Effect of Governmental Subsidies on Green Energy Supply Chains: A Perspective of Meteorological Disasters

Abstract

The energy sector, serving as a pivotal propellant within the macroeconomic framework, finds its production, distribution, and consumption aspects considerably influenced by climatic variations. In this study, a two-tier Stackelberg model for the green energy supply chain is developed, which is employed to analyze the profit disparities between suppliers and retailers both in the absence and presence of meteorological disasters. Furthermore, the research delves into the optimal supply chain strategies under three distinct scenarios in the context of meteorological disasters. A comparative analysis is conducted to examine the decision-making variances and the shifts in the interests of each supply chain participant under these scenarios. The findings reveal two critical insights: First, meteorological disasters detrimentally affect the environmental friendliness of energy products, as well as the profits of both retailers and suppliers. Second, the selection of the optimal strategy varies depending on the evaluation criterion used. When product greenness is the metric, subsidies aimed at promoting sales costs emerge as the superior strategy. Conversely, for retailers and suppliers, subsidies that target the environmental friendliness of energy products prove to be the most effective. Based on the conclusions, the paper also makes recommendations for governments and companies.

1. Introduction

In the aftermath of the Industrial Revolution, there has been a consistent escalation in the quantity of greenhouse gases yielded by human activities and lifestyles. With the advent of the 21st century, a notable amplification in the rate of global climate alteration is observable, which is projected to exert detrimental effects on both the ecosystem and human existence [1,2]. The energy sector, serving as a pivotal propellant within the macroeconomic framework, finds its production, distribution, and consumption aspects considerably influenced by climatic variations. The energy sector, being the fulcrum of the socioeconomic construct [3,4], encounters the impact of climatic variations across various stages including production, distribution, and consumption. These impacts are predominantly categorized into two sectors: (1) the accelerative impact of meteorological changes on energy demand; (2) the destructive influence of weather catastrophes on energy production. The relative magnitude of these impacts dictates the direction and extent of the influence of extreme climate conditions on the energy sector. Specifically, supply-wise, renewable energy resources, encompassing bioenergy, hydropower, solar, and wind energy, are affected to differing extents due to alterations and variabilities in factors such as precipitation, temperature, wind speed, and solar radiation [5,6,7,8]. Demand-wise, climatic alterations shape energy needs by modifying the duration and magnitude of diurnal and seasonal heating and cooling requirements [9]. Furthermore, climate change and severe weather conditions potentially influence the resilience of energy systems and the dependability of energy provision by affecting the strategic decision of transmission systems or infrastructure location [10,11,12].

The energy sector is the focal point and stronghold for the advancement of sustainable, low-carbon progress. The vigorous implementation of environmentally friendly low-carbon strategies; robust cultivation of green, low-carbon supply chains; and the deep integration of sustainable practices have become indispensable choices for energy corporations seeking to enhance efficiency, reduce costs, and pursue low-carbon growth [13,14]. Green supply chains take into account both resource utilization and environmental impact, thus alleviating the adverse repercussions of weather-related disasters. Nonetheless, the execution of green supply chain management within energy companies is significantly constrained due to an array of limiting elements such as insufficiency of research and development funds and technical competencies. As a countermeasure to this, a multitude of nations have enacted corresponding financial aid policies.

In recent years, the issue of green supply chain management considering government subsidy policies or consumer green preference behavior has received increasing attention both domestically and internationally. Many scholars have explored this issue, and a wealth of academic achievements have been made [15,16]. However, previous research on green supply chain incentive mechanisms is primarily centered on manufacturers. Although manufacturers play the most critical role in product production and their main function cannot be ignored, the role of retailers is gradually increasing as they become closer to consumers. However, there is a lack of research on supply chain issues where retailers are in a core position. In previous studies, the sales efforts of retailers are generally reflected by the market demand function, and then their impact on supply chain decisions is considered [17,18,19]. In fact, the marketing efforts in the green supply chain environment are significantly different from existing research. The essence is to promote green products (a strategy of Walmart’s green supply chain), and there are differences in the perspective and intensity of marketing efforts. If the government can provide appropriate marketing subsidies, the strategic choices of the supply chain and the interests of the participants may change. However, existing research mostly targets manufacturers and consumers, rarely considering the “green” sales subsidies of retailers.

Furthermore, in green supply chain research considering both product greenness and government subsidies, ref. [20] established a three-stage green supply chain game model considering product greenness and government subsidies. They discussed the impact of changes in two parameters, the consumer environmental preference payment coefficient and the government subsidy lower limit, through numerical simulation. Ref. [21] constructed two game models of R&D cooperation between green supply chain members considering government subsidies and consumer green preferences, and compared them with the non-cooperation scenario. Ref. [22] built a game model between manufacturers and retailers in the green supply chain considering government subsidies and consumer green preferences under fuzzy uncertainty. They determined the equilibrium price and greenness under three power structures of manufacturer dominance, retailer dominance, and Nash game, and compared the results of the three models. Although there has been a lot of research in recent years on green supply chain decision-making issues considering consumer green preference behavior or government subsidy strategies, there is little literature comparing different government subsidy incentive strategies and their effects on green supply chain management. Ref. [23], through theoretical proof and numerical simulation, analyzed the effects of cost subsidies, research and development subsidies, and sales subsidies policies. The research shows that these three subsidy methods can promote the greening of products, increase market sales, and increase the profits of manufacturers and retailers, and the effect of R&D subsidies is more obvious. Ref. [24], based on a two-level transnational green supply chain composed of an exporting manufacturer and a retailer in an importing country, established a Stackelberg game model in this paper. The effects of importing country tariffs, consumers’ green preferences, the subsidy intensity of the government in the exporting country on decision-making, optimal profits of the transnational green supply chain and social welfare are discussed in the two cases of no government subsidy and a government subsidy. To achieve the best pricing decisions for supply chain members, ref. [25] compared the optimal pricing under consistent and inconsistent sales prices in both online and offline channels.

