# Carbon Tax and Trading Price on Power Plant with Carbon Capture and Storage under Incentive Regulation Theory

Authors: Huan Zhang; Xinxin Xu; Jianli Jiang; Meimei Zhang
Journal: Discrete Dynamics in Nature and Society
 (2020)

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## Abstract

This paper investigates how the government can develop subsidies or tax policies to incent power plants to effectively carry out carbon capture to reduce carbon emissions. According to the government’s incentive model for carbon capture power plants, the regulation mechanism is developed when government controls carbon emission. When regional or national carbon emission quota is tense, significant effect can be obtained when regulators make regulations to take off low efficiency power plants. In addition, it is verified that the regulators should not blindly pursue a reduction in carbon emissions regardless of the cost. Therefore, regulators need to pay more attention to control the costs of carbon capture equipment and technology. Finally, by parametric and numerical analyses, the conditions of the power plant to maximize corporate surplus are further studied.


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## Body

## 1. Introduction

With the global warming problem becoming more and more serious, the international situation pays more and more attention to the issue of carbon emissions, and the low carbon issue has become an important aspect of China’s participation in the world game. As one of the largest sectors ofCO2 emissions in China’s national economy, the power industry accounts for about 40% of total carbon emissions and power generation industry plays an important role in the development of low carbon economy in china. The proportion of China’s thermal power generation is more than 77%, the development of carbon emissions reduction policy for the thermal power industry is the most urgent and effective part of the low-carbon policy in the power generation industry [1–4]. However, the existing low-carbon policy research on the power industry is mainly focused on optimizing the power supply structure [5] and the development and application of low-carbon technologies [6], how to reduce the carbon emissions of thermal power enterprises through government regulation, but the research on the low carbon policy of thermal power enterprises is relatively lacking. As Xie [7] pointed out that such low carbon technology is one of the important factor of low-carbon electricity, but technological progress turning into energy-saving emission reduction performance needs a process, and need policy incentives and support. Considering Laffont et al. [8] pointed out that many implemented policy or important policy is brewing is always lack of economic theory under the guidance of. At the same time, China’s power industry low-carbon policy formulation method is relatively simple [9, 10], lacking solid theoretical support, cannot demonstrate the interaction between the various factors.Therefore, for the thermal power plant with carbon capture equipment, considering the carbon capture rate of the power plant as its private information, the controllable carbon capture rate of power plant as its efforts, this paper establishes the government’s incentive model for carbon capture power plants and study how the government can develop subsidies or tax policies to incent power plants to effectively carry out carbon capture to reduce carbon emissions.


## 2. Literature Review

Early research involved multiple fields, here we main discuss the research that is highly relevant to this paper. With the increasing of CO2 emissions, it brings the dramatic changes in climate and also has an affected on the development of social economy. Therefore, in order to achieve low-cost, high-efficiency carbon emissions, there is an urgent need for the government to set supportive and motivating regulations to reduce carbon emissions effectively [11]. In this context, scholars have explored this situation actively, a lot of research has been done and a series of related conclusions have been made on the power plant with carbon capture and storage (CCS) technology in carbon emissions and carbon tax and trading price on power plant under incentive regulation theory.


### 2.1. Power Plant with Carbon Capture and Storage (CCS) Technology in Carbon Emissions

There have been many papers studying carbon capture and storage (CCS) technology. To reduce the carbon emissions. Rubin et al. [12] used historical experience curves as the basis for estimating future cost trends for four types of electric power plants equipped with CO2 capture systems. They first assessed the rates of cost reductions achieved by other energy and environmental process technologies in the past. Then, by analogy with leading capture plant designs, they estimated the future cost reductions that might be achieved by power plants employing CO2 capture. Abu-Zahra et al. [13] studied for a CO2 capture process from flue gas of a 600 MWe bituminous coal fired power plant, based on absorption process with MEA solutions, using ASPEN Plus with the RADFRAC subroutine, was performed. It is aimed to reduce the energy requirement for solvent regeneration, by investigating the effects of CO2 removal percentage, MEA concentration, lean solvent loading, stripper operating pressure and lean solvent temperature. In addition, Abu-Zahra et al. [14] defined the economic baseline for post-combustion CO2 capture from 600 MWe bituminous coal-fired power plant is described. The baseline capture process is based on 30% (by weight) aqueous solution of monoetha-nolamine (MEA). A process model has been developed previously using the Aspen Plus simulation programme where the baseline CO2-removal has been chosen to be 90%. The results from the process modeling have provided the required input data to the economic modeling. Rongrong et al. [15] pointed out that the efficiency drop due to CO2 removal plant is approximately 12.9%, and the cost of CO2 captured and the cost of CO2 avoided are respectively 13 euros/tCO2 and 18 euros/tCO2. In order to popularize large-scale CCS to power plants, technology improvement is greatly needed. Furthermore, the feasibility, mechanism, and options of flexible operation in capture plant are first clarified by Chen et al. [16], Then, based on a benchmark capture plant with post combustion and solvent separation technology, a generic quantitative model is established to formulate the process of CO2 capture and the interaction between capture system and generation system. Plant performances as well as its effects on power-system operation are examined, revealing the different characteristics between CO2 capture power plant and conventional non-capture plants. On this basis, typical operation modes of CO2-capture power plant are defined and identified. Rasodjio and Darmawan [17] developed a model, optima carbon capture and storage (CCS), that combines economic and spatial optimization for the integration of CCS transport, storage and injection infrastructure to minimize costs. The model solves for the lowest-cost set of pipeline routes and storage/injection sites that connect CO2 sources to the storage. Carbon capture and storage (CCS) policy in the United States, a new coalition endeavors to change existing policy are investigated by Pollak et al. [18]. Finally, they find that the newly formed climate coalition seeks to change existing geologic storage policy to support their proactive vision: to maximize energy supply or greenhouse gas reductions using CCS when climate policy is enacted. Stechow et al. [19] focused on the particular case of carbon capture and storage (CCS) technologies and conducts a qualitative multi-criteria analysis of different public policy support schemes for CCS demonstration to evaluate their suitability. The results show that two alternative schemes, a CCS bonus incentive or a carbon dioxide (CO2) price guarantee, perform best in comparison with the other assessed instruments. While they reduce the uncertainty of CCS investments in the face of low European Union Allowance prices, they also avoid significant adverse impacts on operational and investment decisions in electricity markets. Meadowcroft [20] applied concepts, theories, and methodologies from the social and policy sciences, to elucidate how societies are engaging with CCS as a mitigation option and to point toward a future research agenda which, while exploring basic aspects of technology development as situated in a social context, would also be aligned with the needs of the climate and environmental policy community. Markusson et al. [21] explored the complexity of social learning associated with demonstration projects. Variety in expectations of the demonstration projects’ objectives, learning processes, information sharing mechanisms, public engagement initiatives, financing and collaborative partnerships are highlighted. The result shows that multiple factors including the process of building support for the project, the governance context and the framing of the project matter for the learning in demonstration projects. Finally, Liu and Gallagher  [22] examined the current state of Carbon Capture, Utilization, and Storage (CCUS) in China as well as the related climate change policy, laws, and initiatives that might be used to encourage the large-scale deployment of carbon sequestration in China. Meanwhile, Haszeldine [23] pointed that the capture of carbon dioxide at the point of emission from coal- or gas-burning power plants is an attractive route to reducing carbon dioxide emissions into the atmosphere. To commercialize carbon capture, as well as transport of liquified carbon dioxide and its storage in exploited oil fields or saline formations, many technological, commercial, and political hurdles remain to be overcome. The variation in the state-level energy context for CCS development by exploring energy policy stakeholder’ perceptions of CCS in four geographically and demographically diverse states is accessed by Chaudhry et al. [24], the variation in state and stakeholder energy priorities and perceptions revealed in this study highlights challenges in the development and implementation of national-level energy policy and also specific challenges in the deployment of CCS. Kuckshinrichs [25] integrated the technology study to discuss and assess the technical, economic, environmental, and social perspectives of CCS technologies, in addition, the research described the contributions on using and storing CO2 comprehensively.However, the above studies mainly concentrated on CCS technology developing process, Few scholars study the problem that how the government can develop subsidies or tax policies to incent power plants to effectively carry out carbon capture to reduce carbon emissions. Therefore, we fill this gap and explore the optimal strategic decisions of the government.


