Research on Carbon Emission Reduction Investment Decision of Power Energy Supply Chain—Based on the Analysis of Carbon Trading and Carbon Subsidy Policies

: This study examines the carbon reduction investment decisions of the electric power energy supply chain considering carbon trading and carbon subsidy policies in China’s “dual carbon” context. By building a three-level supply chain system including electric power producers, retailers, and consumers, we discuss the optimal decision-making problem of the supply chain for three models of decentralized supply chain decision making without government subsidies, centralized supply chain decision making with government subsidies, and centralized supply chain decision making with government subsidies and carbon emission reduction cost sharing. Through model solving and further numerical simulations, the results showed that the increase in carbon emission reduction investment cost has a signiﬁcant negative impact on power price and the total expected income of the supply chain. However, a reasonable level of government carbon emission reduction subsidy can effectively alleviate the increase in power price and improve the total expected income of supply chain. In addition, carbon mission reduction investment and supply chain cost allocation can effectively improve the carbon emission reduction level of the power supply chain, improve the income and enthusiasm of electric power producers, and realize the sustainable development of electric power energy consumption and the environment.


Introduction
At present, global climate change is increasingly a concern for a wide range of international organizations and countries.Climate change is considered to be a serious threat to sustainable development and international security.In response to this crisis, developed countries have introduced carbon emission reduction measures, such as the emissions trading system (ETS) proposed by Australia in 2012; Canada's national emissions trading system, launched in 2018; and the carbon pricing in the north of the United States and the carbon tax imposed on all people [1].For less developed countries and regions, their awareness of carbon emission reduction is weak, and their laws are lax, which poses a huge obstacle to the global joint response to climate change.Therefore, it is particularly important to improve the capacity of developing countries to cope with the risks of climate change and improve environmental laws and regulations.The issue of global climate change is one of the most severe challenges facing human society in the 21st century and has attracted great attention from all over the world.In order to deal with global climate issues, China has proposed a "Dual carbon" goal, which has also made all industries in China begin to make policy adjustments to the "Carbon peak" and "Carbon neutral" goals and measures."Carbon peak" refers to the process of carbon dioxide emissions reaching the highest value in history and then going through a plateau period and entering a continuous decline.It is a historical inflection point of carbon dioxide emissions from increase to decline, marking the decoupling of carbon emissions and economic development."Carbon neutral" refers to the carbon dioxide emitted directly and indirectly by human activities in a certain area within a certain period of time (generally refers to one year).The carbon dioxide absorbed through afforestation and other activities offset each other to achieve "net zero carbon dioxide emission" [2].The "Double carbon" goal is not only a solemn commitment China has made to the world to tackle climate change but also the main theme of China's development in the coming decades.In particular, the electric power industry, which emits the largest amount of carbon dioxide, is a major challenge.The electric power industry is the core of China's entire energy system, and industries such as transportation, industrial production, construction, and animal husbandry have increasing consumer demand for electric power.Therefore, the low-carbon emission reduction transformation in the electric power industry plays an important role in promoting the sustainable consumption of electric power and implementing the "Dual carbon" goal.
The low-carbon transformation of the electric power industry mainly includes two directions: cleaning coal electric power with high carbon emissions and promoting the development of non-fossil energy sources with low carbon emissions or no carbon emissions, all of which require electric power companies in related fields to carry out vigorous investment and construction.For the realization of carbon emission reduction in the electric power industry, cooperation between enterprises is the only effective way to achieve the carbon emission reduction goal of the supply chain [3].Cooperation between upstream and downstream companies in the supply chain is critical to the successful operation of the supply chain, as differences in management capabilities, technologies, and equipment related to carbon reduction enable them to collaborate on carbon reduction [4].Therefore, it is necessary to guide and coordinate the carbon emission reduction activities and decisions of various entities in the supply chain.At the same time, a very important factor in the process of the low-carbon transformation of the power industry is the government's attitude and policies.On one hand, enterprises can follow the government's attitude to actively seek changes, and on the other hand, the government can also issue policies to give enterprises a certain low-carbon transformation pressure.Subsidies are one of the common policy tools used by the Chinese government to promote low-carbon production [5].Due to the consideration of self-interest and risk avoidance of enterprises, when there is no corresponding government subsidy incentive, the motivation of active carbon emission reduction is insufficient [6].Therefore, the carbon subsidies provided by the government will have a significant impact on the decision making and strategy of enterprises.Especially in the early stage of enterprises' initiative to reduce emissions, the government's lowcarbon subsidies will have strong guidance and can effectively encourage enterprises to increase innovation and invest in efforts to improve the level of carbon emission reduction of enterprises [7].So how should the members of the power supply chain make decisions when considering low-carbon government subsidies?What if the cooperation of members in the supply chain is further considered?
To sum up, this paper considers three cases of decentralized decision making in the supply chain without government subsidies, centralized decision making in the supply chain with government subsidies, and decentralized decision making in the electric power supply chain with government subsidies and carbon emission reduction costs sharing.The three-level power supply chain system is composed of electricity producers, retailers, and consumers.By solving the model and conducting further simulations, we verify the effects of the carbon emission reduction cost coefficient, the government carbon subsidy rate, and the carbon emission reduction cost-sharing rate on the price of electricity, the most efficient supply chain members' optimal decision making, and the carbon emission reduction levels.Starting from the electric power supply chain system, this paper analyzes and discusses the rationality and necessity of carbon emission reduction investment activities by electric power companies and further discusses the important role of government carbon subsidies and electric power supply chain carbon emission reduction cost allocation.We provide a reference for the carbon emission reduction investment and carbon emission reduction cooperation of power companies as well as the future policy direction of the government to promote the low-carbon transformation of power companies, improve energy cleanliness and safety, and promote sustainable consumption of energy and the maximization of environmental benefits.
The main contributions are: (1) building a supply chain carbon emission reduction revenue model to study the optimal strategies for carbon emission reduction in the electric power supply chain under different scenarios and using the matrix positive definiteness to determine the existence of the optimal carbon emission reduction strategy while solving the optimal strategy; (2) considering the important role of the government's carbon emission reduction subsidy policy in the carbon emission reduction activities of the electric power supply chain and analyzing the specific role of the government's carbon emission reduction subsidy; and (3) finally, the carbon emission reduction cost-sharing and coordination mechanism in the electric power supply chain is introduced to explore the optimal carbon emission reduction strategy of the electric power supply chain at this time.

