Cooperation control strategies for China’s cross-region pollution in a lake basin based on green reduction cost

ABSTRACT

The cross-region water pollution issue has always been the widespread concern around the world. It becomes especially critical for China due to the imbalance relates to environmental costs that have accompanied rapid growth of economy. Though the government makes great efforts to improve it, the potential for water pollution conflict is still great. We consider the problem of determining combined control strategies for China’s cross-region lake pollution based on the environmental green costs. The problem is first formulated as a generalized bilevel mathematical program where the upper level consists in each region that reduces environmental green costs including three parts: the reduction cost, pollution permit trade cost and cost of environment damage, while the lower level is represented by pollution permit equilibrium market. Finally, we take an empirical analysis in Taihu lake. The numerical study shows that the minimum costs of both total and regional are obviously superior to the current processing costs, which provides theoretical basis for the price of emission permits.

Implications: Today, China’s rapid gross domestic product (GDP) growth has come at a very high cost, as real estate prices have skyrocketed, the wealth gap has widened, and environmental pollution has worsened. China’s central government is urged to correct the GDP-oriented performance evaluation system that is used to judge administrative region leaders. The cross-region water pollution issue has become a troubling issue that urgently needs to be resolved in China. This paper will not only actively aid efforts to govern Lake Taihu and other cross-region valleys, but it will also provide a supplement for theoretical research on cross-region pollution issues.

Introduction

With the rapid development of China’s economy, the problem of cross-region lake pollution has become a focus in China. In May 2007, a large algae bloom overwhelmed the waterworks that supply Wuxi City on Taihu’s northern shore, causing more than 2 million people to be without drinking water for a week. When temperatures rise each year in the early summer, a severe blue-green algae will bloom. In 2012–2013, the Tianji Coal Chemical Industry Group chemical spill occurred in Shanxi Province, China. More than 39 tons of anilines leaked from a loose drainage valve at a plant and then contaminated the Zhuozhang River, which is the source of drinking water for more than 1 million people. This caused a water crisis in the downstream cities of Hebei and Heban, which are administrative regions in China. The development of the economy has moved ecology out of balance. Noting the deteriorating environment, China’s new leadership is poised to tolerate slower growth in an attempt to rid itself of its long-term gross domestic product (GDP) mania and put social progress and environmental welfare at the top of the nation’s agenda (He, 2013). “China should no longer judge leaders solely by GDP growth. Instead, we should look at welfare improvements, development and environmental indicators to evaluate leaders,” China’s president Xi Jinping told party leaders in a speech in June 2013. A variety of measures, such as the urban environmental improvement assessment, the government environmental responsibility system, and the environmental performance evaluation, are also involved in the control of the cross-region pollution. The China National Development and Reform Commission notes that there will be approximately 16 billion yuan allocated for water pollution prevention in 2014 (Securities Times Online, 2014). Despite various efforts, the effect of this investment is not obvious, and the cross-region pollution situation remains unimproved.

There is much research regarding ecological problems around the world, and papers about the treatment of cross-region water pollution are numerous. Bayramoglu (2006) analyzed the cross-region pollution between Romania and Ukraine and their coastal states along the Black Sea and studied the welfare consequences of institutional arrangements to control this problem. Varis et al. (2008) analyzed and explored the governance of the Great Lakes in North America.

One effective method to analyze water resource allocation and pollution control is game theory. Madani (2010) introduced the relationship between water resources and game theory generally. In his paper, Maldani described how the interactions of different parties who gave priority to their own objectives, rather than the system’s objective, resulted in a system’s evolution using several simple examples of water resource problems. Additionally, the outcomes predicted by game theory often differ from the results suggested by optimization methods. Loáiciga (2004) analyzed the roles of cooperation and noncooperation in the sustainable exploitation of a jointly used groundwater resource using an analytical game theoretic formulation; for cooperative equilibrium to hold, enforcement must be effective. Mahjouri and Ardestani (2010) issued a new game theoretic methodology that was developed for interbasin water transfer management with regard to economic, equity, and environmental criteria. Additionally, the model, which used economic objectives regarding physical and environmental constraints of the system, could be utilized to proportionally allocate water and net benefits to the users. Kucukmehmetoglu (2012) studied transboundary water resource allocations of the Euphrates and the Tigris rivers and introduced a composite water resources allocation approach that integrated both game theory and Pareto frontier concepts. Fernandez (2013) compared three game theory scenarios to demonstrate how cross-region water institutions facilitated sovereign country management of transboundary water pollution along the international borders of the United States and Mexico through pollution abatement costs, shared water monitoring responsibility, and formal decision-making for pollution control. The upstream country can control water pollution in its watershed in cooperative and Stackelberg arrangements of shared abatement and can thereby greatly help the downstream country minimize costs and damage. Raquel et al. (2007) studied how to arrive at a socially acceptable compromise. In their study, game theory was applied to a multiobjective conflict problem. Pham Do et al. (2012) introduced a special class of games with externalities and issue linkages to promote cooperation on cross-region water resources. Whenever opportunities for linkages exist, countries might contribute towards cooperation.