### 2.2. Carbon Tax on Power Plant under Incentive Regulation Theory

Recently, the role of the government low carbon policies has also been considered. Studies mainly include two aspects: one is designing a carbon tax to control global warming, and the other is optimizing the incentive regulation of the government.Regarding the first aspect, Borchiellini et al. [26] studied the carbon tax vs CO2 sequestration effects on environmental analysis of existing power plants. Nissen [27] derived the efficient tax-subsidy policy in an energy-economy-environment growth model with carbon emission externalities, and a carbon capture and sequestration (CCS) sector with learning by doing (LBD) externalities. Abadie and Chamorro [28] assessed the option to install a carbon capture and storage (CCS) unit in a coal-fired power plant operating in a carbon-constrained environment and pointed out that that, at current permit prices, immediate installation does not seem justified from a financial point of view. This need not be the case, though, if carbon market parameters change dramatically, carbon capture technology undergoes significant improvements, and/or a specific governmental policy to promote these units is adopted. Jeong et al. [29] investigated the economic comparison between coal-fired and liquefied natural gas combined cycle power plants considering carbon tax of Korean case. It aims at making an economic analysis of Korea’s power plant utilities. In addition, Kemmoku et al. [30] investigated the buying price of photo voltaic electricity under a carbon tax regime. It assuming that photo voltaic (PV) systems are adopted in residential houses under a carbon tax regime, the economic performance of PV systems is investigated from the standpoint of an electric utility. Mendelevitch et al. [31] presented a mixed integer, multi-period, cost-minimizing model for a carbon capture, transport and storage network in Europe. The model incorporates endogenous decisions about carbon capture, pipeline and storage investments. The capture, flow and injection quantities are based on given costs, certificate prices, storage capacities, and point source emissions. Huang et al. [32] conducted a optimal cleaning power generation investment strategy in a carbon tax and CO2 emission trading framework and studied a two-staged cleaning energy investment problem under uncertainty. The results indicate that, because of the variation fluctuation of electricity price, the investor tends to delay investing when the electricity price is lower, whereas the higher price–price ratio of electricity is helpful for him to deploy ahead the carbon capture device. Renner [33] conducted a literature review on public studies about CCS costs and constructed a net present value model to calculate the cost of electricity and the break even CO2 price to objectively assess the profitability of CCS plants. Oei et al. [34] developed a model to analyze the economics of carbon capture, transport, and storage in the wake of expected rising CO2 prices. In addition, the model determined a cost minimizing strategy on whether to purchase CO2 certificates, or to abate the CO2 through investments into a CCTS-chain on a site by site basis. Cai et al. [35] considered a situation where a tax on emissions is imposed on carbon dioxide (CO2) producers to encourage their participation in CCS. Operators of CO2 transportation pipelines and storage sites enter into individual contracts with emissions producers to store CO2. They also study the problem of selecting the optimal price and volume of these contracts under both cost and emissions uncertainty to optimize the storage operators expected profit.For the second aspect, Yi et al. [36] gave an introduction to incentive regulation, and analyses the experiences and lessons of price cap, which is one of methods of the theory of incentive regulation, applied widely in these reforms. Jamasb and Pollitt [37] reviewed the recent experience of the UK electricity distribution sector under incentive regulation. Furthermore, Castillo and Linn [38] compared the incentives a carbon dioxide emissions price creates for investment in low carbon dioxide-emitting technologies in the electricity sector. Finally, Menezes and Xuemei [39] reviewed the incentives for pursuing a low-carbon electricity sector that are embedded in China’s regulatory and policy framework and pointed out that different institutions and agents who face different and often conflicting incentives for pursuing environmental and energy efficiency objectives.For now, most of the papers in this area is about the development of CCS technology or the establishment of a single incentive regulation, but there are a growing number of nations setting a carbon tax and trading price on power plant with carbon capture under incentive regulation theory. They attempt to force the power industry to reduce carbon emissions to relieve environmental stress, and while the government sets corresponding policies, it also encourages the power industry to use CCS emission reduction technologies. According to the Section2, we find that there is relatively little research on this. Most studies focus on CCS technology to reduce carbon emissions. Therefore, we discuss the effect of the government sets policy on the power plant with carbon capture and storage. In the next section, we will describe the model used in this paper.In this paper, we consider the problem of how the government develops subsidies or tax policy to encourage power plant make carbon capture to reduce carbon emissions more effectively, and use the government regulation incentive model to research the problem that regulators is in the information disadvantage considering the carbon capture rate of the power plant as its private information. The main contributions of this paper are: (1) A set of regulation mechanism which applies where the government regulates the power plant for capturing carbon emission have be established and be proved efficient to reveal the power plant private information and encourage it to improve carbon capture rates. (2) We obtain the conditions of the power plant achieve the largest corporate surplus. (3) We provide some meaningful advice for the regulators to make reasonable regulations.The reminder of this paper is organized as follows. In Section2, a literature review is presented. Section 3 presents the assumptions of the model. Section 4 presents the basic models of the problem. Sections 5 and 6 presents a numerical example and parametric analysis for better understanding. In Section 7, Conclusions and suggestions for future research are presented.