Literature Review
There is broad consensus on the need to achieve sustainable development of the world through carbon emission reduction to reduce greenhouse gas emissions and achieve control of climate change.There are also many studies on carbon emission reduction and supply chain carbon emission reduction.Many countries are trying to promote carbon emission compliance through some systems and policies.Existing carbon emission regulation policies can be divided into two categories: One is binding policies, mainly based on carbon quota trading and carbon tax collection.The other type is incentive policies, mainly based on industrial policies, legislative protection, and government subsidies [8].The carbon trading policy in the government's binding policy means that the government first allocates carbon allowances to relevant enterprises for free, and enterprises can sell or buy additional allowances based on actual emissions [9].However, since China's carbon trading is in its infancy, only eight regions, Beijing, Shanghai, Tianjin, Chongqing, Hubei, Guangdong, Shenzhen, and Fujian, conducted pilot carbon emission trading from 2013.In recent years, many scholars have studied the carbon trading system from different perspectives.Considering the carbon trading mechanism and emission reduction technologies, Zhang et al. (2019) studied the choice of low-carbon strategies for manufacturers and analyzed the impacts of carbon caps and emission reduction technologies on production decisions and corporate profits [10].Considering the impact of carbon footprints and low-carbon preference, Du et al. (2016) constructed an optimal production decision-making model based on caps and easy systems [11].He et al. (2016) studied the optimal pricing of manufacturing enterprises based on carbon trading and emission reduction technology [12].In addition, some scholars have studied the problem of supply chain coordination and decision making based on the carbon trading system.Considering a two-level low-carbon supply chain, Xu et al. (2016) studied the impact of the emission trading price on the optimal decision making of the supply chain and achieved a perfect coordination of the supply chain through two tariff contracts [13].Yang et al. (2017) considered the carbon trading system, studied the impact of vertical and horizontal competition in the supply chain on carbon emission reduction rates, and achieved a Pareto improvement between node enterprises through revenue-sharing contracts [14].
Regarding government incentive policies, under the background of accelerating the deployment of strategic emerging industries in China, financial subsidies for low-carbon industries are the main method of policy support.Zhu and Xu (2003) conducted an empirical study of panel data in Shanghai and obtained government funding for science and technology funding and tax relief.These two policy tools have positive effects on large-and medium-sized industrial enterprises in increasing their self-funded research and development investment and government funding support.The more stable the results, the better the research results [15].By designing three differential game models, Zu et al. (2008) concluded that government subsidies can increase the profits of upstream companies [16].Zhou and Nie (2011) found that carbon subsidies are helpful for the commercialization of low-carbon technologies and greatly improve the level of low-carbon technologies in this country [17].Fang et al. (2012) studied the R&D investment and social welfare of enterprises under the government's R&D subsidies and product innovation subsidies [18].
The power industry has to undertake the transfer of carbon emissions brought about by the electrification of other industries.At the same time, the new electricity demand in the peak carbon stage cannot be fully met by non-fossil energy power generation.The combination of these two factors may lead to a peak of electricity carbon emissions that may lag behind other industries.On the whole, it is conducive to the early peaking of carbon emissions in the whole society.For negative carbon scenarios, the power system will assume more carbon emission reduction responsibilities [19].However, in the short term, thermal power is still the main force in this country's power supply system.It is necessary to gradually eliminate high-emission and low-efficiency coal-fired power units and expand the investment and construction of clean energy to complete the low-carbon transformation of the power industry [20].The current research on carbon emission reduction in the power industry mainly focuses on the following two aspects.On one hand, it is a study of the carbon emission reduction benefits of the power industry.Zhao et al. (2014) compared the cost and electricity price of wind power under the income with carbon emission and income without carbon emission and discussed the possibility of cost competition between wind power and thermal power [21].Duan et al. (2015) introduced the carbon emission reduction benefits of power generation with various energy sources into power supply planning and established a power supply planning model considering the carbon emission reduction benefits, with the goal of minimizing the operating cost of power generation and CO 2 treatment cost.Another aspect is the study of the carbon emission reduction potential of the power industry [22].Liu et al. (2012) comprehensively considered the impact of various factors on carbon emission reduction in the power industry and proposed a model to analyze and evaluate different carbon emission reduction scenarios.They analyzed the low-carbon development prospects and carbon emission characteristics of the power industry under different low-carbon element scenarios [23].Chen et al. (2009) and Zhang (2014) introduced carbon emission trading into the traditional power dispatch model and constructed a new low-carbon economic dispatch model with carbon emission reduction costs [24,25].
The studies above have conducted a lot of research on carbon emission reduction in the supply chain and the power industry and have achieved certain results.However, with the continuous advancement of China's "Dual carbon" goal, the government has continued to improve its policies and measures in carbon trading and carbon subsidies.Coupled with the continuous advancement of China's power system reform, the power industry will eventually achieve marketization, and an effective competition mechanism will be formed on the power generation and sales sides.Therefore, power generation enterprises need to make decisions based on the entire power supply chain and carry out carbon emission reduction while maximizing their own interests.However, at present, there are very few studies that explore the carbon emissions of the power industry from the perspective of the power supply chain as a whole, and research based on the perspective of carbon emission reduction investment, government carbon subsidies, and supply chain carbon emission reduction cost allocation is even rarer.The Stackelberg game model is widely used in the supply chain's optimal decision problem and further through numerical simulation to validate the results of model and increase the reliability of the model and conclusions, such as the Guo study of supply chain cost allocation to reduce emissions [26], Jiang considering carbon allowances and the corporate social responsibility of the emission reduction strategy research of the supply chain [8], and Zhao's research on the carbon emission reduction investment decision of the power industry supply chain [27].Therefore, based on the above analysis, this paper starts from the power supply chain system, considers the influence of factors such as carbon emission reduction investment, government carbon subsidies, and supply chain carbon emission reduction cost allocation and explores the carbon emission reduction problem of the entire power industry.The main research problem of this paper is to explore the optimal decision-making problem of carbon emission reduction activities for each subject of the power supply chain under the three models, verify the effectiveness of the Chinese government's carbon emission reduction policy, and draw conclusions based on the model's results and numerical simulation to provide a reference for practice.