Economists advocated a transferable discharge permit (TDP) system as another efficient control strategy that requires the user to pay a fixed price for each unit of pollution (Montgomery, 1972). Hung and Shaw (2005) proved that a tradable discharge permit system could address predetermined water quality standards. Using fuzzy nonlinear regression, Mesbah et al. (2010) proposed a pollution permit trading model and showed that the TDP was a potentially more cost-effective method compared with other pollution control strategies. Considering the electric market, Mansur (2013) discussed the advantages and the efficiency of a TDP system compared with a pollution tax in a market with imperfect competition. Zhao et al. (2012) developed bilevel programming models to curb transboundary lake and river basin pollution using a transfer tax. In their model, the upper decision-makers determined the level of transfer tax; then, each individual region around the basin determined transferable quantities and reduction quantities according to its object (the reduction cost and the transferable cost) under that tax. Although the entire basin’s quality standard was obtained by that model, the environment of certain regions may have been damaged due to overpollution by the transferring region because each region never considered their environment damage costs. Furthermore, due to the mandatory power of the central administration, all regions lost certain ideal environmental conditions such as complete, free, and instantaneous availability of all relevant information from each other. Taschini (2010) compared the key pollution control instruments, taxes, subsidies, and marketable permits, and discussed why experts focused more attention on market performance. Moreover, the damage caused by pollution to the environment is also difficult to measure and cannot be ignored in a control strategy. Certain scholars have conducted much research in this area. Deng et al. (2011) used the environmental computable general equilibrium model to identify the most effective means to balance economic growth with reduction of nitrogen and phosphorus pollution. Qu et al. (2011) proposed a methodology suitable for ecological risk assessment of pesticide residues for wetland ecosystems based on the risk quotient method coupled with a probabilistic risk assessment model. You et al. (2014) applied an ecosystem service valuation to the optimization process; their findings facilitate the ability of local decision-makers to gain insights into the tradeoff between socioeconomic development and ecoenvironmental sustainability. Establishing a standard pollution permit trading market can provide each region with more flexibility than China’s current command-and-order program, which is required to reduce transboundary pollutions in a water basin while stimulating technological innovation and economic growth. A pollution permit system is already the policy instrument of choice in many U.S. states, the European Union (EU), New Zealand, and Australia, and has proven to be effective as in the case of the U.S. Acid Rain Program.

Currently, China usually uses the command-and-order program to curb water pollution. In this program, the central government sets the total maximum quantity of water pollutants and then allocates an allowable quantity of water pollutants to each province according to the province’s economic situation, including its economic potential, industrial structure, and reported quota. Each province must follow the central government’s regulation and must individually complete the pollution control task. Under this regulation, all provinces lost the initiative to reduce pollution following their own pollution processing capacity. China’s severe pollution situation implies that the command-and-order program fails on pollution control. Realizing the problem, the central government began to attempt to establish a pollution permit trading system in polluted cross-regions; however, in China, it is far from complete in practice and in theory.