## 2.1. Power Plant with Carbon Capture and Storage (CCS) Technology in Carbon Emissions

There have been many papers studying carbon capture and storage (CCS) technology. To reduce the carbon emissions. Rubin et al. [12] used historical experience curves as the basis for estimating future cost trends for four types of electric power plants equipped with CO2 capture systems. They first assessed the rates of cost reductions achieved by other energy and environmental process technologies in the past. Then, by analogy with leading capture plant designs, they estimated the future cost reductions that might be achieved by power plants employing CO2 capture. Abu-Zahra et al. [13] studied for a CO2 capture process from flue gas of a 600 MWe bituminous coal fired power plant, based on absorption process with MEA solutions, using ASPEN Plus with the RADFRAC subroutine, was performed. It is aimed to reduce the energy requirement for solvent regeneration, by investigating the effects of CO2 removal percentage, MEA concentration, lean solvent loading, stripper operating pressure and lean solvent temperature. In addition, Abu-Zahra et al. [14] defined the economic baseline for post-combustion CO2 capture from 600 MWe bituminous coal-fired power plant is described. The baseline capture process is based on 30% (by weight) aqueous solution of monoetha-nolamine (MEA). A process model has been developed previously using the Aspen Plus simulation programme where the baseline CO2-removal has been chosen to be 90%. The results from the process modeling have provided the required input data to the economic modeling. Rongrong et al. [15] pointed out that the efficiency drop due to CO2 removal plant is approximately 12.9%, and the cost of CO2 captured and the cost of CO2 avoided are respectively 13 euros/tCO2 and 18 euros/tCO2. In order to popularize large-scale CCS to power plants, technology improvement is greatly needed. Furthermore, the feasibility, mechanism, and options of flexible operation in capture plant are first clarified by Chen et al. [16], Then, based on a benchmark capture plant with post combustion and solvent separation technology, a generic quantitative model is established to formulate the process of CO2 capture and the interaction between capture system and generation system. Plant performances as well as its effects on power-system operation are examined, revealing the different characteristics between CO2 capture power plant and conventional non-capture plants. On this basis, typical operation modes of CO2-capture power plant are defined and identified. Rasodjio and Darmawan [17] developed a model, optima carbon capture and storage (CCS), that combines economic and spatial optimization for the integration of CCS transport, storage and injection infrastructure to minimize costs. The model solves for the lowest-cost set of pipeline routes and storage/injection sites that connect CO2 sources to the storage. Carbon capture and storage (CCS) policy in the United States, a new coalition endeavors to change existing policy are investigated by Pollak et al. [18]. Finally, they find that the newly formed climate coalition seeks to change existing geologic storage policy to support their proactive vision: to maximize energy supply or greenhouse gas reductions using CCS when climate policy is enacted. Stechow et al. [19] focused on the particular case of carbon capture and storage (CCS) technologies and conducts a qualitative multi-criteria analysis of different public policy support schemes for CCS demonstration to evaluate their suitability. The results show that two alternative schemes, a CCS bonus incentive or a carbon dioxide (CO2) price guarantee, perform best in comparison with the other assessed instruments. While they reduce the uncertainty of CCS investments in the face of low European Union Allowance prices, they also avoid significant adverse impacts on operational and investment decisions in electricity markets. Meadowcroft [20] applied concepts, theories, and methodologies from the social and policy sciences, to elucidate how societies are engaging with CCS as a mitigation option and to point toward a future research agenda which, while exploring basic aspects of technology development as situated in a social context, would also be aligned with the needs of the climate and environmental policy community. Markusson et al. [21] explored the complexity of social learning associated with demonstration projects. Variety in expectations of the demonstration projects’ objectives, learning processes, information sharing mechanisms, public engagement initiatives, financing and collaborative partnerships are highlighted. The result shows that multiple factors including the process of building support for the project, the governance context and the framing of the project matter for the learning in demonstration projects. Finally, Liu and Gallagher  [22] examined the current state of Carbon Capture, Utilization, and Storage (CCUS) in China as well as the related climate change policy, laws, and initiatives that might be used to encourage the large-scale deployment of carbon sequestration in China. Meanwhile, Haszeldine [23] pointed that the capture of carbon dioxide at the point of emission from coal- or gas-burning power plants is an attractive route to reducing carbon dioxide emissions into the atmosphere. To commercialize carbon capture, as well as transport of liquified carbon dioxide and its storage in exploited oil fields or saline formations, many technological, commercial, and political hurdles remain to be overcome. The variation in the state-level energy context for CCS development by exploring energy policy stakeholder’ perceptions of CCS in four geographically and demographically diverse states is accessed by Chaudhry et al. [24], the variation in state and stakeholder energy priorities and perceptions revealed in this study highlights challenges in the development and implementation of national-level energy policy and also specific challenges in the deployment of CCS. Kuckshinrichs [25] integrated the technology study to discuss and assess the technical, economic, environmental, and social perspectives of CCS technologies, in addition, the research described the contributions on using and storing CO2 comprehensively.However, the above studies mainly concentrated on CCS technology developing process, Few scholars study the problem that how the government can develop subsidies or tax policies to incent power plants to effectively carry out carbon capture to reduce carbon emissions. Therefore, we fill this gap and explore the optimal strategic decisions of the government.