Problem Description
This paper considers a three-level supply chain game system dominated by power producers and followed by power retailers under the background of government carbon subsidies and carbon trading in the market.Power producers have the ability to comply with national policies, improve carbon reduction technologies, and upgrade clean energy power generation systems.Electricity retailers are responsible for delivering electricity to consumers and promoting the sale of electricity products.Under the carbon cap and trading mechanism, the government gives power producers a certain free carbon emission limit, and the excess or saved carbon emissions can be traded through the carbon trading market.At the same time, the government provides carbon emission reduction subsidies to enterprises that reduce carbon emissions, stimulate enterprises to reduce emissions, and ease the pressure on enterprises to reduce emissions.In addition, it is assumed that consumers have low-carbon preferences; that is, consumers are willing to buy low-carbon products, are willing to pay higher prices for them, and consumers' demand will also be affected by price changes.

1.
Power producers reduce carbon emissions by increasing the input of carbon reduction technologies in their production process.Therefore, it is assumed that the rate of the difference between the carbon emission before and after the emission reduction activities of the producer and the carbon emission before emission reduction is ϕ (1 < ϕ < 1), where ϕ is inversely proportional to the degree of carbon reduction.The smaller the ϕ, the higher the level of carbon reduction.The larger the is ϕ, the lower the carbon reduction level.

2.
In order to reduce carbon emissions, the power producer must make some emission reduction input.Assuming that the carbon emission reduction cost input is η is the carbon emission reduction cost coefficient [28], assuming that the failure of the emission reduction investment of power producers and the risk aversion of investment of power producers is not considered.