Based on China’s actual pollution control regulations, this paper intends to find a suitable cross-region pollution control countermeasure for China from the perspective of regional cooperation, considering each administrative region’s environmental protection cost in water pollution. To reflect the relationship between economic cost and environmental damage in the process of controlling contamination for each administrative region in a lake basin, we developed a green reduction cost function. Through this function, we can observe the real economic situation and observe watershed protection efforts for each region. Finally, we construct a cross-region pollution control model. According to the administrative area’s development plan, we can predict the annual optimal reduction quantities of each area’s own sewage and the optimal pollution permit price. All these can help competent authorities by providing a theoretical basis for policy making. In our model, we will use variational inequality theory, which has been widely applied to supply chain economy (Zhang, 2006), online shopping supply chain (Hu and Qiang, 2013), and transportation (Nagurney et al., 2002) models, among others. Our numerical results also showed that the interprovincial trade model can encourage pollution exchange activities between provinces in the region and produce a win-win outcome for the region and all provinces.

Models

Variable definitions

This model assumes that the regions around a lake basin compose a set . The variables involved in the paper are defined as shown in Table 1.

Table 1. Variable definitions.

Variable	Definition
	The production of a pollutant for region i, where .
	The reduction quantity of a pollutant for region i, pollution resource j, where . represent the reduction quantity of a pollutant produced by industry and livelihood, respectively.
	The initial quantities of pollution permits for region i, where .
	The actual quantity of pollution permit requirements for region i, where .
	The price of a unit pollution permit.
	The treatment cost function of a pollutant for region , pollution resource j, where . and represent the treatment costs of a pollutant produced by industry and livelihood, respectively.

Assumptions

Assume that regions surround the lake, and each region has an individual preference and a cost of pollutant reduction. The lake has maximum pollution endurance under closure and self-purification capacity. To maintain the sustainable development of the lake, the administration initially establishes the specific pollution permit for each region . However, as time passes, different developments will come into being across the entire region, and the actual demand will differ from the original . Nevertheless, there is no redundant pollution quota for the sake of the pollutant reduction target. Thus, a secondary market appears in which trade in spare pollution permits can be freely achieved, and a region that discharges more pollutants can purchase a pollution permit from a region that discharges less pollution. This market ensures the utilization of resources. Additionally, each region needs to balance the cost of pollutant treatment , where , and the expense of buying a permit. Moreover, we assume that, if the pollution discharge of all regions around the lake exceeds the pollution limits , it will generate damage to the lake’s ecology; that damage is difficult to estimate. This finding implies that . This paper attempts to use the quadratic polynomial function to fit the cost of environmental damage based on Song et al. (2012). This function is with respect to the quantities of actual pollution discharge .

Throughout the paper, we make the following assumptions on the reduction cost function and the environmental damage cost function , for any , :

1. is strictly increasing and strictly convex and .

2. The partial differential of environmental damage cost function .

Note that Assumption (a) is a standard assumption indicating that the marginal reduction cost is increasing, whereas Assumption (b) is reasonable, since the environmental damage cost is high when each region does not take any action.

Cross-region lake pollution control modeling

Based on the above analysis, given any price of the pollution permit , the cross-region lake pollution control problem can be formulated as the following generalized Nash equilibrium problem (GNEP) with a coupled linear inequality constraint. For each region ,

GNEP

(1)

The objective function, which is called the green reduction cost and regards region , consists of three parts: the summation of pollution treatment costs caused by industry and livelihood , the pollution permit trade cost , and the cost of environmental damage , where , , and represent quadratic, monomial, and constant coefficients of the environmental damage cost, respectively. Because each individual region’s pollution discharge can influence the other surrounding regions, the coupled constraint means that all regions attempt to find a joint pollution control strategy that will meet the total cross-regional pollution discharge standard.

The above GNEP is based on the given price of the pollution permit; however, the price is generally determined by the market. We acknowledge that there are always many disadvantages when putting our model into practice, since successful implementations of pollution permit trading system must rely on complete legal systems and perfect market mechanisms. The insufficient information and the imperfect competition in China’s emissions trading market may cause relatively high transaction costs. Currently, relevant theories and marketing experiences about it are still limited in China. Instead of blindly copying foreign countries’ pollution permit trading modes, we should construct the pollution permit trading system connected with Chinese special conditions.