In summary, there is a lack of empirical research on (1) the impact of climate condition changes, especially extreme meteorological events from the perspective of the energy industry; (2) supply chain issues where retailers occupy a central position; (3) comparing different government subsidy incentive strategies and their effects on green supply chain management. Given these limitations, this paper constructs a two-tier energy supply chain composed of a supplier and a retailer in the context of meteorological disasters, where the retailer takes a dominant position. The retailer will make corresponding efforts to increase profits, and the government will subsidize the retailer to encourage it. Common government subsidy methods include two types; one is to subsidize according to the promotion of the retailer, and the other is to subsidize according to the greenness of the product. This paper studies the profit difference between suppliers and retailers without considering meteorological disasters; in the context of meteorological disasters, it considers no subsidy under meteorological disasters, subsidies based on retailer sales promotion under meteorological disasters, and subsidies based on product greenness under meteorological disasters. The optimal decisions of the supply chain in these three cases are given, and their decision differences and the interests or changes in interests of each member of the supply chain are compared.

This paper has made the following contributions: First, it constructs a supply chain model considering meteorological disasters. Previous studies have rarely considered the impact of meteorological disasters [23,24,25]. This paper introduces meteorological disaster variables when establishing the market demand model, considers its impact on the entire energy supply chain, and conducts research and analysis on its impact results. Second, it constructs a supply chain model dominated by retailers. At present, domestic and foreign research on energy supply chains and their performance mainly focuses on situations dominated by manufacturers, and there is little research on situations centered on retailers. Third, it compares the effects of different subsidy modes. Although there has been a lot of research on green energy supply chain decision-making issues considering consumer green preference behavior or government subsidy strategies in recent years, there is little literature comparing different government subsidy incentive strategies and their effects on green energy supply chain management. This paper will explore the impact of different types of subsidy methods on the energy supply chain and compare and analyze the impact of different types of subsidy methods on the energy supply chain. The research results will have certain reference significance for green energy supply chain management in our country, and for retailers and suppliers implementing energy supply chain strategies.

The rest of the paper is organized as follows. Section 2 presents the problem description and model hypothesis. Section 3 presents the model construction and solution. Section 4 reports the comparative analysis of the effect of two kinds of subsidies. Section 5 presents the numerical simulation and Section 6 reports the concluding remarks, which summarizes and discusses the possible policy implications. Section 7 discusses the limitations of the study and future research directions.

2. Problem Description and Model Hypothesis

2.1. Symbol Description

Table 1. The symbols and meanings involved in this document.

Symbol	Meaning
a	Market base size
p	Unit retail price of energy products set by the retailer (CNY)
w	Wholesale price per unit of energy products set by the supplier (CNY)
c	Supplier of energy products’ unit cost (CNY)
x	Greenness of energy products
f	The sensitivity of market demand to price of energy products
b	Sensitivity of market demand to energy product greenness
β	Sensitivity of energy supply to meteorological hazards
ų	Meteorological disaster risk
η	Retailers’ promotion subsidy coefficient
g	The difference between retail and wholesale prices (CNY)
n	Retailer promotion cost coefficient
$\sigma$	Unit energy product subsidy coefficient based on greenness

lists the symbols and meanings involved in this document.

2.2. Model Assumptions

In this paper, a foundational assumption is made regarding the long-term interactions between suppliers and retailers. It posits that retailers, in their role as leaders, will increasingly command greater influence and resources, thus gaining enhanced proactive decision-making rights [26]. This concept aligns with the resolution process of the Stackelberg model, where retailers, positioned dominantly, hold elevated decision-making authority. Within this framework, retailers utilize their decision variables, price (p) and quantity (x) to optimize their interests. During their strategic interactions with retailers, suppliers, who occupy a lower tier in the decision-making hierarchy, find themselves in a subordinate role. Their strategic objective is to determine their own optimal solutions, based on the leading retailer’s optimized outcome. In the second stage of this theoretical game model, suppliers must identify their own optimal solutions through their decision variable and wholesale price (w), aiming to maximize their benefits. The resolution of Stackelberg games typically employs a reverse-solving approach [27,28]. In this method, the decision-making process begins with the subordinate player (the supplier), solving for the optimal wholesale price (w). Following this, the optimal retail price (p) and quantity (x) are determined by solving for the dominant player (the retailer). This inverse solution method ensures that each player’s strategy is optimally aligned within the defined hierarchical structure of the Stackelberg model.

In addition, this paper makes the following assumptions:

1.

Both suppliers and retailers are rational people, their information is completely symmetrical, and the information in the market is transparent. This paper studies the Stackelberg game between the retailer and supplier, in which only the retailer is the leader and the supplier is the follower.

2.

Consideration of profit-oriented approach, usually $\mathrm{p} \text{>} \mathrm{w} \text{>} \mathrm{c}$, in order to facilitate calculations. With reference to the research of [13], we assume that $\mathrm{p}=\mathrm{w}+\mathrm{g}$, where $\mathrm{g} \text{>} 0$.

3.

Retailers sell energy products at the same price, but need to add additional promotion costs. It is assumed that the promotion cost has a quadratic relationship with greenness, that is, ${\mathrm{nx}}^2/2$ [20,29,30].

4.

The market demand for green energy products is influenced by both the price and the greenness of the products. Therefore, consumers have a certain preference for green energy products, and they are more willing to buy green energy products with a high degree of green and low sale price [29,31]. When there is no meteorological disaster, the market demand function is ${\mathrm{D}}_1=\mathrm{a}-\mathrm{fp}+\mathrm{bx}$, where $\mathrm{a}-\mathrm{fp} \text{>} 0$ is satisfied. Considering the background of meteorological disaster, the market demand function is ${\mathrm{D}}_2=\mathrm{a}-\mathrm{fp}+\mathrm{bx}-\mathsf{\beta }\mu$, where $\mathrm{a}-\mathrm{fp}-\beta \mu \text{>} 0$ is satisfied.