3.
Assume that the market demand function of electric power products is Q + βϕ − bp, where Q is the market size, p is the market retail price, β is the low-carbon preference of consumers, and b is the consumer price sensitivity coefficient [29].4.
In order to encourage a low-carbon power industry and sustainable consumption of the energy economy, the government sets a carbon emission cap, E, for power producers to constrain the carbon emissions of enterprises and allow carbon trading.The market price for carbon is t.At the same time, the government also provides help and support for enterprises' carbon emission reduction activities, that is, carbon emission reduction subsidies, with a subsidy rate of λ (0 < λ < 1).

5.
The supply chain system introduces a cost-sharing contract.In order to encourage electric power producers to reduce emissions, electric power retailers are willing to share the carbon emission reduction costs of electric power producers.The sharing rate is recorded as θ (0 < θ < 1) [26].
Based on the above assumptions, Figures 1-3 describe the supply chain system model with or without carbon subsidies and centralized decision making.Figure 1 is the case of decentralized decision making without carbon subsidies (model D), Figure 2 shows centralized decision making with government carbon subsidies (model C), and Figure 3 shows the centralized decision-making situation with government carbon subsidies and retailer carbon emission reduction cost sharing (model U).

Decentralized Supply Chain Decision Making without Government Carbon Subsidies (Model D)
In the process of decentralized decision making in the electric power supply chain, electric power producers make a certain amount of carbon emission reduction investment.Electric power producers and retailers only consider their own interests and set ex-factory electricity prices and retail electricity prices, respectively, so as to maximize their expected benefits.The profit functions for the electricity producer and electricity retailer are given, respectively: Using the reverse derivation method, since functional relationship between the electricity price and the carbon emission reduction rate can be obtained as p = Q + βϕ + bw 2b .At this time, the function is put into formula (1), and the Hessian matrix of the ex-factory price of electricity and the carbon emission reduction rate can be obtained as: Because the first-order sequential main subform is −b < 0, the second-order sequential main subform is 4bη(1 − λ) − (β + bet) 2 /4 > 0. The Hessian matrix is a negative definite matrix.At this time, the profit function, π D M , is a concave function of the decision variables ω and ϕ, and there is an optimal solution.
Let ∂π D M ∂w = 0 and ∂π D M ∂ϕ = 0.By simultaneous equations, the decentralized optimal decision of electric power producers and retailers under the condition of no government subsidy can be obtained: By substituting ω D * and ϕ D * into the function p = Q + βϕ + bw 2b , the optimal electricity price of the electric power retailer can be obtained: If all the above results are put into π D R and π D M , the expected revenue of electric power producers and retailers can be obtained as follows: M is a concave function with respect to decision variables w and ϕ.In order to ensure that the above results are non-negative, it is necessary to satisfy Property 1.In the Stackelberg game model with electricity producers as leaders and retailers as followers, when faced with a decentralized decision-making condition in the supply chain without government subsidies, it can be drawn that Property 1 shows that under the condition without the government carbon subsidies, the higher the carbon emission reduction cost coefficient of the investment projects of electric power producers, the higher the power generation costs of electric power producers will continue to increase, which will lead to an increase in the ex-factory price of electricity and the retail price of electricity.However, for power producers and retailers, the increase in the carbon emission reduction cost coefficient will increase the carbon emission reduction investment of power producers, resulting in a decrease in expected benefits.
The proof is as follows: taking the derivation of the electric power producer's optimal power ex-factory price, the electric power retail price, the electric power producer's expected revenue, and the retailer's expected revenue with respect to the carbon emission reduction cost coefficient, we can obtain: Through algebraic operations, it can be found that the ex-factory price and market price of electricity have a negative correlation with the carbon emission reduction cost coefficient.The expected benefits of electricity producers and the expected benefits of retailers are also negatively correlated with the carbon emission reduction cost coefficient.When 4bη − (β + bet) 2 > 0, the above relationship holds.

Centralized Supply Chain Decision Making with Government Carbon Subsidies (Model C)
In the centralized decision-making process of the low-carbon electric power supply chain, electric power producers and retailers cooperate and make decisions together.Both of them face the electric power market as a whole.Both parties aim to maximize the overall revenue of the supply chain and achieve vertical integration.At this time, only electric power producers invest in carbon emission reduction technologies, and the total carbon emission reductions in the electric power supply chain all come from the efforts of electric power producers.Considering that the government subsidizes the carbon emission reduction technology investment of electric power producers and enterprises, the subsidy rate is λ.At this point, the supply chain can determine the optimal unit price of electricity.At this time, the overall revenue function of the electric power supply chain is: By calculating the second-order partial derivatives of formula ( 6) with respect to p and ϕ, respectively, we can obtain: and From this, the Hessian matrix determinant of the expected revenue of the electric supply chain about the decision variables p and ϕ can be obtained as: Since the sequential principal formula is −b < 0 and when 2bη(1 − λ) − (β + bet) 2 > 0 the Hessian is negative definite matrix, it can be known that the benefit function of the electric supply chain under centralized decision making is a concave function of decision variables p and ϕ, and there is an optimal solution.
When we calculate the first-order partial derivative of the total profit function of the supply chain with respect to p and ϕ, respectively, and set it equal to 0, we obtain: The optimal electricity market retail price and carbon emission reduction rate of the electric power supply chain under centralized decision making can be further obtained as follows: At this time, the two optimal solutions, ϕ C * and p C * , are brought into formula (6), and the relationship between the optimal government subsidy ratio and the optimal carbon emission rate can be obtained as:

