 2 η 2 k μ + λ λ + μ 2 < 0  ,  p T R * μ < 0  ,  e T R * μ > 0  ,  θ T R * μ > 0  .
Proposition 4 indicates that under the TR scenario, the green technology level and sales effort level exhibit positive correlations with the consumer green preference and government subsidy level. When k > 2 η μ λ + μ 2 ( 4 η λ + b 2 μ ) , the wholesale price increases with rising consumer green preference. When k > 2 η μ λ + μ 2 4 η λ + 2 b 2 λ + 3 b 2 μ , the retail price increases with rising consumer green preference. When b 2 k λ + 2 μ + 2 η 2 k μ + λ λ + μ 2 > 0 , the wholesale price increases with a rising government subsidy level. When b 2 k 3 λ + 4 μ + 2 η 2 k μ + λ λ + μ 2 > 0 , the retail price increases with a rising government subsidy level.
The proof is in Appendix A.

5. Simulation Analysis

To more intuitively demonstrate the impact of changes in the parameters (such as consumers’ green preferences and government subsidies) on the optimal decisions, environmental benefits, and profits, this section conducts a simulation analysis using specific numerical values. With reference to [35,36], the baseline values are set as follows: a = 50 , b = 0.5 , c = 5 , k = 1000 , η = 500 , λ = 3 , h = 0.5 , s = 6 , μ = 20 , t = 20 .

5.1. Analysis of the Impact of Consumers’ Green Preferences

Setting the consumer green preference, we explore the impact of changes in consumers’ green preferences on the optimal pricing strategies (such as the wholesale price and retail price). The simulation results are shown in Figure 2, Figure 3, Figure 4 and Figure 5.

5.1.1. Effects of Consumers’ Green Preferences on Wholesale Price and Retail Price

Figure 2a and Figure 2b, respectively, illustrate the impact of changes in consumers’ green preferences on the manufacturer’s wholesale price and the retailer’s retail price. As seen in Figure 2a, under the product subsidy scenario, the wholesale price increases with rising consumer green preference. This is because, in the context of consumer subsidies, a stronger consumer preference for green products leads to higher tolerance for green product prices, prompting manufacturers to raise wholesale prices to capture part of the green premium. Conversely, under the technology subsidy scenario, the wholesale price in the manufacturer-led supply chain exhibits a “U-shaped” trend, decreasing first and then increasing. In contrast, the wholesale price in the retailer-led supply chain shows a decreasing trend. This suggests that technology subsidies granted to manufacturers can lower the wholesale price; however, when the manufacturer holds a dominant position in the supply chain and consumer green preferences are strong, the manufacturer will increase the wholesale price to capture the premium. Furthermore, compared to scenarios where the retailer is dominant, the wholesale price of green products is higher when the manufacturer is the dominant player in the supply chain. This demonstrates that the supply chain channel power has a significant influence on the wholesale price. These findings are also consistent with Propositions 1 to 4.
As seen in Figure 2b, when the consumer green preference strengthens, the retail price decreases only under the TR scenario. In the other three scenarios, the retail price rises with increasing consumer green preference. This occurs because the wholesale price is lower under the TR scenario, and the government subsidy is given directly to the manufacturer. Even when the retailer is the dominant player in the supply chain, it lacks absolute pricing power. Analysis combining Figure 2a reveals that the retail price premium for green products is higher under retailer dominance, generally exceeding twice the wholesale price. Comparing the product subsidy policy and the technology subsidy policy, it is found that the sales price of green products is higher under the product subsidy policy. Further analysis of the retailer-led scenarios under both policies reveals that retailers possess greater pricing power under the product subsidy policy. This suggests that the green technology subsidy policy weakens the retailer’s channel power. The above conclusions are consistent with the analysis of the retail prices in Propositions 1 to 4.