5.

Within the scope of meteorological disasters, the government plays a pivotal role in incentivizing retailers to sell green energy products and foster energy conservation and emission reductions. To this end, the government provides subsidies to retailers based on the input costs associated with promoting these products. These promotion cost subsidies are specifically aimed at covering the expenses incurred by retailers in marketing and publicizing green energy products. This form of subsidy is not only instrumental in enhancing the willingness of retailers to sell green energy products but is also recognized as one of the most direct and effective strategies to encourage such behavior. The effectiveness and dynamics of this subsidy approach have been previously explored and documented in the research conducted by [13], providing valuable insights into its impact and utility.

The promotion cost of green energy products for retailers is ${\mathrm{nx}}^2/2$. The government subsidizes the promotion of retailers, and the proportion is $\mathsf{\eta }\in$ [0, 1]. Then, the government subsidy expenditure per unit product is ${\displaystyle \frac{\eta }{2}}{\mathrm{nx}}^2$.

6.

In response to meteorological disasters, the government adopts a strategy of subsidizing retailers for selling green energy products, with the aim of promoting energy conservation and emission reductions. These subsidies are twofold: Firstly, promotion cost subsidies cover the expenses incurred by retailers in marketing and publicizing green energy products, thereby enhancing their motivation to sell such products. This subsidy strategy has been effectively analyzed by [13]. Secondly, the government provides direct subsidies to energy products based on their greenness, as detailed in the research by [20]. The amount of these subsidies usually correlates with the greenness of the products. To represent the subsidy coefficient per unit product based on greenness, refs. [21,22] introduced an approach which denotes the government’s subsidy expenditure per unit. This comprehensive subsidy approach, encompassing both promotional costs and direct subsidies based on product greenness, is designed to foster the sale of green energy products, especially in the challenging context of meteorological disasters.

3. Model Construction and Solution

3.1. Energy Supply Chain Game Model without Considering Meteorological Disasters

In the absence of meteorological disasters, the retailer’s profit (${\pi }_r$) and the supplier’s profit (${\pi }_s$) are expressed as

$${\mathsf{\pi }}_{\mathrm{r}}{=(\mathrm{p}-\mathrm{w})\mathrm{D}}_1-{\displaystyle \frac{1}{2}}{\mathrm{nx}}^2$$

(1)

$${\mathsf{\pi }}_{\mathrm{s}}{=(\mathrm{w}-\mathrm{c})\mathrm{D}}_1$$

(2)

First, we take the first partial derivative of W in Equation (2) and set it equal to 0, i.e.,

$${\displaystyle \frac{{\mathrm{d}\mathsf{\pi }}_{\mathrm{s}}}{\mathrm{dw}}}=\mathrm{a}-\mathrm{f}(\mathrm{g}+\mathrm{w})+\mathrm{bx}+\mathrm{f}(\mathrm{c}-\mathrm{w})=0$$

$${\mathrm{w}}_1={\displaystyle \frac{\mathrm{a}+\mathrm{cf}-\mathrm{fg}+\mathrm{bx}}{2\mathrm{f}}}$$

(3)

$\mathrm{ddw}=-2\mathrm{f} \text{<} 0$ can be obtained by calculating the second-order partial derivative of W in Equation (2), so Equation (3) is the optimal value of the supplier unit cost.

By bringing Formula (3) into Formula (1), we obtain

$${\mathsf{\pi }}_{\mathrm{r}}=\mathrm{g}({\displaystyle \frac{\mathrm{a}}{2}}-{\displaystyle \frac{\mathrm{cf}}{2}}-{\displaystyle \frac{\mathrm{fg}}{2}}+{\displaystyle \frac{\mathrm{bx}}{2}})-{\displaystyle \frac{{\mathrm{nx}}^2}{2}}$$

(4)

Taking the derivative of Equation (4) with respect to g and setting it to 0, we obtain

$${\mathrm{g}}_1={\displaystyle \frac{\mathrm{a}-\mathrm{cf}+\mathrm{bx}}{2\mathrm{f}}}$$

(5)

$\mathrm{ddg}=-\mathrm{f} \text{<} 0$ can be obtained by calculating the second-order partial derivative of g in Equation (4), so Equation (5) is the optimal value of the difference between retail price and wholesale price.

By bringing Formula (5) into Formula (4), we obtain

$$\pi {}_{r1}={\displaystyle \frac{(\mathrm{a}-\mathrm{cf}+\mathrm{bx})(\frac{\mathrm{a}}{4}-\frac{\mathrm{cf}}{4}+\frac{\mathrm{bx}}{4})}{2\mathrm{f}}}-{\displaystyle \frac{{\mathrm{nx}}^2}{2}}$$

(6)

Taking the derivative of Equation (6) with respect to x and setting it to 0, we obtain

$${\mathrm{x}}_1={\displaystyle \frac{\mathrm{b}(\mathrm{a}-\mathrm{cf})}{{4\mathrm{fn}-\mathrm{b}}^2}}$$

(7)

By calculating the second partial derivative of x in Equation (4), $\mathrm{ddx}={\displaystyle \frac{{\mathrm{b}}^2}{4\mathrm{f}}}-\mathrm{n}$ can be obtained; that is, when ${4\mathrm{fn}-\mathrm{b}}^2 \text{>} 0$, Equation (7) is the optimal value of the greenness of energy products.