−2bη
Furthermore, the overall expected benefit of the supply chain can be obtained as: the above conclusion holds.Property 2. In the case of government carbon subsidies to electric power producers, Property 2 shows that, from the perspective of the electric power producers' carbon emission reduction investment, the higher the carbon emission reduction cost coefficient of the electric power producer's investment project, the higher the electric power producer's carbon emission reduction cost, which will make all supply chain electric energy prices increase.At this time, the higher the carbon emission reduction cost coefficient of the electric power producer's investment project, the lower the expected benefit to the entire electric power supply chain.
From the perspective of government carbon subsidies, when the actual subsidy rate is below the optimal government carbon subsidy rate, the carbon subsidy rate given by the government to electric power producers is negatively correlated with the market price of electricity; that is, the higher the carbon subsidy rate, the cheaper the electricity price will be.The carbon subsidy rate given by the government to electric power producers is positively correlated with the expected revenue of the entire supply chain.The higher the carbon subsidy rate, the higher the supply chain revenue.
The proof is as follows: The power price of the electric power supply chain and the expected benefit of the supply chain are derived from the carbon emission reduction cost coefficient and the government carbon emission reduction subsidy coefficient, respectively.In addition, taking the derivation of the electric power supply chain carbon emission reduction rate with respect to the government carbon emission reduction subsidy rate, we obtain: When 2bη(1 − λ) − 2(β + bet) 2 > 0, the above relationship holds.
Property 3.For the entire supply chain, the benefits brought by centralized decision making in the supply chain with government carbon emission reduction subsidies are better than those brought by decentralized decision making in the supply chain without government carbon emission reduction subsidies; that is, E π The proof is as follows: > 0 and 4bη − (β + bet) 2 > 0, the relationship holds.

Centralized Supply Chain Decision Making with Government Carbon Subsidies and Carbon Emission Reduction Investment Allocation (Model U)
In order to optimize the decentralized decision-making model in the case of carbon subsidies, a cost-sharing contract is introduced into model U to coordinate the electric power supply chain.Under this contract, the electric power producer and the retailer cooperate to some extent.It is assumed that the retailer shares the carbon emission reduction cost of proportion θ for the electric power producer to encourage the electric power producer to invest in carbon emission reduction and make investment decisions.In this centralized decision making model, the electric power producer and the power retailer still aim to maximize their own profits.At this time, the profit function of electric power producer and the power retailer is: At this time, the total expected revenue function of the supply chain remains unchanged, and the second-order partial derivatives are calculated with respect to p and ϕ in Formula (11), respectively.From this, it can be obtained that when the second-order sequence main sub-formula 4bη(1 − λ − θ) − (β + bet) 2 /4 > 0, the Hessian matrix is a negative definite matrix.At this time, the profit function, π U M , is a concave function of the decision variables p and ϕ, and there is an optimal solution.
Letting ∂π U M ∂ϕ = 0 and ∂π U M ∂p = 0, simultaneous equations can obtain the centralized optimal decision of power generation producers and retailers when there are no government subsidies: At this time, taking all the above results into π U R and π U M , the expected benefits of the power producer and the retailer can be obtained as: With centralized decision making in the supply chain under the condition that the government provides carbon subsidies to power producers and the cost of carbon emission reduction is shared, Property 4 shows that, from the perspective of the carbon emission reduction investment of power producers, the higher the carbon emission reduction cost coefficient of the investment projects of electric power producers, the higher the carbon emission reduction cost of electric power producers, which will make the entire electricity supply chain increase energy prices.
From the perspective of government carbon subsidies, the carbon subsidy rate given by the government to electric power producers is negatively related to the market price of electricity; that is, the higher the carbon subsidy rate, the cheaper the electricity price.
Taking the derivation of the electricity price with respect to the carbon emission reduction cost coefficient and the government's carbon emission reduction subsidy ratio, we can obtain: < 0 At this time, there is a positive correlation between the electricity price and the carbon emission reduction cost coefficient, which is inversely proportional to the government's carbon emission reduction subsidy rate.Property 5.Under the circumstance that the government provides carbon subsidies to electric power producers and the cost of carbon emission reduction is shared, ∂p U * ∂θ < 0 and ∂ϕ U * ∂θ > 0.
Property 5 shows that retailers share the cost of carbon emission reduction for electric power producers, which is beneficial to ease the electricity price in the market.The higher the retailer's share, the lower the electricity price.The carbon reduction rate of electricity producers is related to the proportion of carbon reduction costs that retailers share on behalf of electric power producers.Specifically, under the premise of (1 − λ − θ) > 0, the carbon emission reduction rate is positively correlated with the carbon emission reduction cost-sharing rate.The higher the sharing rate, the higher the carbon emission reduction rate.
Taking the derivation of the ex-factory price of electricity and the retail price of electricity with respect to the proportion of carbon emission reduction costs shared by retailers and the derivation of the carbon emission reduction rate with respect to the proportion of carbon emission reduction costs shared by retailers, we can obtain: For the entire electric power supply chain, whether to carry out cost sharing has no impact on the total electric power supply chain revenue, but the centralized decision making of the supply chain with government carbon emission reduction subsidies and retailers sharing carbon emission reduction costs brings benefits to electric power producers.The benefits are better than the benefits of centralized decision making in the electric power supply chain with only government carbon emission reduction subsidies, and The proof is as follows: the above relationship holds.