5.1.2. Effects of Consumers’ Green Preferences on Green Technology Level and Sales Effort Level

Figure 3a and Figure 3b, respectively, illustrate the impact of changes in consumers’ green preferences on the green technology level and the sales effort level. As seen in Figure 3a, the green technology level of the product increases with strengthening consumer preference under all four scenarios. This suggests that consumers’ green preferences can promote the enhancement of a product’s green technology level. A comparative analysis of the changes in the green technology level across the four scenarios reveals that the product’s green technology level under the TR scenario is most sensitive to consumers’ green preferences, exhibiting the fastest growth rate. Comparing the green technology levels under different channel power structures reveals that the green technology level is higher when the retailer holds a dominant position in the supply chain. This occurs because the retailer, as the endpoint directly facing consumers, responds more rapidly to the market demand. Being dominant in the supply chain, the retailer transmits information prompting the manufacturer to enhance the green technology level. These findings are consistent with the analysis of the green technology level in Propositions 1 to 4.
As seen in Figure 3b, the retailer’s sales effort level exhibits a positive correlation with consumers’ green preferences under all four scenarios. The change in the sales effort level is most pronounced under the TR scenario, while the growth is slowest under the PM scenario. A comparative analysis reveals that when a retailer dominates the supply chain, it exerts a greater sales effort. This is because the retailer possesses pricing power for the product, leading to higher profit margins, which in turn incentivize a greater sales effort. Furthermore, the comparative analysis also reveals that the green technology subsidy policy has a significantly more substantial effect on boosting the sales effort level than the product subsidy policy. This occurs because the green technology subsidy policy directly targets manufacturers, leading to a more significant improvement in the green technology level of the supply chain’s products. Consequently, retailers are also motivated to increase sales efforts to drive profit growth. The above conclusions are consistent with the analysis of the sales effort level in Propositions 1 to 4.

5.1.3. Effects of Consumers’ Green Preferences on Sales Volume and Environmental Benefits

Figure 4a and Figure 4b, respectively, illustrate the impact of changes in consumers’ green preferences on the sales volume and environmental benefits. As shown in Figure 4a, when consumers’ preference for green products increases, the sales volume of green products also exhibits varying degrees of growth. The sales growth of green products is fastest under the TR scenario, followed by the TM scenario, while the growth is slowest under the PM scenario. A comparative analysis reveals that the sales volume of green products is higher in retailer-dominated supply chains. This occurs because retailers can promptly capture changes in consumer demand and utilize their channel power within the supply chain to adjust key strategies, thereby achieving higher sales volumes and better profits. Although the product subsidy policy directly targets end consumers, its impact on the sales volume is not significant. This is because the final retail price under the product subsidy policy is significantly higher than that under the green technology subsidy policy. This also suggests that, even with an enhanced green preference, consumers are unwilling to pay excessive green premiums. As shown in Figure 4b, strengthening consumer green preferences can lead to improved environmental benefits. Among the four scenarios, the ecological benefits are highest under the TR scenario and lowest under the PM scenario. A comparative analysis reveals that the changes in environmental benefits are most sensitive to the green technology subsidy policy.

5.1.4. Effects of Consumers’ Green Preferences on Profit

Figure 5a and Figure 5b, respectively, illustrate the impact of changes in consumers’ green preferences on the manufacturer’s and retailer’s profits. As seen in Figure 5a, the manufacturer’s profits increase with rising consumer green preference across all four scenarios, though the growth rates differ. The profit growth for manufacturers is more pronounced under the green technology subsidy policy. Although the manufacturer’s profits also rise under the product subsidy policy, the magnitude of the growth is not significant. Comparing the manufacturer’s profits across the four scenarios reveals that the profits are higher when the manufacturer holds the dominant position in the supply chain compared to when the retailer is dominant. Moreover, under the PM scenario, the manufacturer’s profits substantially exceed those in the other three scenarios.
As shown in Figure 5b, the retailer’s profits exhibit varying degrees of growth across the four scenarios. The profits are higher when the retailer itself holds the dominant position in the green supply chain compared to subordinate positions. Comparing the profits across the scenarios, the profit value is highest under the PR scenario and lowest under the TM scenario. The two policies also differ in their impact on the retailer’s profits: the manufacturer’s profits under the green technology subsidy policy are more sensitive to changes in consumers’ preferences for green products. This occurs because key factors, such as the level of green technology, sales effort, and sales volume, exhibit more substantial changes under this policy.