## 2.2. Carbon Tax on Power Plant under Incentive Regulation Theory

Recently, the role of the government low carbon policies has also been considered. Studies mainly include two aspects: one is designing a carbon tax to control global warming, and the other is optimizing the incentive regulation of the government.Regarding the first aspect, Borchiellini et al. [26] studied the carbon tax vs CO2 sequestration effects on environmental analysis of existing power plants. Nissen [27] derived the efficient tax-subsidy policy in an energy-economy-environment growth model with carbon emission externalities, and a carbon capture and sequestration (CCS) sector with learning by doing (LBD) externalities. Abadie and Chamorro [28] assessed the option to install a carbon capture and storage (CCS) unit in a coal-fired power plant operating in a carbon-constrained environment and pointed out that that, at current permit prices, immediate installation does not seem justified from a financial point of view. This need not be the case, though, if carbon market parameters change dramatically, carbon capture technology undergoes significant improvements, and/or a specific governmental policy to promote these units is adopted. Jeong et al. [29] investigated the economic comparison between coal-fired and liquefied natural gas combined cycle power plants considering carbon tax of Korean case. It aims at making an economic analysis of Korea’s power plant utilities. In addition, Kemmoku et al. [30] investigated the buying price of photo voltaic electricity under a carbon tax regime. It assuming that photo voltaic (PV) systems are adopted in residential houses under a carbon tax regime, the economic performance of PV systems is investigated from the standpoint of an electric utility. Mendelevitch et al. [31] presented a mixed integer, multi-period, cost-minimizing model for a carbon capture, transport and storage network in Europe. The model incorporates endogenous decisions about carbon capture, pipeline and storage investments. The capture, flow and injection quantities are based on given costs, certificate prices, storage capacities, and point source emissions. Huang et al. [32] conducted a optimal cleaning power generation investment strategy in a carbon tax and CO2 emission trading framework and studied a two-staged cleaning energy investment problem under uncertainty. The results indicate that, because of the variation fluctuation of electricity price, the investor tends to delay investing when the electricity price is lower, whereas the higher price–price ratio of electricity is helpful for him to deploy ahead the carbon capture device. Renner [33] conducted a literature review on public studies about CCS costs and constructed a net present value model to calculate the cost of electricity and the break even CO2 price to objectively assess the profitability of CCS plants. Oei et al. [34] developed a model to analyze the economics of carbon capture, transport, and storage in the wake of expected rising CO2 prices. In addition, the model determined a cost minimizing strategy on whether to purchase CO2 certificates, or to abate the CO2 through investments into a CCTS-chain on a site by site basis. Cai et al. [35] considered a situation where a tax on emissions is imposed on carbon dioxide (CO2) producers to encourage their participation in CCS. Operators of CO2 transportation pipelines and storage sites enter into individual contracts with emissions producers to store CO2. They also study the problem of selecting the optimal price and volume of these contracts under both cost and emissions uncertainty to optimize the storage operators expected profit.For the second aspect, Yi et al. [36] gave an introduction to incentive regulation, and analyses the experiences and lessons of price cap, which is one of methods of the theory of incentive regulation, applied widely in these reforms. Jamasb and Pollitt [37] reviewed the recent experience of the UK electricity distribution sector under incentive regulation. Furthermore, Castillo and Linn [38] compared the incentives a carbon dioxide emissions price creates for investment in low carbon dioxide-emitting technologies in the electricity sector. Finally, Menezes and Xuemei [39] reviewed the incentives for pursuing a low-carbon electricity sector that are embedded in China’s regulatory and policy framework and pointed out that different institutions and agents who face different and often conflicting incentives for pursuing environmental and energy efficiency objectives.For now, most of the papers in this area is about the development of CCS technology or the establishment of a single incentive regulation, but there are a growing number of nations setting a carbon tax and trading price on power plant with carbon capture under incentive regulation theory. They attempt to force the power industry to reduce carbon emissions to relieve environmental stress, and while the government sets corresponding policies, it also encourages the power industry to use CCS emission reduction technologies. According to the Section2, we find that there is relatively little research on this. Most studies focus on CCS technology to reduce carbon emissions. Therefore, we discuss the effect of the government sets policy on the power plant with carbon capture and storage. In the next section, we will describe the model used in this paper.In this paper, we consider the problem of how the government develops subsidies or tax policy to encourage power plant make carbon capture to reduce carbon emissions more effectively, and use the government regulation incentive model to research the problem that regulators is in the information disadvantage considering the carbon capture rate of the power plant as its private information. The main contributions of this paper are: (1) A set of regulation mechanism which applies where the government regulates the power plant for capturing carbon emission have be established and be proved efficient to reveal the power plant private information and encourage it to improve carbon capture rates. (2) We obtain the conditions of the power plant achieve the largest corporate surplus. (3) We provide some meaningful advice for the regulators to make reasonable regulations.The reminder of this paper is organized as follows. In Section2, a literature review is presented. Section 3 presents the assumptions of the model. Section 4 presents the basic models of the problem. Sections 5 and 6 presents a numerical example and parametric analysis for better understanding. In Section 7, Conclusions and suggestions for future research are presented.