By substituting Formula (7) into Formula (5), we obtain

$${\mathrm{g}}_2={\displaystyle \frac{2\mathrm{n}(\mathrm{a}-\mathrm{cf})}{{4\mathrm{fn}-\mathrm{b}}^2}}$$

(8)

We can substitute (7) and (8) into (3) to obtain

$${\mathrm{w}}_2={\displaystyle \frac{{-\mathrm{cb}}^2+\mathrm{an}+3\mathrm{cfn}}{{4\mathrm{fn}-\mathrm{b}}^2}}$$

(9)

We can substitute (7), (8), and (9) into (1) and (2)

$${\pi }_{\mathrm{s}1}={\displaystyle \frac{{\mathrm{fn}}^2{(\mathrm{a}-\mathrm{cf})}^2}{{{(4\mathrm{fn}-\mathrm{b}}^2)}^2}}$$

(10)

$${\pi }_{\mathrm{r}2}={\displaystyle \frac{{\mathrm{n}(\mathrm{a}-\mathrm{cf})}^2}{{2(4\mathrm{fn}-\mathrm{b}}^2)}}$$

(11)

3.2. Energy Supply Chain Game Model Considering Meteorological Disasters

In the context of meteorological disasters, the profit of the retailer and the profit of the supplier are expressed as

$${{\mathsf{\pi }}^{\ast }}_{\mathrm{r}}{=(\mathrm{p}-\mathrm{w})\mathrm{D}}_2-{\displaystyle \frac{1}{2}}{\mathrm{nx}}^2$$

(12)

$${{\mathsf{\pi }}^{\ast }}_{\mathrm{s}}{=(\mathrm{w}-\mathrm{c})\mathrm{D}}_2$$

(13)

When the parameter meets the condition ${4\mathrm{fn}-\mathrm{b}}^2 \text{>} 0$, the optimal value of product greenness and the difference between retail price, wholesale price and supplier price can be obtained by the same method as above

$${\mathrm{x}}^{\ast }=-{\displaystyle \frac{\mathrm{b}(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{4\mathrm{fn}-\mathrm{b}}^2}}$$

(14)

$${\mathrm{g}}^{\ast }=-{\displaystyle \frac{2\mathrm{n}(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{4\mathrm{fn}-\mathrm{b}}^2}}$$

(15)

$${\mathrm{w}}^{\ast }={\displaystyle \frac{{-\mathrm{cb}}^2+\mathrm{an}+3\mathrm{cfn}-\beta \mu \mathrm{n}}{{4\mathrm{fn}-\mathrm{b}}^2}}$$

(16)

The optimal profit of supplier and retailer is

$${{\pi }^{\ast }}_{\mathrm{s}1}={\displaystyle \frac{{\mathrm{fn}}^2{(\mathrm{cf}-\mathrm{a}+\beta \mu )}^2}{{{(4\mathrm{fn}-\mathrm{b}}^2)}^2}}$$

(17)

$${{\pi }^{\ast }}_{\mathrm{r}1}={\displaystyle \frac{\mathrm{n}(\mathrm{cf}-\mathrm{a}+\beta \mu {)}^2}{{2(4\mathrm{fn}-\mathrm{b}}^2)}}$$

(18)

Result 1.

In the context of meteorological catastrophes, an escalation in the frequency and severity of these disasters correlates with a diminution in both the environmental sustainability of products and the financial gains of suppliers and retailers. This trend illustrates that meteorological disasters exert an adverse influence on energy supply, underscoring the interconnection between environmental phenomena and economic outcomes.

Proof. 

We find the first derivative of $\beta$, then we find the first derivative of (14), (17) and (18), respectively. From ${{\mathrm{d}}^{\ast }}_{\beta 1}={\displaystyle \frac{\mathrm{b}\mu }{{\mathrm{b}}^2-4\mathrm{fn}}}$, ${{\mathrm{d}}^{\ast }}_{\beta 2}={\displaystyle \frac{2\beta {\mathrm{fn}}^2(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{{(4\mathrm{fn}-\mathrm{b}}^2)}^2}}$, and ${{\mathrm{d}}^{\ast }}_{\beta 2}={\displaystyle \frac{2\beta {\mathrm{fn}}^2(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{{(4\mathrm{fn}-\mathrm{b}}^2)}^2}}$, it can be seen that $\mathrm{a}-\mathrm{fp}-\mathsf{\beta }\mu \text{>} 0$, $\mathrm{a}-\mathrm{fp}-\mathsf{\beta }\mu \text{>} 0$, and $\mathrm{cf}-\mathrm{a}+\beta \mu <0$. In addition, from $\mathrm{cf}-\mathrm{a}+\beta \mu <0$, we can see that the above first derivatives are less than 0, so Result 1 is valid. □

3.3. Energy Supply Chain Game Model in Which the Government Subsidizes the Promotion Cost of Retailers

When the government subsidizes the retailer’s promotion, the retailer’s profit (${{\pi }^{•}}_r$) and the supplier’s profit (${{\pi }^{•}}_s$) are expressed as

$${{\mathsf{\pi }}^{•}}_{\mathrm{r}}{=(\mathrm{p}-\mathrm{w})\mathrm{D}}_2-{\displaystyle \frac{1-\eta }{2}}{\mathrm{nx}}^2$$

(19)

$${{\mathsf{\pi }}^{•}}_{\mathrm{s}}{=(\mathrm{w}-\mathrm{c})\mathrm{D}}_2$$

(20)

When the parameter meets the condition ${\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn}<0$, the optimal value of product greenness and the difference between retail price, wholesale price and supplier price can be obtained by the same method as above

$${\mathrm{x}}^{•}={\displaystyle \frac{\mathrm{b}(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn}}}$$

(21)

$${\mathrm{g}}^{•}={\displaystyle \frac{-\left(2\mathrm{n}\right(\eta -1\left)\right(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn}}}$$