Establishing a unified pollution permit trading market is obviously unrealistic in our whole country. Absorbing the advanced experience of the United States and other developed countries, we suggest that establishing the pollution permit trading market in the cross-boundary area, and each region’s administrator as the decision-maker in that market. As described in section Introduction, realizing the growth came at a very high cost as real estate prices skyrocketed, the wealth gap widened and environmental pollution worsened, China’s government pays more and more attach on its environment protection. According to China’s 12th five-year plan, China invests 40 billion RMB to strengthen the construction of environmental monitoring ability and the improvement of legal supervision. Therefore, we assume the objective function for each decision-maker is to minimize the total cost that only includes pollution treatment cost, net emissions trading cost, and cost of environmental damage without considering all costs in the processing of water quality monitoring and administrative legal supervision. Furthermore, all data used in this paper are all free from the national statistical yearbook, and we assume that the regulatory data are accurate and reliable.

Based on the equilibrium principle of economics (Mansur, 2013), when the pollution trade market reaches equilibrium, the price meets the conditions

(2)

Equation 2 shows that when the actual pollution demand is equal to the initial pollution permit quantities, the equilibrium price of the market is greater than 0. It is easy to check whether the above equilibrium condition equals the following formula.

(3)

We are now in the position to reformulate and solve the cross-region pollution control model (eqs 1–3). As noted by Han et al. (2012), for any given price of pollution permit , various solution methods have been proposed to solve the complex GNEP. Due to the structure specificity of GNEP, the following theorem reveals that we can obtain one equilibrium solution from a relatively simple nonlinear optimization problem.

Theorem 1:

Given the price of pollution permit , if meets the nonlinear optimization problem as follows.

(4)

then is the optimal solution of GNEP.

Proof:

Given the price of pollution permit , let meet eq 4. Then, for any , where and ,

(5)

for an arbitrary , and

Then, eq. 5 transforms to

Thus, is one solution of GNEP.

Theorem 2:

Given the price of pollution pollutant , is the optimal reduction quantity and requirement of a pollution permit if and only if it meets the variational inequality () as follows.

(6)

where the inner product means that if are two n-dimensional vectors, then

Proof:

From Theorem 1, we need to prove eq 2 is equivalent to formula 6.

(Necessity)

Suppose that are the optimal reduction quantities and requirements of pollution permits. Taking the partial derivative of eq 1 with respect to , , , the conclusion is obtained from the convexity of .

(Sufficiency)

Assume satisfies the variational inequality 6 for any and the green reduction cost is assumed to be convex. We can obtain

thus, is the optimal reduction quantities and requirements of pollution permits.

Given eqs 3 and 6, we can obtain the following Theorem 3.

Theorem 3:

Based on measures of the pollutant pollution trade permit, is the equilibrium price if and only if the following variational inequality is obtained, where are the optimal reduction quantities and requirements of pollution permits.

(7)

Variational inequality 7 contains an inequality constraint. The following theorem suggests that the inequality constraint can be removed by introducing an auxiliary variable.

Theorem 4:

is the optimal reduction quantity and requirement of the pollution permit under the condition that is the equilibrium price if and only if there is that makes solutions of the following variational inequality.

(8)

Proof:

(Necessity)

If is the optimal reduction quantity and requirement of the pollution permit under the condition that is the equilibrium price, then they are the optimal solution of the following linear programming problem.

By the strong duality theorem of linear programming, we can obtain , such that

(9)

and , , , are the solutions of the following optimization problem.

or the equivalent variational inequality problem

Combining with eq 9, we can obtain eq 8.

(Sufficiency)

If , , where are the solutions of variational inequality eq 8, for any ,

Thus, , , where are the solutions of variational inequality eq 7.

Theorem 5: (Existence and uniqueness): Variational inequality eq 8 has one and only one solution.

This theorem’s detailed proof can be found in Kinderlehrer and Stampacchia (2012). The unique optimal solution can be obtained directly by project method.

Theorem 6:

The optimal reduction quantities , for any , if the equilibrium price .

Proof:

If not. Without loss of generality, suppose , . Choose , , , , and . Then take into the variational inequality 8, we have

Take into variational inequality 8, we have

Therefore, . Equivalently,

Choose , , , , for any , . We have

It is a contradiction. Therefore, we complete the proof.

From the above analysis, using the similarly technique in Theorem 6, we can easily conclude the following theorem.