Numerical Simulation
In this section, in order to verify the above properties and analysis, numerical simulations of individual parameters are carried out with specific numerical values, assuming the original electricity market demand is Q = 500, the unit cost of electricity produced by electricity producers is c = 4, the carbon emission per unit of electricity produced by electricity producers before emission reductions is e = 2, the government-mandated free carbon allowance is E = 500, the market transaction price of a unit of carbon emission is t =1, consumer price sensitivity is b = 2, and consumers' low-carbon preferences is β = 1 [26,30].

The Influence of Carbon Abatement Investment Cost Coefficient on Electric Power Price and Supply Chain Benefit
The first influence is that, under the decentralized decision-making model of the supply chain without government subsidies, for the electric power producer's carbon emission reduction technology investment decision, the electric power producer bears all the carbon emission reduction costs, and the carbon emission reduction cost depends on the carbon emission reduction cost coefficient.Therefore, η ∈ [50, 500] is taken to observe the impact of the carbon emission reduction cost coefficient on the electricity price and the revenue of the supply chain.Taking the cost of the carbon emission reduction coefficient as the horizontal axis and taking the ex-factory electricity price of the electric power producer and the electricity retail price as the vertical axis, the relationship between the electricity price and the carbon emission reduction cost coefficient can be obtained.As shown in Figure 4, as the carbon emission reduction cost coefficient increases.The ex-factory price and retail price of electricity both rise.There is a positive correlation between the two, and the change in the ex-factory price of electricity is more obvious than the change in the market price of electricity.The first clause of Property 1 is verified.Taking the carbon emission reduction cost coefficient as the horizontal axis and the expected revenue of each main body in the supply chain as the vertical axis, the relationship between the expected revenue of electric power producers, retailers, and the total supply chain and the carbon emission reduction cost coefficient can be obtained, as shown in Figure 5.As shown, an increase in the carbon emission reduction cost coefficient brings about a reduction in the expected benefits of each member of the supply chain and the total expected benefit of the supply chain; that is, there is a negative correlation between the two.The second clause of Property 1 is verified.

The Influence of Carbon Emission Reduction Investment Cost Coefficient and Government Carbon Subsidy Rate on Electric Power Price and Supply Chain Benefit
When governments give carbon subsidies to electric power producers, members of the supply chain make centralized decisions.In order to ensure that the value of the carbon emission reduction rate is positive, take λ ∈ [0.1, 0.8].Taking the government carbon subsidy rate as the horizontal axis and the carbon emission reduction rate as the vertical axis, as shown in Figure 6, L1 represents the situation with a fixed carbon emission reduction cost coefficient of η = 50.L2 represents the situation with a fixed carbon emission reduction cost coefficient of η = 500.It can be clearly seen that the increase in the carbon emission reduction cost coefficient leads to an increase in electricity price, and there is a positive correlation between the two.The first clause of Property 2 is verified.Next, the influence of the carbon emission reduction subsidy rate of different governments on the electric power price is further analyzed.As shown in Figure 7, the three broken lines represent the impact of the carbon emission reduction cost coefficient on the electric power price when the government's carbon emission reduction rate is 0.3, 0.5, and 0.7, respectively.It can be seen that the government's carbon subsidy rate is inversely proportional to the electric power price; that is, the higher the subsidy rate, the lower the electric power price of the supply chain.The third clause of Property 2 is verified.At the same time, different government carbon subsidy rates affect the total expected revenue of the supply chain.As shown in Figure 8, the broken line with a government carbon a subsidy rate of 0.7 is above the broken lines with subsidy rates of 0.5 and 0.3; the government carbon subsidy rate is the broken line of 0.5 above the broken line of the subsidy rate of 0.3; that is, the proportion of government carbon subsidies is positively correlated with the total supply chain revenue.The higher the subsidy rate, the higher the supply chain revenue.The fourth clause of Property 2 is verified.Here, we further compare the difference in the total expected revenue of the supply chain under models D and C, as shown in Figure 9.It can be clearly seen that the centralized decision making of the supply chain with government subsidies is higher than the supply chain without government subsidies, demonstrating the benefits of decentralized decision making.Property 3 is verified.Since the first clauses of Properties 4 and 5 are similar to the above verification, no simulation was performed.