(22)

$${\mathrm{w}}^{•}={\displaystyle \frac{{\mathrm{cb}}^2-\mathrm{an}+\mathrm{a}\eta \mathrm{n}-3\mathrm{cfn}+\beta \mu \mathrm{n}-\beta \eta \mu \mathrm{n}+3\mathrm{c}\eta \mathrm{fn}}{{\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn}}}$$

(23)

The optimal profit of the supplier and retailer is

$${{\pi }^{•}}_{\mathrm{s}1}={\displaystyle \frac{{\mathrm{fn}}^2{(\eta -1)}^2{(\mathrm{cf}-\mathrm{a}+\beta \mu )}^2}{{{(\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn})}^2}}$$

(24)

$${{\pi }^{•}}_{\mathrm{r}1}={\displaystyle \frac{\mathrm{n}(\eta -1\left)\right(\mathrm{cf}-\mathrm{a}+\beta \mu {)}^2}{{2(\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn})}}$$

(25)

Result 2.

In scenarios marked by meteorological disasters, it becomes evident that, notwithstanding the intervention of government subsidies, a rise in the frequency and intensity of these disasters is inversely associated with both the ecological attributes of products and the economic returns of suppliers and retailers. This pattern persists, implying that meteorological disasters, irrespective of governmental financial support, adversely affect the provision of energy, highlighting the profound impact of such environmental calamities on the nexus of sustainability and commerce.

Proof. 

We find the first derivative of $\beta$, ${{\mathrm{d}}^{•}}_{\beta 1}={\displaystyle \frac{\mathrm{b}\mu }{{\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn}}}$, ${{\mathrm{d}}^{•}}_{\beta 2}={\displaystyle \frac{2\mathrm{f}\mu {\mathrm{n}}^2{(\eta -1)}^2(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{{(\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn})}^2}}$, and ${{\mathrm{d}}^{•}}_{\beta 3}={\displaystyle \frac{\mu \mathrm{n}(\eta -1\left)\right(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{(\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn})}}$, by Equations (21), (24) and (25), respectively. From $\mathrm{cf}-\mathrm{a}+\beta \mu <0$, $b^2-4fn+4\eta fn<0$ and $\eta <1$, we can see that the above first derivatives are all less than 0, so Result 2 is valid. □

Result 3.

When there are government subsidies, with the increase in government subsidies, the greenness of products and the profits of suppliers and retailers will increase correspondingly, that is, government subsidies have a positive impact on energy supply.

Proof. 

We find the first derivative of $\eta$, ${{\mathrm{d}}^{•}}_{e1}=-{\displaystyle \frac{4\mathrm{bfn}(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{{(\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn})}^2}}$, ${{\mathrm{d}}^{•}}_{\mathrm{e}2}={\displaystyle \frac{{2\mathrm{b}}^2{\mathrm{fn}}^2(\eta -1\left)\right(\mathrm{cf}-\mathrm{a}+\beta \mu {)}^2}{{{(\mathrm{b}}^2-4\mathrm{fn}+4\eta \mathrm{fn})}^3}}$, and ${{\mathrm{d}}^{•}}_{\mathrm{e}3}={\displaystyle \frac{{\mathrm{b}}^2\mathrm{n}(\mathrm{cf}-\mathrm{a}+\beta \mu {)}^2}{{2(\mathrm{b}}^2-4\mathrm{fn}+4\eta {\mathrm{fn})}^2}}$, by Equations (21), (24) and (25), respectively. From $\mathrm{cf}-\mathrm{a}+\beta \mu <0$, $b^2-4fn+4\eta fn<0$ and $\eta <1$, we can see that the above first derivatives are all greater than 0, so Result 3 is valid. □

3.4. Energy Supply Chain Game Model of Government Subsidies to Retailers Based on Product Greenness

When the government subsidizes the promotion of the retailer based on the greenness of the product, the retailer’s profit (${{\pi }^o}_r$) and the supplier’s profit (${{\pi }^o}_s$) are expressed as

$${{\mathsf{\pi }}^{\circ }}_{\mathrm{r}}=(\mathrm{p}-\mathrm{w}+\sigma x{)\mathrm{D}}_2-{\displaystyle \frac{1}{2}}{\mathrm{nx}}^2$$

(26)

$${{\mathsf{\pi }}^{\circ }}_{\mathrm{s}}{=(\mathrm{w}-\mathrm{c})\mathrm{D}}_2$$

(27)

When the parameter meets the condition ${(\mathrm{b}+\mathrm{f}\sigma )}^2-4\mathrm{nf}<0$, the optimal value of product greenness and the difference between retail price, wholesale price and supplier price can be obtained by the same method as above

$${\mathrm{x}}^{\circ }={\displaystyle \frac{(\mathrm{b}+\mathrm{f}\sigma \left)\right(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{\mathrm{b}}^2+2\mathrm{bf}\sigma {+\mathrm{f}}^2{\sigma }^2-4\mathrm{nf}}}$$

(28)

$${\mathrm{g}}^{\circ }=-{\displaystyle \frac{(\mathrm{cf}-\mathrm{a}+\beta \mu \left)\right(\mathrm{f}{\sigma }^2+\mathrm{b}\sigma -2\mathrm{n})}{{\mathrm{b}}^2+2\mathrm{bf}\sigma {+\mathrm{f}}^2{\sigma }^2-4\mathrm{nf}}}$$

(29)

$${\mathrm{w}}^{\circ }={\displaystyle \frac{{\mathrm{cb}}^2+2\mathrm{cbf}\sigma {+\mathrm{cf}}^2{\sigma }^2-3\mathrm{cnf}-\mathrm{an}+\beta \mu \mathrm{n}}{{\mathrm{b}}^2+2\mathrm{bf}\sigma {+\mathrm{f}}^2{\sigma }^2-4\mathrm{nf}}}$$

(30)

The optimal profit of the supplier and retailer is

$${{\pi }^{\circ }}_{\mathrm{s}1}={\displaystyle \frac{{\mathrm{fn}}^2{(\mathrm{cf}-\mathrm{a}+\beta \mu )}^2}{{{(\mathrm{b}}^2+2\mathrm{bf}\sigma {+\mathrm{f}}^2{\sigma }^2-4\mathrm{nf})}^2}}$$

(31)

$${{\pi }^{\circ }}_{\mathrm{r}1}=-{\displaystyle \frac{\mathrm{n}(\mathrm{cf}-\mathrm{a}+\beta \mu {)}^2}{{2(\mathrm{b}}^2+2\mathrm{bf}\sigma {+\mathrm{f}}^2{\sigma }^2-4\mathrm{nf})}}$$

(32)

Result 4.