## 3. Assumptions

The notations in paper to solve the problem is shown in Table1, the game sequence is shown in Figure 1.Table 1
Notations.
Notations
Explanations
β
Original carbon capture rate (real carbon capture rate) Effort made
e
by the power plant
r
Carbon capture rate with effort (monitored by government)
q
Power quantity
c
Unit output cost
I
Investment made by the power plant for effort
p
1
Power price to the power plant
p
2
Power price to the consumer
p
3
Carbon trading price
k
Coefficient of cost increase for carbon capture
λ
Coefficient of shadow cost
T
Transferring payment
U
Utility of the power plant
V
Utility of the consumer
N
Social welfare coefficient of power
W
Social welfare
A
Original carbon quota of the power plant
M
Coefficient of carbon emissionFigure 1
Game sequence.Assumption 1.
We consider moral hazard and adverse selection in this paper.The original carbon capture rateβ is private information of the power plant, and it can be improved by effort e, which can’t be observed by government, such as updating equipment, technical improvement and so on, but the effort costs Ie. So the carbon capture rate with effort is shown as:(1)r=β+e.Whereβ∈β̲,β¯, Fβ means the absolutely continuous distribution function and its density is fβ While β∈β̲,β¯, fβ>0 and the monotone hazard rate dFβ/fβ/dβ≥0, for most distributions, such as uniform distribution, normal distribution, logarithmic distribution, exponential distribution and Laplace distribution, satisfy the condition e is the moral hazard parameter, and it relates to the carbon capture rate, in other words, e=eβ. Meanwhile, we assume I′·>0, I″·>0, and I″′·=0.Assumption 2.
Based on emissions trading scheme (ETS), the power plant obtains A units original carbon quota according to the natural absorption [40] and the power plant scale. If A is not sufficient, the power plant should purchase more, otherwise, it can sell some to obtain profit with price p3. Let I′=A−Mqβ1−rβP3 be the relationship, where M is the coefficient of carbon emission.Assumption 3.
Carbon capture will increase the output cost of the power plant [41], and it follows:(2)
c
1
=
k
·
r
=
k
β
+
e
,wherek is coefficient of cost increase for carbon capture.Assumption 4.
We designateNp2q as the utility to consumer when he consumes q unit power. p2 is power price to the consumer and it satisfies:(3)
p
2
=
a
−
b
q
.Assumption 5.
Power plant aims at more profit. Government with the target of maximizing the social welfare, pays transferring paymentT to encourage power plant to invest and get its private information β.


## 4. Model

### 4.1. Utility of the Power Plant

Power plant offers power with the pricep1, obtains the transferring payment T from government and suffers some costs, as it is shown below:(4)Uβ=p1qβ+Tβ−1+krβqβc−Ie+I′,wherec the unit output cost of the power plant.


### 4.2. Utility of the Consumer

We denoteNp2qβ as the power social welfare to the consumer, meanwhile, we consider the shadow cost λ in the model. Accordingly, the utility of the consumer is given by:(5)Vβ=Np2qβ−1+λTβ.


### 4.3. The Target of Government

Government as the regulator maximizes the social welfare which includes the power plant and the consumer. In other words, it isW=U+V. Therefore, the total social welfare from various power plant with different carbon capture rate is given by:(6)W¯=∫β̲β¯U+VdFβ.


### 4.4. The Incentive Constraints

The power plant chooses one contract offered by government according toβ̂ which is given by itself, and government pays transferring payment according to the contract chosen by power plant, which maybe cannot reveal the true carbon capture rate. So the power plant utility is the following function:(7)Uβ,β̂=p1qβ̂+Tβ̂−1+krβ̂qβ̂c−Irβ̂−β+A−Mqβ̂1−rβ̂P3.Furthermore, when eachβ1,β2∈β̲,β¯, we get the incentive constraints:(8)p1qβ1+Tβ1−1+krβ1qβ1c−Irβ1−β1+A−Mqβ11−rβ1P3≥p1qβ2+Tβ2−1+krβ2qβ2c−Irβ2−β1+A−Mqβ21−rβ2P3.(9)p1qβ2+Tβ2−1+krβ2qβ2c−Irβ2−β2+A−Mqβ21−rβ2P3≥p1qβ1+Tβ1−1+krβ1qβ1c−Irβ1−β2+A−Mqβ11−rβ1P3.


### 4.5. The Participant Constraints

In order to let the power plant take part in the project willingly, government should let it keep the profit no less than that it is absent (normalized to 0 here). It is:(10)Uβ,β̂≥0.