The Influence of Carbon Emission Reduction Investment Cost Coefficient and Government Carbon Subsidy Rate on Electric Power Price and Supply Chain Benefit
Next, we consider the case of centralized decision making in the supply chain with both government carbon subsidies and supply chain carbon emission reduction cost sharing.Taking the retailer's carbon emission reduction cost-sharing cost rate as the horizontal axis and the carbon emission reduction rate on the vertical axis, we can obtain the relationship between the retailer's carbon abatement cost-sharing rate and the carbon abatement rate under different carbon abatement cost coefficient levels.
Retailers share the cost of carbon emission reduction investment with electric power producers, which has a positive impact on the carbon emission reduction rate of the supply chain.Taking four different levels of the carbon emission reduction cost coefficients to draw an image, as shown in Figure 10, regardless of the carbon emission reduction cost coefficient level, the cost sharing of retailers significantly increases the carbon emission reduction rate of the supply chain.The second clause of Property 5 is verified.Finally, considering the impact of different retailers' carbon emission reduction costsharing rates on the benefits of members of the electric power supply chain, since the total expected revenue function of the centralized decision-making supply chain does not change, the total supply chain revenue remains unchanged.However, as retailers share costs, the expected benefits for both electricity producers and retailers are changed.As shown in Figure 11, taking the carbon emission reduction coefficient as the horizontal axis and the expected revenue of the electric power producer as the vertical axis, it is possible to plot the expected revenue curves for two electric power producers in two cases with only the government carbon subsidy and with both the government carbon subsidy and the retailer's carbon abatement cost-sharing.It can be seen that the expected benefits of electric power producers with both government carbon subsidies and retailers' carbon emission reduction cost sharing are significantly improved; that is, retailers' carbon emission reduction cost sharing can increase the expected benefits of electric power producers.Property 6 is verified.In the condition of centralized decision making in the supply chain with government carbon subsidies and supply chain carbon emission reduction cost sharing, the impact of the carbon emission reduction cost factor on the expected earnings of electric power producers is shown.