5.2. Analysis of the Impact of the Government Subsidy Level

Setting the subsidy levels under both government subsidy policies as t [ 0 , 40 ] and μ [ 0 , 40 ] , we explore the impact of changes in the government subsidy levels on the optimal strategies (such as the wholesale price and retail price). The simulation results are shown in Figure 6, Figure 7, Figure 8 and Figure 9.

5.2.1. Effects of Government Subsidy Level on Wholesale Price and Retail Price

Figure 6a and Figure 6b, respectively, illustrate the impact of the government subsidy level on the wholesale price and retail price. As seen in Figure 6a, the wholesale price movements exhibit opposite trends under the two different subsidy policies. Under the product subsidy policy, the wholesale price increases as the government subsidy level rises. Conversely, under the green technology subsidy policy, the wholesale price decreases as the government subsidy level increases. This divergence arises because the product subsidy enhances the end purchaser’s purchasing power, leading to increased demand for green products. Consequently, retailers raise the retail prices, and manufacturers need to capture a portion of the premium. In contrast, the green technology subsidy reduces the manufacturing costs for producers, resulting in a lower wholesale price. A comparative analysis reveals that when a manufacturer holds a dominant position in the green supply chain, it commands a higher wholesale price. The above conclusions are consistent with Propositions 1 to 4.
As shown in Figure 6b, under the product subsidy policy, the retail price exhibits an upward trend, whereas under the green technology subsidy policy, it displays an accelerating downward trend. The rise in the retail price under the product subsidy policy stems primarily from the subsidy stimulating market prices via the demand side. Conversely, the accelerating decline in the retail price under the green technology subsidy policy originates from supply-side technological progress and cost compression. Analysis of the prices across the four models reveals that the retail prices are higher under manufacturer dominance than under retailer dominance. This is mainly driven by the higher wholesale prices under manufacturer dominance, as shown in Figure 6a. Combining this with the analysis in Figure 6a, it is evident that retailers set higher retail prices when they are dominant, resulting in higher retailer profit margins in this scenario. The above conclusions are consistent with Propositions 1 to 4.

5.2.2. Effects of Government Subsidy Level on Green Technology Level and Sales Effort Level

Figure 7a and Figure 7b, respectively, illustrate the impact of the government subsidy level on the green technology level and sales effort level. As seen in Figure 7a, the technology level increases with a rising government subsidy level across all four scenarios, but the magnitude of the change varies significantly. Under the product subsidy policy, the level of green technology shows a slight increase. In contrast, under the green technology subsidy policy, the green technology level exhibits an accelerating rise, resulting in a higher level of green technology for the product at this point. Comparative analysis reveals that the green technology level of products in the supply chain is higher under retailer dominance. This is also because retailers are sensitive to changes in the end consumer demand and can leverage their dominant power within the supply chain to achieve optimal technological adjustments. The above conclusions are consistent with Propositions 1 to 4.
As shown in Figure 7b, the sales effort level increases with rising government subsidies under all four scenarios; however, the extent of the change differs. Under the green technology subsidy policy, the sales effort level shows an accelerating increase as the government subsidy level strengthens. Conversely, under the product subsidy policy, the sales effort level exhibits a linear relationship with the level of government subsidy. Comparing the impact of different channel power structures on the sales effort level, the analysis shows that the sales effort level is higher under retailer dominance than under manufacturer dominance. This is because, when dominant, retailers possess product pricing power and are more willing to exert effort in selling green products to enhance their performance and profits. The above conclusions are consistent with Propositions 1 to 4.

5.2.3. Effects of Government Subsidy Level on Sales Volume and Environmental Benefits

Figure 8a and Figure 8b, respectively, illustrate the impact of the government subsidy level on the sales volume and environmental benefits. As shown in Figure 8a, when the government subsidy level increases, the sales volume also rises accordingly. Among the four scenarios, under the green technology subsidy policy, the sales volume exhibits an accelerating increase. Conversely, under the product subsidy policy, the sales volume shows a linear relationship with the subsidy level. The sales volume is higher under retailer dominance than under manufacturer dominance. As shown in Figure 8b, the environmental benefits exhibit a positive correlation with the level of government subsidy. Under the product subsidy policy, an increase in the subsidy level results in only a slight rise in the environmental benefits. Therefore, it can be concluded that the green technology subsidy policy is more effective in promoting ecological benefits.