### 4.6. The Model and Solution

Above all, the general problem established is the following:(11)P:W¯=maxe⋅,q⋅∫β̲β¯U+VdFβs.t.8,9,10.Let us consider the problem. We can combine Equations (8) and (9) to obtain Equation (12):(12)∫β1β2∫rβ1rβ2I″x−ydxdy≥0.SinceI″·>0, due to Equation (12), we know r˙β is the non decreasing function of β, we obtain r˙β≥0, or equivalently:(13)e˙β≥−1.The power plant with low carbon capture rate maybe fakes it for more profit, so we take the envelope theorem to Equation (7), we get:(14)U˙β=I′rβ−β≥0.In order to save cost, government will letUβ̲=0. From Equation (14):(15)Uβ=∫β̲βI′eβ~dβ~.Proposition 1.
The redundant profit obtained by power plant with high carbon capture rate is shown by Equation (15), and we also call it information rent.Proposition1 shows that, the redundant profit is only related to the function of its effort under regulation. In reality, the government encourages the power plant to reduce the carbon emissions by effort and will make a portion of the investment up. So the benefit from investing to reduce carbon emissions is kept by the power plant reasonable.Corollary 1.
Equation (14) shows that the redundant profit varies with its carbon capture rate β in the same direction. It means, the higher the carbon capture rate is, the more profit the power plant gets. Obviously, the regulation mechanism can encourage the power plant to improve the carbon capture rate for more redundant profit.So the total information rent from variousβ is formulated by Equation (16):(16)∫β̲β¯UβdFβ=∫β̲β¯∫β̲βI′eβ~dβ~dFβ=∫β̲β¯1−FβfβI′eβdFβ.By replacing Equations (5), (7), and (16) into Equation (11), we can reformulate government’s problem as:(17)W¯=maxeβ,qβ∫β̲β¯Na−bqβqβ−1+λ1+krβqβc+Ie−A−Mqβ1−rβp3−p1qβ−λ1−FβfβI′eβdFβs.t.13.We denoteJ as the integral part of Equation (17) and we obtain:(18)∂2J∂q2=−2bN≤0.Furthermore, from∂J/∂q=0:(19)q∗=a2b−1+λ1+krβc+Mp31−rβ−p12bN.Now let us consider the constraint Equation (13). From ∂J/∂e=0, we get:(20)I′e=Mp3−kcqβ−λ1+λ·1−Fβfβ·I″e.Proposition 2.
The optimal effort level is decided by Equation (20) under regulation. Equation (20) describes a one-to-one correspondence between the carbon capture rate β and the optimal effort e. The power plant with different carbon capture rate will select different effort.Corollary 2.
The optimal effort level of power plant has the same trend with its carbon capture rateβ.The derivative ofβ from Equation (20) is:(21)e˙β=1+λMp3−kc2r˙βI″e2bN−λ1+λd1−Fβ/fβdβ.Obviously,e˙β>0 and we get Corollary 2. And it satisfies the constraint Equation (13). Consequently, we can get e∗β from Equation (20).Finally, we know the optimal information rent, the carbon capture rate and the transferring payment follow the following formulations:(22)U∗β=∫β̲βI′eβ~dβ~(23)r∗β=β+e∗β(24)T∗β=U∗β+Ie∗β+1+kr∗βcq∗β−A−Mq∗β1−r∗βp3−p1q∗β.Replacer∗β by its inverse function β=β∗r into Equation (24), the optimal transferring payment is shown as:(25)T∗r=∫β̲βI′e∗β~rdβ~+Ie∗βr+1+kβr+e∗βrcq∗βr−A−Mqβr1−βr−e∗βrp3−p1qβr,where the carbon capture rate with effortr is visible for government.Proposition 3.
To monitor the carbon capture rate with effortr∗β, the government derives the original carbon capture rate β from r∗β=β+e∗β, where e∗β is given by Equation (20).Proposition 4.
T
∗
β
,
q
∗
β is the optimal regulation mechanism between the government and the power plant. In other words, the government decides the power quantity q∗β and the transferring payment T∗β according to Equation (19) and Equation (24) as soon as it obtains the carbon capture rate with effort r∗β.In summary, this paper provides a set of regulation mechanism (Proposition 4) which applies where the government regulates the power plant for capturing carbon emission. With this regulation mechanism, we can get: (1) The government can calculate the original carbon capture rate of the power plant while it monitors the carbon capture rate with effort (Proposition 3); (2) The power plant will select the optimal power quantityq∗β and the transferring payment T∗β that is one-to-one correspondence with its original carbon capture rate β; (3) The power plant makes optimal effort decided by Equation (20) (Proposition 2), and obtains some redundant profit(Proposition 1). In a word, the government reaches its goals that revealing the real carbon capture rate and encouraging the power plant to make optimal effort to reduce the carbon emission.


## 4.1. Utility of the Power Plant

Power plant offers power with the pricep1, obtains the transferring payment T from government and suffers some costs, as it is shown below:(4)Uβ=p1qβ+Tβ−1+krβqβc−Ie+I′,wherec the unit output cost of the power plant.


## 4.2. Utility of the Consumer

We denoteNp2qβ as the power social welfare to the consumer, meanwhile, we consider the shadow cost λ in the model. Accordingly, the utility of the consumer is given by:(5)Vβ=Np2qβ−1+λTβ.


## 4.3. The Target of Government

Government as the regulator maximizes the social welfare which includes the power plant and the consumer. In other words, it isW=U+V. Therefore, the total social welfare from various power plant with different carbon capture rate is given by:(6)W¯=∫β̲β¯U+VdFβ.


## 4.4. The Incentive Constraints

The power plant chooses one contract offered by government according toβ̂ which is given by itself, and government pays transferring payment according to the contract chosen by power plant, which maybe cannot reveal the true carbon capture rate. So the power plant utility is the following function:(7)Uβ,β̂=p1qβ̂+Tβ̂−1+krβ̂qβ̂c−Irβ̂−β+A−Mqβ̂1−rβ̂P3.Furthermore, when eachβ1,β2∈β̲,β¯, we get the incentive constraints:(8)p1qβ1+Tβ1−1+krβ1qβ1c−Irβ1−β1+A−Mqβ11−rβ1P3≥p1qβ2+Tβ2−1+krβ2qβ2c−Irβ2−β1+A−Mqβ21−rβ2P3.(9)p1qβ2+Tβ2−1+krβ2qβ2c−Irβ2−β2+A−Mqβ21−rβ2P3≥p1qβ1+Tβ1−1+krβ1qβ1c−Irβ1−β2+A−Mqβ11−rβ1P3.


## 4.5. The Participant Constraints

In order to let the power plant take part in the project willingly, government should let it keep the profit no less than that it is absent (normalized to 0 here). It is:(10)Uβ,β̂≥0.