Theorem 7:

1. If the optimal pollution permit price , for any , , where

(10)

1. If , for any , , , where

(11)

(12)

According to the strict convexity assumption on , is strictly increasing. Therefore, are strictly decreasing function with one variable. Then we just need to solve equation at interval or equation at interval to find the optimal pollution permit price. The strict monotone of also implies the uniqueness of equilibrium price.

Based on Theorem 7, we construct the following algorithm to our proposed model:

• Step 1: Let , , and calculate and for any according to (a) in Theorem 7. If , terminate. , , and for any are the optimal solution. Otherwise, go to Step 2.

• Step 2: Calculate the formula and . Choose the tolerance factor . Go to Step 3.

• Step 3: Calculate and . If , go to Step 5. Otherwise, go to Step 4 and set .

• Step 4: Use the bisection method to solve equation :

  • Step 4.1: Let . If , take as the approximate equilibrium price and go to Step 6. Otherwise, go to Step 4.2.

  • Step 4.2: If , then define and . Otherwise, and . Set . Go to Step 4.1.

• Step 5: Calculate and , where is a sufficient large number. Set and go to Step 6.

• Step 6: Use the bisection method to solve equation :

• Step 6.1: Let . If , take as the approximate

• solution and go to Step 7. Otherwise, go to Step 6.2.

• Step 6.2: If , then define and . Otherwise, and . Set . Go to Step 6.1.

• Step 7: Calculate for any , according to (b) in Theorem 7.

Theorem 8:

(Convergent rate) Let be the sequence generated by the proposed algorithm and be the equilibrium solution to our proposed model. Then, .

Case study

In this paper, we study the pollutant control measures of three regions around Lake Taihu, Jiangsu Province, Zhejiang Province, and Shanghai City, based on 10-year statistical data from the China environmental yearbook 2002–2011. The following variables are extracted from the data of three areas of industrial and living sewage data as follows: wastewater treatment facilities operating cost, wastewater treatment facilities capacity, waste pollution, wastewater treatment, and investment. We selected COD (chemical oxygen demand) as an example to propose certain countermeasures and methods; the rest of the pollutants, such as ammonia nitrogen and total phosphorus, use the same processing method. Integrated wastewater discharge standard (GB8978-1996) secondary standards were adopted. A personal computer with Intel Core 2 Duo 1.86 GHz CPU, 4 GB RAM, and Windows 7 Ultimate operating system was used for all tests.

According to the model of pollutant treatment costs of Zhao et al. (2012) and through statistical calculations using SPSS 17.0 (SPSS, Chicago, IL, USA), we can obtain the cost function of the three regions, as shown in Table 2.

Table 2. Cost functions of the three regions.

Region	Treatment Cost of COD Produced by Industry	Treatment Cost of COD Produced by Livelihood	Quadratic Coefficient of Environmental Damage Cost	Monomial Coefficient of Environmental Damage Cost	Constant of Environmental Damage Cost
Shanghai			55979	710041	2267462
Jiangsu			27059	1418603	18679926
Zhejiang			7254	229526	1920568

Then, we can obtain the solution of the optimal pollution permit price p* = 373.85/t by solving the variational inequality using Matlab 7.0. The optimal COD reduction quantity and the optimal requirements of pollution permits are shown in Table 3.

Table 3. Comparison results of process costs.

Parameter		Shanghai	Jiangsu	Zhejiang
Current COD reduction Quantity (kiloton)	Industrial	260.2	1274.5	1495.1
	Household	633.8	883.6	1018.3
Initial pollution permits (kiloton)		252.1	688.1	479.8
Current treatment cost (million dollars)		8600.8	12177.9	3645.5
Optimal reduction quantity (kiloton)	Industrial	153.3	1120.3	779.8
	Household	275.5	1725.2	1511.5
Optimal pollution permitsrequirement (kiloton)		717.6	0.0	70.3
Optimal treatment cost (million dollars)		8560.7	12161.6	3635.4
Cost reduction percentage		0.47%	0.13%	0.28%

Currently, China uses the command-and-order approach to alleviate cross-region lake pollution, under which the central government regulates the maximum sewage level through compulsory administrative intervention. The results in Table 3 illustrate that the treatment costs for our proposed cross-region lake pollution control model are 0.47%, 0.13%, and 0.28% less than the current strategies for Shanghai, Jiangsu, and Zhejiang, respectively. Additionally, the total cost of the optimal treatment is 0.27% less than the current treatment. In conclusion, both in overall cost and in the individual region cost, the cross-region lake pollution control model is able to achieve lake pollution control and meet overall pollutions targets. Moreover, this model can provide a theoretical basis for the price of pollution permits.