5.2.4. Effects of Government Subsidy Level on Profit

Figure 9a and Figure 9b, respectively, illustrate the impact of the government subsidy level on the manufacturer’s and retailer’s profits. As seen in Figure 9a, the manufacturer’s profits increase as the government subsidy level strengthens. Among the four scenarios, the profits are highest under the PM scenario and lowest under the TR scenario. This indicates that retailer dominance in the green supply chain severely compresses the manufacturer’s profits. Even though the government subsidy level leads to rapid sales growth under the TR scenario, it cannot compensate for the profit loss caused by the compressed wholesale price. The manufacturer’s profits under the TR scenario exceed those in other scenarios only when the government subsidies reach a certain threshold.
As seen in Figure 9b, the retailer’s profits also rise with an increase in the government subsidy level. Under the product subsidy policy, the retailer’s profits exhibit a linear relationship with the level of government subsidy. Conversely, under the green technology subsidy policy, the retailer’s profits show an accelerating increase. Comparative analysis reveals that the rise in the green product retail price caused by the product subsidy policy is key to its profit increase. Since the profits under the TM and TR scenarios exhibit an accelerating upward trend, this indicates that as the government subsidies increase, the earnings under the green technology subsidy policy surpass those under the product subsidy policy.

6. Conclusions and Discussion

This study constructs Stackelberg game models under four scenarios based on the linkage between government subsidies and supply chain channel power structures. Theoretical analysis of the optimal decisions across these scenarios is conducted, supplemented by simulation analysis using specific numerical values. The main conclusions are as follows.
(1) There are significant differences in the impact of consumers’ green preferences on the optimal decision-making under the different modes. In the presence of product subsidy policies, the enhancement of consumers’ green preferences will lead to green premiums, which are manifested in the increase of wholesale prices and retail prices, which are significantly higher than those under technology subsidy policies. In the presence of technology subsidy policies, consumers’ green preferences will suppress the wholesale and retail prices, but there is a threshold in the manufacturer-led case (the simulation results in this paper show that the threshold is around 2.5), and a “green premium” will be claimed when this threshold is exceeded. The impact of consumers’ green preferences on the other optimal decisions is positive.
(2) The impact of government subsidies on the optimal decision-making under the different models varies. The effect of the product subsidy policy on the price is opposite to that of the green technology level subsidy policy, with an increase in the product subsidy increasing the wholesale price and retail price, while an increase in the green technology subsidy will reduce the wholesale price. The technology subsidy policy has a more significant effect on the promotion of the green technology level, sales effort, sales volume and environmental benefits. However, manufacturers and retailers are more profitable under the product subsidy policy.
(3) The power of the supply chain channels will directly affect the corporate profits, and the leader of the supply chain often has higher profits. When retailers dominate green supply chains, they are more sensitive to changes in the consumer demand, but they compress manufacturers’ wholesale prices and raise retail prices. Technology subsidies can alleviate this problem compared to product subsidies.

Theoretical and Practical Implications

(1) Manufacturers and retailers can appropriately increase the wholesale and retail prices to obtain “green premiums” when consumers’ green preferences are high, but they cannot suppress demand. If there is a technology subsidy policy, you should take the initiative to reduce the price to gain market share. Manufacturers and retailers should balance the channel power, including through long-term agreements.
(2) The government should refine the subsidy policy and give priority to the technology subsidy policy, which directly stimulates the R&D of enterprises, improves environmental benefits, and helps reduce the “green premium”. In addition, dynamic subsidy adjustment is needed to strictly limit the “green premium” motivation of enterprises when consumers’ green preferences are enhanced. In the retailer-led supply chain, increase the proportion of technology subsidies to reduce the profit squeeze of retailers on manufacturers and maintain the stability of the supply chain.
(3) Consumers should consume rationally, identify the true environmental value of green products, and avoid paying for the “green premium”. Consumers are encouraged to supervise their pricing behavior through platform evaluations, social media and other channels and resist unreasonable price increases.
This paper enriches the research on green supply chain manufacturing decision-making and provides practical enlightenment for governments, enterprises, and consumers. Due to the difficulty of obtaining real data, the simulation benchmark values in this paper are all borrowed from the existing literature, which is the limitation of this study. There are still some areas that can be expanded in this paper, and the present study only considers a single policy, and in the future, it can be further studied from the perspective of the combination of carbon tax and subsidy policies.