## 4.6. The Model and Solution

Above all, the general problem established is the following:(11)P:W¯=maxe⋅,q⋅∫β̲β¯U+VdFβs.t.8,9,10.Let us consider the problem. We can combine Equations (8) and (9) to obtain Equation (12):(12)∫β1β2∫rβ1rβ2I″x−ydxdy≥0.SinceI″·>0, due to Equation (12), we know r˙β is the non decreasing function of β, we obtain r˙β≥0, or equivalently:(13)e˙β≥−1.The power plant with low carbon capture rate maybe fakes it for more profit, so we take the envelope theorem to Equation (7), we get:(14)U˙β=I′rβ−β≥0.In order to save cost, government will letUβ̲=0. From Equation (14):(15)Uβ=∫β̲βI′eβ~dβ~.Proposition 1.
The redundant profit obtained by power plant with high carbon capture rate is shown by Equation (15), and we also call it information rent.Proposition1 shows that, the redundant profit is only related to the function of its effort under regulation. In reality, the government encourages the power plant to reduce the carbon emissions by effort and will make a portion of the investment up. So the benefit from investing to reduce carbon emissions is kept by the power plant reasonable.Corollary 1.
Equation (14) shows that the redundant profit varies with its carbon capture rate β in the same direction. It means, the higher the carbon capture rate is, the more profit the power plant gets. Obviously, the regulation mechanism can encourage the power plant to improve the carbon capture rate for more redundant profit.So the total information rent from variousβ is formulated by Equation (16):(16)∫β̲β¯UβdFβ=∫β̲β¯∫β̲βI′eβ~dβ~dFβ=∫β̲β¯1−FβfβI′eβdFβ.By replacing Equations (5), (7), and (16) into Equation (11), we can reformulate government’s problem as:(17)W¯=maxeβ,qβ∫β̲β¯Na−bqβqβ−1+λ1+krβqβc+Ie−A−Mqβ1−rβp3−p1qβ−λ1−FβfβI′eβdFβs.t.13.We denoteJ as the integral part of Equation (17) and we obtain:(18)∂2J∂q2=−2bN≤0.Furthermore, from∂J/∂q=0:(19)q∗=a2b−1+λ1+krβc+Mp31−rβ−p12bN.Now let us consider the constraint Equation (13). From ∂J/∂e=0, we get:(20)I′e=Mp3−kcqβ−λ1+λ·1−Fβfβ·I″e.Proposition 2.
The optimal effort level is decided by Equation (20) under regulation. Equation (20) describes a one-to-one correspondence between the carbon capture rate β and the optimal effort e. The power plant with different carbon capture rate will select different effort.Corollary 2.
The optimal effort level of power plant has the same trend with its carbon capture rateβ.The derivative ofβ from Equation (20) is:(21)e˙β=1+λMp3−kc2r˙βI″e2bN−λ1+λd1−Fβ/fβdβ.Obviously,e˙β>0 and we get Corollary 2. And it satisfies the constraint Equation (13). Consequently, we can get e∗β from Equation (20).Finally, we know the optimal information rent, the carbon capture rate and the transferring payment follow the following formulations:(22)U∗β=∫β̲βI′eβ~dβ~(23)r∗β=β+e∗β(24)T∗β=U∗β+Ie∗β+1+kr∗βcq∗β−A−Mq∗β1−r∗βp3−p1q∗β.Replacer∗β by its inverse function β=β∗r into Equation (24), the optimal transferring payment is shown as:(25)T∗r=∫β̲βI′e∗β~rdβ~+Ie∗βr+1+kβr+e∗βrcq∗βr−A−Mqβr1−βr−e∗βrp3−p1qβr,where the carbon capture rate with effortr is visible for government.Proposition 3.
To monitor the carbon capture rate with effortr∗β, the government derives the original carbon capture rate β from r∗β=β+e∗β, where e∗β is given by Equation (20).Proposition 4.
T
∗
β
,
q
∗
β is the optimal regulation mechanism between the government and the power plant. In other words, the government decides the power quantity q∗β and the transferring payment T∗β according to Equation (19) and Equation (24) as soon as it obtains the carbon capture rate with effort r∗β.In summary, this paper provides a set of regulation mechanism (Proposition 4) which applies where the government regulates the power plant for capturing carbon emission. With this regulation mechanism, we can get: (1) The government can calculate the original carbon capture rate of the power plant while it monitors the carbon capture rate with effort (Proposition 3); (2) The power plant will select the optimal power quantityq∗β and the transferring payment T∗β that is one-to-one correspondence with its original carbon capture rate β; (3) The power plant makes optimal effort decided by Equation (20) (Proposition 2), and obtains some redundant profit(Proposition 1). In a word, the government reaches its goals that revealing the real carbon capture rate and encouraging the power plant to make optimal effort to reduce the carbon emission.


## 5. Numerical Example

Taking Hebei Province in China as example to analyze, and we list these data after investigating: the coefficient of shadow costλ=0.1; the coefficient of carbon emission M=0.997; the social welfare coefficient of power N=0.47; the coefficient of cost increase for carbon capture k=0.25; the power price to the power plant p1=397 yuan/MW, the carbon trading price p3=100 yuan/t, the unit power production cost c=245 yuan/MW, the original carbon quota of the power plant A=0 t, the cost for the effort of the plant I=1/2δe2, and δ=105; the market scale a=2000, and b=5; the carbon capture rate β is uniformly distributed on 0,0.7, with cumulative distribution function Fβ=10/7β, and density function fβ=10/7.We calculate these outcomes listing in Table2 based on Proposition 1–4.Table 2
Regulation mechanism and its effect.
Regulation based onβ
Regulation based onr
Original carbon capture rateβ
β
0.9135
∗
r
−
0.0164
Optimal effort made by power plante∗
0.0180
+
0.0947
∗
β
0.0865
∗
r
+
0.0164
Carbon capture rate monitored by governmentr∗
0.0180
+
1.0947
∗
β
r
Regulation mechanism
Power quantityq∗
9.8511
∗
β
+
212.4027
8.9990
∗
r
+
212.2411
Transferring paymentT∗
4957.96
β
2
−
7488.29
β
−
11239.67
4137.3296
∗
r
2
−
6989.1073
∗
r
−
11115.5286According to Table2, regulators can regulate coal fired power plant in distinct ways, such as the regulation based on β (as shown in Table 2, column second), or the regulation based on r (as shown in Table 2, column third). For the original carbon capture rate reported by a power plant and the carbon capture rate observed by the regulator, the regulator provides the corresponding regulation rules, that is, the power generation and transfer payment.In addition, we illustrate how the redundant profitU varies with the original carbon capture rate β and the carbon capture rate claimed by the power plant β̂, shown in Figure 2.Figure 2
Figure ofU varying with β and β̂.As shown in Figure2, the power plant with the lowest carbon capture rate obtains 0 redundant profit, U0,0=0 or Uβ̲=0. Meanwhile, the redundant profit U increases while the original carbon capture rate β increases just as Corollary 1, which is also shown in Figure 3 more clearly. Furthermore, when x=y in Figure 2, z attains the peak. That is, if and only if the claimed carbon capture rate is the same with its real one (β̂=β), the redundant profit is maximum. Hence, the power plant will reveal its real carbon capture rate and choose contract suitable for itself under this regulation mechanism.Figure 3
Relationship betweenU and β.We give Figure4 to show how the optimal carbon capture rate with effort r∗β and the optimal effort e∗β change with the real carbon capture rate β.Figure 4
Figure of carbon capture rate and effort varying withβ.As Figure4 shown, both the carbon capture rate with effort r∗β and the effort e∗β increase while the original carbon capture rate β increases. Specially, at the point of β=0, r∗β=e∗β>0, it means the regulator encourages the power plant to reduce the carbon emission not only by improving carbon capture technology but also by management or other methods (the effort e).Under the regulation mechanism, the coal power plants’ total carbon emissions quantity of different carbon capture rate is shown in Figure5.Figure 5
Figure of the coal power plants’ total carbon emission quantity.As seen in Figure5, the coal power plants’ total carbon emissions quantity decrease sharply with the increasing of β. The power quantity of power plants increases while the original carbon capture rate β increases according to corollary 3, so power quantity of power plants of the larger original carbon capture rate is more than the smaller. Although the power quantity of power plants with larger original carbon capture is bigger, but its total carbon emissions is much smaller and the ratio even up to 4 times (when, Qcarbon=182t; and when β=0.7, Qβ=42t). Therefore, the power plants with small original carbon capture rate become the main source of carbon emissions, when regional or national carbon emissions quota tense, significant effect can be obtained when regulators make regulations to take off the low efficiency power plants (or the power plants with small original carbon capture rate).