In instances of meteorological disasters, it is observed that despite the presence of government subsidies, an augmentation in the occurrence and magnitude of these disasters inversely correlates with the environmental sustainability of products and the financial profitability of suppliers and retailers. This inverse relationship suggests that, even in the face of governmental financial support, meteorological disasters yield a detrimental effect on the supply of energy, thereby elucidating the significant and negative repercussions of such environmental events on both ecological and economic dimensions.

Proof. 

We find the first derivative of $\beta$, ${{\mathrm{d}}^{\circ }}_{\beta 1}={\displaystyle \frac{\mu (b+f\sigma )}{{(\mathrm{b}+\mathrm{f}\sigma )}^2-4\mathrm{fn}}}$, ${{\mathrm{d}}^{\circ }}_{\beta 2}={\displaystyle \frac{2f\mu n^2(cf-a+\beta \mu )}{{\left(\right(\mathrm{b}+\mathrm{f}\sigma {)}^2-4\mathrm{fn})}^2}}$, and ${{\mathrm{d}}^{\circ }}_{\beta 3}=-{\displaystyle \frac{\beta \mathrm{n}(\mathrm{cf}-\mathrm{a}+\beta \mu )}{(\mathrm{b}+\mathrm{f}\sigma {)}^2-4\mathrm{nf}}}$, by Equations (28), (31) and (32), respectively. From $\mathrm{cf}-\mathrm{a}+\beta \mu <0$ and ${(\mathrm{b}+\mathrm{f}\sigma )}^2-4\mathrm{nf}<0$, we can see that the above first derivatives are all less than 0, so Result 4 is valid. □

Result 5.

In circumstances where government subsidies are implemented, it is observed that an escalation in the level of these subsidies is positively correlated with an enhancement in the environmental sustainability of products and an increase in the economic returns of suppliers and retailers. This correlation indicates that government subsidies exert a favorable influence on the supply of energy, thereby underscoring the pivotal role of governmental financial interventions in bolstering both ecological sustainability and commercial profitability within the energy sector.

Proof. 

We find the first derivative of $\sigma$, ${{\mathrm{d}}^{\circ }}_{e1}=-{\displaystyle \frac{f(cf-a+\beta \mu )({(b+f\sigma )}^2+4fn)}{{\left(\right(\mathrm{b}+\mathrm{f}\sigma {)}^2-4\mathrm{fn})}^2}}$, ${{\mathrm{d}}^{\circ }}_{\mathrm{e}2}=-{\displaystyle \frac{{4\mathrm{f}}^2{\mathrm{n}}^2(\mathrm{b}+\mathrm{f}\sigma \left)\right(\mathrm{cf}-\mathrm{a}+\beta \mu {)}^2}{{{(\mathrm{b}}^2+2\mathrm{bf}\sigma {+\mathrm{f}}^2{\sigma }^2-4\mathrm{nf})}^3}}$, and ${{\mathrm{d}}^{\circ }}_{\mathrm{e}3}={\displaystyle \frac{\mathrm{fn}(\mathrm{b}+\mathrm{f}\sigma \left)\right(\mathrm{cf}-\mathrm{a}+\beta \mu {)}^2}{{{(\mathrm{b}}^2+2\mathrm{bf}\sigma {+\mathrm{f}}^2{\sigma }^2-4\mathrm{nf})}^2}}$, by Equations (28), (31) and (32), respectively. From ${(\mathrm{b}+\mathrm{f}\sigma )}^2-4\mathrm{nf}<0$, we can see that the above first derivatives are all greater than 0, so Result 5 is valid. □

4. Comparative Analysis of the Effect of Two Kinds of Subsidies

4.1. Comparability of Subsidy Effect

The aforementioned findings indicate that irrespective of the specific subsidy approach employed by the government, the provision of subsidies to retailers results in a commensurate increase in the profits of both suppliers and retailers. Concurrently, there is a modification in both the wholesale and retail prices of products. In order to conduct a comparative analysis of these two distinct subsidy policies, it is essential to ascertain their comparability. Within the context of a uniform fiscal subsidy framework, this study aims to undertake an analytical comparison of the effects arising from varying fiscal subsidy policies. The subsidy expenditure associated with these two divergent government subsidy strategies can be described as follows:

$$\mathrm{E}\eta ={\displaystyle \frac{{\mathrm{b}}^2\eta \mathrm{n}(\mathrm{cf}-\mathrm{a}+\beta \mu {)}^2}{{2(\mathrm{b}}^2-4\mathrm{fn}+4\eta {\mathrm{fn})}^2}}$$

(33)

$$\mathrm{E}\sigma ={\displaystyle \frac{\mathrm{fn}\sigma (\mathrm{b}+\mathrm{f}\sigma \left)\right(\mathrm{cf}-\mathrm{a}+\beta \mu {)}^2}{{{(\mathrm{b}}^2+2\mathrm{bf}\sigma {+\mathrm{f}}^2{\sigma }^2-4\mathrm{nf})}^2}}$$