Author Contributions

L.W.: Conceptualization and methodology. T.X.: Writing—original draft preparation and analysis. T.C.: Supervision, funding acquisition and calculation. L.W., T.X. and T.C. contributed equally to this work. They are co-first authors. All authors have read and agreed to the published version of the manuscript.

Funding

We wish to express our gratitude to the referees for their invaluable comments. This work was supported by the Major Projects of the National Social Fund [No. 22&ZD122].

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

Proof of Proposition 1.
w P M * λ = 2 k a c + t b 2 2 η η λ 2 b 2 k + η 4 k + λ 2 2 , because 2 η b 2 > 0 , a c + t > 0 ; therefore, w P M * λ > 0 . p P M * λ = 2 k a c + t b 2 3 η η λ 2 b 2 k + η 4 k + λ 2 2 ; similarly, p P M * λ > 0 . Since 4 k η η λ 2 2 k b 2 > 0 , e P M * λ = a c + t η 2 b 2 k + η 4 k + λ 2 2 b 2 k + η 4 k + λ 2 2 , we obtain e P M * λ > 0 . θ P M * λ = 2 b k a c + t η λ 2 b 2 k + η 4 k + λ 2 2 ; as above, we can obtain θ P M * λ > 0 . w P M * t = k b 2 2 η 2 b 2 k + η 4 k + λ 2 , since 2 η b 2 > 0 ; therefore, w P M * t > 0 . p P M * t = b 2 k 3 k η 2 b 2 k + η 4 k + λ 2 , b 2 k 3 k η = k ( b 2 3 η ) < 0 , p P M * t > 0 . e P M * t = η λ 2 b 2 k + η 4 k + λ 2 , it follows that p P M * t > 0 . θ P M * t = b k 2 b 2 k + η 4 k + λ 2 ; similarly, θ P M * t > 0 . □
Proof of Proposition 2.
w P R * λ = 4 k a c + t η 2 λ b 2 k + 4 k η 2 η λ 2 2 , since a c + t > 0 ; therefore, w P R * λ > 0 . p P R * λ = 2 k a c + t η b 2 + 2 η λ b 2 k + 2 η 2 k + λ 2 2 ; similarly, p P R * λ > 0 . Due to 4 k η 2 η λ 2 k b 2 > 0 , e P R * λ = a c + t η b 2 k + 2 η 2 k + λ 2 b 2 k + 2 η 2 k + λ 2 2 , we obtain e P R * λ > 0 . θ P R * λ = 4 b k a c + t η λ b 2 k 4 k η + 2 η λ 2 2 ; as above, we can obtain θ P R * λ > 0 . w P R * t = k η b 2 k + 4 k η 2 η λ 2 , since 4 k η 2 η λ 2 k b 2 > 0 ; thus, w P R * t > 0 . p P R * t = η 3 k λ 2 b 2 k + 4 k η 2 η λ 2 , 2 k λ 2 > 0 , p P R * t > 0 . e P R * t = η λ b 2 k + 2 η 2 k + λ 2 , it follows that p P R * t > 0 . θ P R * t = b k b 2 k 4 k η + 2 η λ 2 ; similarly, θ P R * t > 0 . □