## 6. Sensitivity Analysis

This paper focuses on the impact of carbon emissions related parameters, the changes of regulation parameter are given for the varies of the coefficient of cost increase for carbon capturek and the carbon trading price p3 as shown in Tables 3 and 4, when β=0.4.Table 3
Sensitivity analysis for the coefficient of cost increase for carbon capturek.
k
q
e
U
T
P
2
−10%
217.1386
0.0695
2.0534e + 003
−1.3606e + 004
914.3068
−5%
216.7359
0.0627
1.7807e + 003
−1.3521e + 004
916.3206
0.25
216.3431
0.0559
1.5092e + 003
−1.3442e + 004
918.2843
+5%
215.9604
0.0492
1.2387e + 003
−1.3368e + 004
920.1982
+10%
215.5875
0.0424
969.3644
−1.3299e + 004
922.0625Table 4
Sensitivity analysis for the carbon trading pricep3.
p
3
q
e
U
T
P2
−30%
220.0232
−0.0085
−1.0666e + 003
−1.9887e + 004
899.8841
−10%
217.4711
0.0347
659.2488
−1.5515e + 004
912.6445
−5%
216.8949
0.0453
1.0852e + 003
−1.4469e + 004
915.5255
100
216.3431
0.0559
1.5092e + 003
−1.3442e + 004
918.2843
+5%
215.8157
0.0665
1.9314e + 003
−1.2432e + 004
920.9217
+10%
215.3123
0.0770
2.3520e + 003
−1.1439e + 004
923.4383
+30%
213.5390
0.1187
4.0208e + 003
−7.6276e + 003
932.3049With the increasing of the coefficient of cost increase for carbon capturek, power quantity of power plant q and the effort made by the power plant e will decrease under the regulation, the utility of the power plant will reduce at the same time (as shown in Table 3. Inside, the change of the effort made by the power plant e is the largest, and when the change range of k is (±)10%, the change degree of e is more than (∓)24%. The increase in the cost of carbon capture will seriously affect power plant’s enthusiasm of reducing carbon emissions by making efforts. So when regulators encourage carbon capture power plant to reduce carbon emissions by adding equipment or improve technology, regulators need to pay more attention to control the costs of carbon capture equipment and technology. In a short, regulators must not blindly pursue a reduction in carbon emissions regardless of their cost.Nowadays, the rules of international and domestic carbon trading price have large difference. After a comprehensive comparison, this paper take carbon trading pricesp3=100 as a benchmark to research. The research found that when the carbon trading price increases, the carbon capture power plant power quantity q will reduce and the effort made by the power plant e will increase under government regulation (as shown in Table 4. The impact of carbon trading prices on the efforts of the plant to reduce carbon emissions is also evident. When the carbon trading price changes (±)30%, the carbon capture effort parameter changes by more than (±)100%, When the price of carbon trading is small (p3=70), the carbon capture effort of the power plant will even drop to a negative number (e=−0.0085). That is, there will be reverse efforts such as lazy to make carbon emissions increasing. Therefore, increasing the price of carbon trading is an effective mean of reducing carbon emissions from power plants.


## 7. Conclusions and Suggestions for Future Research

Because the power industry plays an important role in the development of low carbon economy in our country, government can develop subsidies or tax policy to encourage power plant make carbon capture to reduce carbon emissions more effectively, and reasonable carbon capture power plant low carbon regulation incentive mechanism is of virtual important for the development of low carbon economy in china. In this paper, we use the government regulation incentive model to research the problem that regulators is in the information disadvantage considering the carbon capture rate of the power plant as its private information. We get the following conclusions(1) A set of regulation mechanism which applies where the government regulates the power plant for capturing carbon emission have be established and be proved efficient to reveal the power plant private information and encourage it to improve carbon capture rates. On the basis, government can make a menu of contracts to regulate the power plant.(2) Regulators can regulate coal fired power plant in distinct ways, such as the regulation based onβ, or the regulation based on r. At the same time, when the carbon capture power plant companies report the true type of carbon capture, the power plant will obtain the largest corporate surplus. Therefore, under this regulation mechanism, the carbon capture power plant will choose the true type of carbon capture, and choose the corresponding contract package.(3) The power plants with small original carbon capture rate become the main source of carbon emissions, when regional or national carbon emissions quota tense, significant effect can be obtained when regulators make regulations to take off the low efficiency power plants (or the power plants with small original carbon capture rate).(4) Regulators must not blindly pursue a reduction in carbon emissions regardless of their cost. Because the increase in the cost of carbon capture will seriously affect power plant’s enthusiasm of reducing carbon emissions by making efforts. So when regulators encourage carbon capture power plant to reduce carbon emissions by adding equipment or improve technology, regulators need to pay more attention to control the costs of carbon capture equipment and technology.It is creative to note the model this paper based on the background of carbon capture power plant, so the conclusion are given with the background of carbon capture power plant. In fact, the conclusion can be spread to more backgrounds. Furthermore, although this paper distinct the high efficiency power plant with the low efficiency power plant and provide distinct policy for distinct power plant. That is, the high efficiency power plant can get some subsidies, but the low efficiency power plant will be closed. However, we do not add a closed policy constraint in the incentive regulation model of thermal power plant, so next we will add the closed policy constraint into our regulation model.



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*Source: 8509834-2020-01-30.xml*