Conclusions and suggestions

Today, China’s rapid GDP growth has come at a very high cost, as real estate prices have skyrocketed, the wealth gap has widened, and environmental pollution has worsened. China’s central government is urged to correct the GDP-oriented performance evaluation system that is used to judge administrative region leaders. Our proposed environmental green reduction cost includes three parts: the reduction cost, the pollution permit trade cost, and the cost of environment damage, which represents the environmental cost caused by the remaining pollution. However, if this cost does not exceed the national standard sewage discharge level, then it can be used as an indicator of social development and environmental health that can be used in turn to evaluate leaders instead of GDP growth. Our proposed model works as follows: firstly, the central government compulsorily establishes the total maximum quantity of water pollution and pollution permits for the lake basin. Secondly, portion the allowable maximum water pollution and the pollution permits to each region according to the province’s actual economic situation such as economic potential, industrial structure, and the reported quota. We suggest that this allocation is valid for 5 years, which is compatible with the fact that China’s strategic decision-making is generally valid for 5 years. The cross-region water pollution issue has become a troubling issue that urgently needs to be resolved in China. This paper will not only actively aid efforts to govern Lake Taihu and other cross-region valleys, but it will also provide a supplement for theoretical research on cross-region pollution issues.

Pollution permit trading system is established as a system when exploring the market mechanism to solve environmental problems in western countries. Although the pollution permit trading system has been questioned on the efficiency, effectiveness, and fairness, this system provides another way to solve the increasingly serious environmental problems. The emissions trading system has been carried out in China for nearly 20 years. It plays a more and more important role in the field of environmental protection areas. Based on China’s actual situation of pollution control, we proposed our model. Finally, we take Taihu lake basin as a case for empirical analysis. It turns out that our model is reasonable according to the results.

However, the lake administrator must consider several factors that maybe affect the efficiency of the model in practice. One important factor is the asymmetry information among all regions. This asymmetry may result from the fact that each region administrator provides inaccurate or false information to maximize their economic benefits. The second factor relates to the time lag of regulatory policies, and the third factor is inflation or deflation. All these problems lead to suboptimal results. In order to weaken the negative effects caused by the above factors, we need to update the pollution reduction and pollution permit price annually. Although the application of emissions trading has many problems in our country, it is still necessary to make an attempt to promote the effective environmental economic policies in our country. As we all know, the implementation of any new policy requires a gradually improvement progress in practice.

Funding

This study was supported by an NSFC grant (NSFC 71401097), the Chinese Ministry of Education, Humanities and Social Sciences (13YJC630072 and 13YJC630196), the Shanghai University Innovation Project (sdcx2012013), the Shanghai Young University Teachers Training Subsidy Scheme (ZZSD12029), the Ministry of Education, Shanghai Philosophy and Social Science (2013EGL010), and Shanghai Education Innovation (14YS002 and B51CX14R003).

Additional information

Funding

This study was supported by an NSFC grant (NSFC 71401097), the Chinese Ministry of Education, Humanities and Social Sciences (13YJC630072 and 13YJC630196), the Shanghai University Innovation Project (sdcx2012013), the Shanghai Young University Teachers Training Subsidy Scheme (ZZSD12029), the Ministry of Education, Shanghai Philosophy and Social Science (2013EGL010), and Shanghai Education Innovation (14YS002 and B51CX14R003).

Notes on contributors

Changmin Li

Changmin Li and Dong Sun are lecturers and masters at the School of Management, Shanghai University, in Shanghai, People’s Republic of China.

Dong Sun

Changmin Li and Dong Sun are lecturers and masters at the School of Management, Shanghai University, in Shanghai, People’s Republic of China.

Xiaoqiang Xie

Xiaoqiang Xie is lecturer at the School of Science, Shanghai Second Polytechnic University, in Shanghai, People’s Republic of China.

Jian Xue

Jian Xue is a postdoctoral researcher at the School of Management, Fudan University, in Shanghai, People’s Republic of China.