Proof of Proposition 3.
w T M * λ = a c η 2 b 2 k λ + η 4 k λ + μ λ + μ 2 2 b 2 k + η 4 k + λ + μ 2 2 , when k > η μ λ + μ 2 ( 4 η λ 2 b 2 λ ) , w T M * λ > 0 , k < η μ λ + μ 2 ( 4 η λ 2 b 2 λ ) , w T M * λ < 0 . p T M * λ = a c η 2 b 2 k λ + η μ λ + μ 2 2 k η 3 λ + μ 2 b 2 k + η 4 k + λ + μ 2 2 , 2 b 2 k λ + η μ λ + μ 2 2 k η 3 λ + μ = 2 b 2 k λ 4 k η λ 2 k η λ + η μ ( ( λ + μ ) 2 2 k ) , since ( λ + μ ) 2 2 k < 0 , 2 b 2 k λ 4 k η λ = 2 k λ ( b 2 2 η ) < 0 ; therefore, p T M * λ > 0 . Similarly, we can obtain e T M * λ > 0 , θ T M * λ > 0 . w T M * μ = a c η η λ λ + μ 2 + 2 k η λ μ + b 2 μ 2 b 2 k + η 4 k + λ + μ 2 2 , when η λ λ + μ 2 + 2 k η λ μ + b 2 μ > 0 , w T M * μ > 0 ; when η λ λ + μ 2 + 2 k η λ μ + b 2 μ < 0 , w T M * μ < 0 . p T M * μ a c η η λ λ + μ 2 + 2 k η λ μ + b 2 μ 2 b 2 k + η 4 k + λ + μ 2 2 ; when η > 2 k ( η μ b 2 μ ) λ ( λ + μ 2 + 2 k ) , p T M * μ > 0 ; when η < 2 k ( η μ b 2 μ ) λ ( λ + μ 2 + 2 k ) , p T M * μ < 0 . Similarly, we can obtain e T M * μ > 0 , θ T M * μ > 0 . □
Proof of Proposition 4.
w T R * λ = a c η 2 η μ λ + μ 2 + k 4 η λ + b 2 μ b 2 k + 2 η 2 k + λ + μ 2 2 , when k > 2 η μ λ + μ 2 ( 4 η λ + b 2 μ ) , w T R * λ > 0 ; when k < 2 η μ λ + μ 2 ( 4 η λ + b 2 μ ) , w T R * λ < 0 . p T R * λ = a c η b 2 k 2 λ + 3 μ + 2 η 2 k λ μ λ + μ 2 b 2 k + 2 η 2 k + λ + μ 2 2 , when k > 2 η μ λ + μ 2 4 η λ + 2 b 2 λ + 3 b 2 μ , p T R * λ > 0 ; when k < 2 η μ λ + μ 2 4 η λ + 2 b 2 λ + 3 b 2 μ , p T R * λ < 0 . Similarly, we can obtain e T R * λ > 0 , θ T R * λ > 0 . Similarly, we can obtain e T R * μ > 0 , θ T R * μ > 0 . For w T R * μ = a c η b 2 k λ + 2 μ + 2 η 2 k μ + λ λ + μ 2 b 2 k + 2 η 2 k + λ + μ 2 2 , when b 2 k λ + 2 μ + 2 η 2 k μ + λ λ + μ 2 > 0 is satisfied, w T R * μ > 0 ; conversely, w T R * μ < 0 . For p T R * μ = a c η b 2 k 3 λ + 4 μ + 2 η 2 k μ + λ λ + μ 2 b 2 k + 2 η 2 k + λ + μ 2 2 , when b 2 k 3 λ + 4 μ + 2 η 2 k μ + λ λ + μ 2 > 0 is satisfied, p T R * μ > 0 ; conversely, p T R * μ < 0 . Similarly, we can obtain e T R * μ > 0 , θ T R * μ > 0 . □