Conclusions
This paper studies the carbon emission reduction of the entire supply chain from the perspective of the electric power supply chain, considering the impact of carbon emission reduction investment decisions on the electric power supply chain, the government's carbon subsidy, and retailers' carbon emission reduction cost allocation on the supply chain electricity price, the supply chain's expected income, and the supply chain carbon emission reduction rate.In this paper, by constructing a three-level electric energy supply chain system composed of electric power producers, retailers, and consumers, we considered supply chain decisions in three cases, which included decentralized supply chain decisions without government subsidies, centralized supply chain decisions with government carbon subsidies, and centralized supply chain decisions with government carbon subsidies and cost sharing of carbon emission reduction investment, to understand the influence of the carbon emission reduction cost coefficient, the carbon emission reduction subsidy rate of the government, and the carbon emission reduction investment cost allocation rate of the supply chain on optimal decision making, the optimal electricity price, the maximum carbon emission reduction rate, and the optimal expected income of the electric power supply chain.
The model analysis results indicate: (1) The high cost of carbon abatement investment of the electric power supply chain will inevitably bring rising production costs and electricity price increases.Therefore, electric power producers need to reasonably analyze and measure the information of various investment projects when investing in carbon emission reduction and seek to invest in projects with lower carbon emission reduction costs.
(2) In the decentralized decision-making model, electric power producers and retailers have their own goals and decision-making rights.When they make decisions based on their own optimal goals, they often conflict with the overall goals of the supply chain.The optimization of each subject in the electric power supply chain cannot achieve the optimization of the entire electric power supply chain system.In the centralized decision making of the supply chain, information sharing and joint decision making between electric power producers and retailers can achieve the optimization of the overall profit of the electric power supply chain; that is, the total expected revenue of the supply chain with centralized decision making is significantly higher than that with decentralized decision making.This conclusion has also been confirmed in the research by Zhao and Guo et al. [21,29].(3) At the same time, the government's carbon emission reduction subsidy has a regulatory effect on the electric power supply chain system.Specifically, the government's carbon emission reduction subsidy can effectively alleviate the rise in electricity price, and the higher the subsidy proportion, the more obvious the reduction effect.Government carbon emission reduction subsidies can also help improve the total expected revenue of the electric power supply chain.Within a certain proportion of subsidies, the higher the subsidy, the higher the expected revenue of the supply chain.This conclusion was also obtained in the research by Jiang and Cao [8,31].(4) In addition, retailers that share the cost of carbon reduction in the supply chain can effectively improve the carbon emission rate of the electric power supply chain, improve the income of electric power producers, stimulate the enthusiasm of supply chain enterprises to reduce emissions, stabilize the electricity price, and promote the sustainable consumption of electric power energy, and achieve the coordinated development of the economy and the environment.
This conclusion for the future of China and an even wider range of references are provided for the formulation and implementation of national policy, effectively exerting carbon allowances and carbon trading policies and methods, such as reasonably guiding and standardizing the carbon reduction of the electric energy supply chain activities.To a certain extent, the government policy of electric power enterprise investment can also be validated to support the necessity and importance of carbon abatement.At the same time, the theoretical contribution of this study lies in the establishment of different supply chain models and the influence of different variables on the optimal decision making of supply chain subjects, which further enriches the related research on the supply chain and supply chain decision-making problems.In terms of practice, the research results can provide theoretical support for future policy formulation by the government and carbon emission reduction investment activities of power enterprises and help the government to maximize social benefits, help power-related enterprises to maximize profits and benefits, and help environmental protection projects to maximize environmental benefits and other goals.
However, it should be pointed out that the model in this paper is based on certain assumptions, and there are some differences compared to the actual situation, so the paper model needs to be modified accordingly with a change in assumptions.In addition, in the actual power and energy supply chain, in addition to the subject considered in this paper, there are carbon emission reduction technology companies, consumers of different consumption scales, and other market subjects to be considered, which will also have an impact on the results of this paper.For example, the rate of return of different carbon emission reduction investment activities can be further considered on the basis of this model because this paper only considers the cost change resulting from carbon emission reduction investment but does not further consider the change in the rate of return resulting from different types of investment projects.As a result, the returns from investments in carbon reduction activities have not been accurately and comprehensively measured.In addition, one can also consider the influence of variables such as the carbon emission reduction investment risk preference of power enterprises and the low-carbon consumption preference of consumers on the carbon emission effect and the supply chain income of the supply chain so that the carbon emission reduction research on the energy supply chain is more detailed and in-depth.Finally, when considering the carbon subsidy policy, this paper ignores the fact that there are certain differences in various industries.In the actual process of developing a low-carbon economy, different industries face different pressures to reduce emissions.Therefore, it is also a direction worthy of further research to discuss the carbon subsidy mechanisms of various industries.

Figure 1 .
Figure 1.Schematic diagram of model D.

Figure 2 .
Figure 2. Schematic diagram of model C.

Figure 3 .
Figure 3. Schematic diagram of model U.

Figure 4 .
Figure 4.The impact of the carbon emission reduction cost coefficient on the ex-factory electricity price and the market electricity price under the condition of decentralized decision making in the supply chain.

Figure 5 .
Figure 5.The impact of the carbon emission reduction cost coefficient on the benefits of electricity producers, retailers, and the entire supply chain under the condition of decentralized decision making in the supply chain.

Figure 6 .
Figure 6.The impact of the carbon emission reduction cost coefficient on electricity price under centralized decision making with government carbon emission reduction subsidies.

Figure 7 .
Figure 7.In the condition of centralized decision making with government carbon emission reduction subsidies, considering the proportion of different government carbon emission reduction subsidies, the impact of the carbon emission reduction cost coefficient on electricity prices shown.

Figure 8 .
Figure 8.In the condition of centralized decision making with government carbon emission reduction subsidies, the impact of the carbon emission reduction coefficient on the expected return of the supply chain under different government subsidy rates is shown.

Figure 9 .
Figure 9.In the condition of centralized decision making with government carbon emission reduction subsidies, the impact of the carbon emission reduction cost coefficient on the expected return of model D and model C supply chains is shown.

Figure 10 .
Figure 10.In the condition of centralized decision making in the supply chain with government carbon subsidies and supply chain carbon emission reduction cost sharing, the impact of the retailer carbon emission reduction cost-sharing rate on the carbon emission reduction rate is shown.

Figure 11 .
Figure 11.In the condition of centralized decision making in the supply chain with government carbon subsidies and supply chain carbon emission reduction cost sharing, the impact of the carbon emission reduction cost factor on the expected earnings of electric power producers is shown.