(34)

Suppose the government first gives and then determines the value of based on E1 = E2

$${\eta }_1={\displaystyle \frac{{(Ab-\sqrt{A^2{b}^2+16fn(4fn-b^2)})}^2}{64f^2{n}^2}}$$

(35)

where

$$\mathrm{A}={\displaystyle \frac{4\mathrm{fn}-(\mathrm{b}+\mathrm{f}\sigma {)}^2}{\sqrt{2\mathrm{f}\sigma (\mathrm{b}+\mathrm{f}\sigma )}}}$$

(36)

4.2. Comparative Analysis

The government’s implementation of green product subsidies for enterprises serves a dual purpose: firstly, to enhance the environmental sustainability of products, and secondly, to benefit the manufacturers and retailers directly. Consequently, this project is dedicated to conducting a comparative analysis of two distinct subsidy policies, considering three critical dimensions: the environmental sustainability (or greenness) of products, the profitability of suppliers, and the profitability of retailers.

Proposition 1.

In scenarios characterized by meteorological disasters, the relative ranking of product environmental sustainability corresponding to the two government subsidy strategies is as follows: $x^{\ast }{\eta }_1>x^{\ast }\sigma$.

$${\displaystyle \frac{\mathrm{b}(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{\mathrm{b}}^2-4\mathrm{nf}(1-{\eta }_1)}}<{\displaystyle \frac{(\mathrm{b}+\mathrm{f}\sigma \left)\right(\mathrm{cf}-\mathrm{a}+\beta \mu )}{{\mathrm{b}}^2+2\mathrm{bf}\sigma {+\mathrm{f}}^2{\sigma }^2-4\mathrm{nf}}}$$

(37)

$$\mathrm{As}E\eta =E\sigma ,\mathrm{we}\mathrm{obtain}{\mathrm{b}}^2-4\mathrm{nf}(1-{\eta }_1)={\displaystyle \frac{b\sqrt{{\eta }_1}\left[(b+f\sigma {)}^2-4fn\right]}{\sqrt{2f\sigma (b+f\sigma })}}$$

(38)

We substitute Formula (38) into Formula (37) and then sort it out

$$\sqrt{{\displaystyle \frac{2f\sigma }{b+f\sigma }}}\le \sqrt{{\eta }_1}$$

(39)

We substitute Equation (29) into Equation (38) and simplify

$$f\sigma (4fn-b^2-bf\sigma )\le 0$$

(40)

$4nf-b^2-bf\sigma >bf\sigma +f^2{\sigma }^2>0$ is obtained from $4nf-(b+f\sigma {)}^2>0$; that is, when $\sigma \ne 0$, there is $f\sigma (4fn-b^2-bf\sigma )>0$, which contradicts Equation (40). The hypothesis is not true, so there is $x^{\ast }{\eta }_1>x^{\ast }\sigma$.

Proposition 2.

In the context of meteorological disasters, the order of retailer profits corresponding to the two government subsidy strategies is as follows: ${{\pi }_{\eta }}_1<{\pi }_{\sigma }$.

Proposition 3.

In the specific context of meteorological disasters, the hierarchical order of retailer profits, as influenced by the two distinct government subsidy strategies, is arranged in the following manner: ${{\pi }_{\eta }}_1<{\pi }_{\sigma }$.

Propositions 2 and 3 have been omitted, as their underlying proof and logic align with that of proposition 1. Based on the preceding proposition, it can be deduced that when assessing government subsidy strategies with product greenness as the criterion, the impact of promotional cost subsidies to retailers surpasses that of product greenness subsidies. Conversely, when evaluating government subsidies based on the profits of retailers and suppliers, the efficacy of product greenness subsidies is superior to that of promotional cost subsidies to retailers.

5. Numerical Simulation

To substantiate the validity of the model and corroborate the accuracy of the conclusions and propositions posited, this study employs Matlab 2019b for the execution of numerical simulations. Through these simulations, the paper methodically analyzes the influence exerted by two types of government subsidy strategies on the green supply chain, utilizing practical examples to demonstrate the outcomes. The relevant parameters in the model are as follows: a = 100, f = 5, β = 5, b = 3, n = 2, c = 8. The value of $\sigma$ in the simulation analysis ranges from 0 to 0.1, and the parameters set meet the conditions for the existence of the equilibrium solution of the model. For example, when $\sigma$ = 0.05, there is ${(\mathrm{b}+\mathrm{f}\sigma )}^2-4\mathrm{nf}=-29.4375<0$, and when $\sigma$ takes other values in the range of 0–0.1, the condition for the existence of the equilibrium solution is also satisfied.

Figure 1, Figure 2 and Figure 3 illustrate the simulation results depicting the impact of meteorological disasters on the greenness of energy products and the profits of retailers and suppliers, respectively. In these figures, the subscripts 0, 1, and 2 denote scenarios without government subsidies, with government subsidies for sales and promotion costs, and with government subsidies for product greenness, respectively. The simulations reveal that under meteorological disaster conditions, the greenness of energy products, as well as the profits of both retailers and suppliers, decline regardless of the presence of government subsidies. Notably, the absence of subsidies results in the lowest levels of product greenness and profits for both retailers and suppliers.

Specifically, Figure 1 demonstrates that meteorological disasters adversely affect the greenness of energy products. In the absence of government subsidies, the greenness of these products is at its lowest. However, when government subsidies are introduced, differences emerge between the two types of subsidies. The subsidy for retail promotion costs leads to greater greenness in energy products compared to when the government subsidizes product greenness.

Figure 2 and Figure 3 focus on the effects of meteorological disasters on the profits of retailers and suppliers. These figures show that while meteorological disasters negatively impact profits in both cases, the presence of subsidies significantly enhances the profits of both suppliers and retailers. Moreover, it is evident that the subsidy for product greenness yields more favorable outcomes than the subsidy for retail promotion costs.