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Figure 1. Schematic illustration of the four-scenario game model.
Figure 1. Schematic illustration of the four-scenario game model.
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Figure 2. Effect of consumers’ green preferences on the wholesale price and retail price. (a) represents impact of consumers’ green preferences on the wholesale prices; and (b) represents impact of consumers’ green preferences on the retail prices.
Figure 2. Effect of consumers’ green preferences on the wholesale price and retail price. (a) represents impact of consumers’ green preferences on the wholesale prices; and (b) represents impact of consumers’ green preferences on the retail prices.
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Figure 3. Effect of consumers’ green preference on the green technology level and sales effort level. (a) represents impact of consumers' green preferences on the green technology level; (b) represents impact of consumers' green preferences on the sales effort level.
Figure 3. Effect of consumers’ green preference on the green technology level and sales effort level. (a) represents impact of consumers' green preferences on the green technology level; (b) represents impact of consumers' green preferences on the sales effort level.
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Figure 4. Effect of consumers’ green preferences on the sales volume and environmental benefits. (a) represents impact of consumers’ green preferences on the sales volume; (b) represents impact of consumers' green preferences on the environmental benefits.
Figure 4. Effect of consumers’ green preferences on the sales volume and environmental benefits. (a) represents impact of consumers’ green preferences on the sales volume; (b) represents impact of consumers' green preferences on the environmental benefits.
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Figure 5. Effect of consumers’ green preferences on the manufacturer’s and retailer’s profits. (a) represents impact of consumers’ green preferences on the manufacturer’s profits; (b) represents impact of consumers’ green preferences on the retailer’s profits.
Figure 5. Effect of consumers’ green preferences on the manufacturer’s and retailer’s profits. (a) represents impact of consumers’ green preferences on the manufacturer’s profits; (b) represents impact of consumers’ green preferences on the retailer’s profits.
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Figure 6. Effect of the government subsidy level on the wholesale price and retail price. (a) represents impact of the government subsidy level on the wholesale price; (b) represents impact of the government subsidy level on the retail price.
Figure 6. Effect of the government subsidy level on the wholesale price and retail price. (a) represents impact of the government subsidy level on the wholesale price; (b) represents impact of the government subsidy level on the retail price.
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Figure 7. Effect of the government subsidy level on the green technology level and sales effort level. (a) represents impact of the government subsidy level on the green technology level; (b) represents impact of the government subsidy level on the sales effort level.
Figure 7. Effect of the government subsidy level on the green technology level and sales effort level. (a) represents impact of the government subsidy level on the green technology level; (b) represents impact of the government subsidy level on the sales effort level.
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Figure 8. Effect of the government subsidy level on the sales volume and environmental benefits. (a) represents impact of the government subsidy level on the sales volume; (b) represents impact of the government subsidy level on the environmental benefits.
Figure 8. Effect of the government subsidy level on the sales volume and environmental benefits. (a) represents impact of the government subsidy level on the sales volume; (b) represents impact of the government subsidy level on the environmental benefits.
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Figure 9. Effect of the government subsidy level on the manufacturer’s and retailer’s profits. (a) represents impact of the government subsidy level on the manufacturer’s profits; (b) represents impact of the government subsidy level on the retailer’s profits.
Figure 9. Effect of the government subsidy level on the manufacturer’s and retailer’s profits. (a) represents impact of the government subsidy level on the manufacturer’s profits; (b) represents impact of the government subsidy level on the retailer’s profits.
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Table 1. Parameters and descriptions.
Table 1. Parameters and descriptions.
ParametersDescriptions
w Wholesale price
p Retail price
m Retailer’s marginal profit
c Unit manufacturing cost of green products
e Green technology level of the product
k Green technology R&D cost coefficient
η Sales effort cost coefficient
θ Retailer’s sales effort level
a Potential market size
λ Consumer’s green preference coefficient
b Consumer’s sensitivity to the sales effort level
t Green product sales subsidy amount
μ Subsidy amount per unit of greenness level
h Manufacturer’s emission reduction efficiency coefficient
s Environmental benefit per unit of emission reduction
Π E N Total environmental benefit
Π M Manufacturer’s profit
Π R Retailer’s profit
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Wang, L.; Xu, T.; Chen, T. Optimal Strategies in Green Supply Chains When Considering Consumers’ Green Preferences and Government Subsidies. Mathematics 2025, 13, 2209. https://doi.org/10.3390/math13132209

AMA Style

Wang L, Xu T, Chen T. Optimal Strategies in Green Supply Chains When Considering Consumers’ Green Preferences and Government Subsidies. Mathematics. 2025; 13(13):2209. https://doi.org/10.3390/math13132209

Chicago/Turabian Style

Wang, Lei, Tao Xu, and Tingqiang Chen. 2025. "Optimal Strategies in Green Supply Chains When Considering Consumers’ Green Preferences and Government Subsidies" Mathematics 13, no. 13: 2209. https://doi.org/10.3390/math13132209

APA Style

Wang, L., Xu, T., & Chen, T. (2025). Optimal Strategies in Green Supply Chains When Considering Consumers’ Green Preferences and Government Subsidies. Mathematics, 13(13), 2209. https://doi.org/10.3390/math13132209

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