Figure 4, Figure 5 and Figure 6 present the simulation outcomes illustrating the effects of government subsidies on the greenness of energy products, and the profits of retailers and suppliers, respectively, in the context of meteorological disasters. In these figures, subscripts 1 and 2 denote scenarios with government subsidies for sales and promotion costs, and for product greenness, respectively. These simulations indicate that under meteorological disaster conditions, the greenness of energy products, along with the profits of both retailers and suppliers, increase with the escalation of the government subsidy coefficient under both subsidy strategies.

Specifically, Figure 4 highlights that government subsidies positively influence the greenness of energy products, yet the impact varies between the two types of subsidies. When the subsidy is directed towards retail promotion costs, the greenness of energy products is higher compared to when the subsidy is for product greenness. This indicates a more significant effect of retail promotion cost subsidies on product greenness.

Figure 5 and Figure 6 focus on the effects of government subsidies on the profits of retailers and suppliers amidst meteorological disasters. While such disasters adversely affect profits, the presence of government subsidies counteracts this negative impact, enhancing the profits of both suppliers and retailers. Furthermore, it is apparent that subsidies aimed at product greenness are more effective than those for retail promotion costs in improving profits.

6. Concluding Remarks

This research, assuming a retailer-dominated context, delves into the optimal supply chain strategies under three distinct scenarios: (1) no subsidies during meteorological disasters, (2) subsidies based on retailers’ sales promotion during meteorological disasters, and (3) subsidies for product greenness during meteorological disasters. These scenarios are juxtaposed against a non-subsidy condition. Game models for energy supply chain decision-making under these varying circumstances are constructed, and equilibrium solutions for the models are determined. Through a comparison of theoretical proofs and numerical simulations, we have reached the following conclusions:

• Irrespective of the presence or type of government subsidies, meteorological disasters exert a negative impact on the greenness of energy products, as well as on the profits of retailers and suppliers. This conclusion is very much in line with reality and is similar to that of previous researchers [32]. The energy sector, as the core driving force for the functioning of the socioeconomic system, is affected by changes in climatic conditions in many aspects such as production, transport, and consumption, and this effect is mainly reflected in two aspects: (1) On the supply side, the pull effect of changes in meteorological conditions on energy demand, for example, extreme weather, disrupts the supply of hydroelectricity and wind power, which results in power tensions [28,29,30,31]. (2) On the demand side, the disruptive effects of meteorological hazards on energy output, e.g., extreme weather, exacerbates electricity and gas demand. The relative strength of the impact of the two effects determines the direction and magnitude of the impact of extreme weather on the energy sector [33,34,35,36].
• The optimal strategy selection varies based on the chosen evaluation criteria. If the focus is on product greenness, the marketing cost subsidy strategy emerges as the most effective. Conversely, when considering the benefits to retailers and suppliers, subsidizing the greenness of energy products proves to be the most advantageous. In fact, research on different subsidies has also received more and more attention in recent years [28,37,38,39,40,41], but there is still a lack of energy supply chain-related research [40,41,42]. This paper compares and analyses the impact of different types of subsidies on the energy supply chain, and the role of government subsidies will be different in different situations, which can provide some reference significance for the choice of subsidy forms in practice.

These findings offer significant insights for the government in selecting subsidy methods for retailer-dominated energy supply chains. The practical implications for energy enterprises and governmental bodies are as follows:

For Energy Companies:

• Increase R&D investment in green technology:

Enterprises should actively respond to the government’s green subsidy policy, increase R&D investment in green technology and clean energy, and enhance the greenness and market competitiveness of energy products.

2.

Optimize supply chain management:

In the face of meteorological disasters and other uncertainties, enterprises should optimize supply chain management, establish a diversified supplier system and reduce single-source risks. At the same time, enterprises should strengthen inventory management to ensure the stability and resilience of the supply chain.

3.

Strengthen co-operation with the government:

Enterprises should actively communicate and co-operate with government departments to understand policy guidance and subsidy standards, and strive for more policy support and financial support. At the same time, enterprises should participate in green project cooperations organized by the government to jointly promote the development of the green energy industry.

For the Government:

• Differentiated subsidy strategies:

Depending on the different evaluation criteria of the subsidy strategy, the government should flexibly adopt a variety of subsidy methods. If product greenness improvement is the main goal, the cost of the sales subsidy strategy should be promoted as a priority in order to incentivize enterprises to improve the greenness of energy products.

2.

Strengthen the meteorological disaster warning and response mechanism:

The government should increase the monitoring and early warning of meteorological disasters and establish a rapid response mechanism to reduce the impact of disasters on the energy supply chain. In addition, it encourages and supports enterprises to establish disaster risk management systems to improve their ability to resist natural disasters.

3.

Policy publicity and guidance:

The publicity of green energy product policies should be strengthened to increase public awareness and acceptance of green consumption. Through policy guidance, the formation and development of the green consumption market should be promoted, and greater market demand for green energy products should be created.

7. Limitation and Directions for Future Research

(1) In terms of model construction and background, the model in the paper is constructed assuming retailer dominance and complete market information, but the optimal decision may change when the retailer has altruistic preferences or when there are fairness concerns for the manufacturer, so the introduction of relevant conditions may be considered for further study in the future.

(2) In terms of subsidies, in this paper, we only consider one type of subsidy based on retailer promotion and one based on product greenness, and we do not consider other forms of subsidies such as government subsidies for retailers and suppliers at the same time, and subsidies for green consumers. In addition, the comparative analysis of the two government subsidy strategies in this study presupposes that the government subsidy expenditures are the same, and that other government objectives, such as maximizing social welfare and maximizing net government revenues, can also be chosen. These analyses are possible directions for future research.