■2012 JSPS Asian CORE Program, Nagoya University and VNU University of Economics and Business Game Analysis of Government Subsidy Mechanism for WEEE Recycling in China Southwest Jiaotong University Zu-Jun MA*, Shu HU**, Yu-Sen YE** ABSTRACT: Electrical and electronic equipment closed-loop supply chains consisting of manufacturers, sellers, and consumers under government regulation was investigated in this paper Based on Cobweb theorem, we analyzed the repeated game process between government and manufacturers, and obtained the equilibrium solution for stage game On this basis, we discussed the impact of government subsidy for WEEE recycling on social welfare, as well as the mutual response strategies of manufacturers and government By the results of our study, we have discovered that, if manufacturers recycle WEEE with the possible maximum recycling rate attained without loss of own revenue after receiving government subsidies, it will cause the loss of social welfare, and that the degree of loss will increase with the increase of unit subsidy for recycling WEEE Therefore, to promote the recycling of WEEE, we should maximize the rate of recycling WEEE without loss of social welfare, and government should enhance as far as possible the degree of sensitivity to the recycling rate adopted by manufacturers, as well as the upper bound of unit subsidy for recycling WEEE KEYWORDS: closed-loop supply chains, government subsidies, WEEE, repeated game, Cobweb theory that recycler should be subsidized with a certain range INTRODUCTION in accordance with the real amounts of finished There are more than 200 millions of Waste Electrical and Electronic Equipment dismantling WEEEs The subsidization criteria are ¥85 (WEEE) per TV set, ¥80 per refrigerator, ¥35 per washing produced every year in China, which has become one machine, ¥35 per room air conditioner and ¥85 per of the major sources of solid waste The Regulation on microcomputer On December 2010, the Ministry of the Administration of the Recovery and Disposal of Industry and Information Technology of China (MIIT) Waste Electrical and Electronic Products came into drafted the Access Conditions of China Comprehensive effect on January 1, 2011, and the Administrative Utilization of Waste Electrical and Electronic Products, Provisions on the Collection of the Fund for Disposing stipulating the limit and target value of recycling rate Waste Electrical and Electronic Products carried into for seven types of WEEE, among which the values for execution from July 1, 2012, which is an important televisions, refrigerators, washing machines, air supporting regulation to the former one It is proposed conditioners, computers *Southwest Jiaotong University, School of Economics and Management **Southwest Jiaotong University, School of Transportation and Logistics were 65% and 75% respectively The formulation and implementation of Hammond and Beullens(2007) established a model relevant regulations for WEEE recycling must have consisting of manufacturers and consumer markets significant effect on manufacturers or retailers in engaged in a Cournot pricing game with perfect closed-loop supply chains (CLSC) The question is information, which is formulated with the intent of whether the mechanism for WEEE recycling is proper, examining issues surrounding the WEEE directive and how it can effectively promote the WEEE Mitra and Webster(2008) examined the effects of recycling government subsidies as a means to promote There are few studies considering the influence of remanufacturing activity, finding that subsidy sharing governmental financial regulation Atasu et al.(2009) creates incentives for the manufacturer to design a considered the impact of take-back legislation on the product that is more suitable for remanufacturing, and economy and look at the efficiency of existing policies to be more open to efforts to increase the return rate of such as the WEEE directive of the European end-of-life products Aksen et al.(2009) presented and Commission They argued that the weight based solved two bi-level programming (BP) models directives and the weight-based categorization of describing the subsidization agreement between the products may not necessarily be efficient (neither government and a company engaged in collection and economically nor ecologically) A better categorization recovery operations They introduced a supportive and of products and the selection of targets would consider: a legislative BP model to tackle this comprehensive (i) the treatment cost or the benefit from recycling, (ii) collection system design problem The results showed the environmental impact of the product, (iii) the that for the same collection rate and profitaility ratio willingness-to-pay of customers for the decrease in the the government has to grant a higher subsidy in the environmental impact, and (iv) the competition supportive model than in the legislative model Sheu et intensity of the specific market Atasu et al.(2008) al.(2005) presented an optimization-based model to pointed out that there exists a contradiction between deal with integrated logistics operational problems of the regenerating of materials and reusing of products in green-supply chain management (G-SCM) Results of the WEEE Directive, causing competitions when numerical studies indicate that the reverse chain-based pursing the goal of recycling Chen and Sheu (2009) net profits increase significantly with the increase of demonstrated that a proper design of environmental the value of the governmental subsidy, and increase regulation pricing strategies can promote EPR for the proportionally with the increase of the return ratio firms in supply chains They established a differential subject to the certain range of the return ratio, and then game model comprising Vidale–Wolfe equation They decline as the return ratio continues to increase Li et found the al.(2011) developed a CLSC network equilibrium effectiveness of environmental policy on the premise model, analyzing the behavior of the various decision- that it is nature for business to pursue maximal profits makers by using network equilibrium theory and Georgiadis and Besiou(2010) used an extension of a variational inequality The results showed that the System Dynamics-based model to investigate the collection rate will increase with the growth of significance of the factors that comprise the subsidies, and that heterogeneous products always environmental the compete in sale and recovery processes Hong and operational features of CLSC, their interactions and the Ke(2011) presented a Stackelberg-type model to type of their impact on the environmental and determine Advanced recycling fees and socially economical sustainability of a WEEE CLSC optimal subsidy fees in decentralized reverse supply that governments sustainability should consider strategies and chains where each entity independently acts according WEEE processing enterprises, not including WEEE to its own interests They found that the two fees collecting ones It is obvious that the researches above achieve the maximum of social welfare at the could not reflect the main features of government equilibrium status, while both MISs (manufacturers, regulation tools for WEEE recycling in China importers, and sellers) and recyclers gain the maximum To encourage and promote the recycling of WEEE, of profits Wang and Shen(2011) studied the incentive the government will develop subsidy criteria and mechanism of RSC under government regulation, related policies in accordance with the situation of resulting that taking both subsidies and punishment is WEEE recycling, regulating and controlling the the optimal program Wang et al.(2010) established recycling variational inequality models considering the penalty manufacturers will adjust the recycling rate based on policy to manufacturers and the allowance policy to its operation situations and the published subsidy collectors by the government The result showed that criteria, to maximize his own profits Thus, there exists the equilibrium quantity results increase with the a dynamic process of repeated game between the increase of the allowance given by the government government and manufacturers In this paper, the whereas they decrease with the increase of the penalty Cobweb model was used to analyze the repeated game to manufacturers process We try to answer the following questions: market As a recycler of WEEE, Most of the literatures above are on the basis of the How to come to an equilibrium state in repeated game? European WEEE Directive or extended producer How WEEE recycling subsidies have any effect on responsibility (EPR)-type policies, which set up a social welfare? What kind of response strategies should minimum collecting rate and recycling rate to design be taken by manufacturers and the government to the incentive and punishment mechanism considering maximize the recycling rate on the premise of suffering the real finished situation of enterprises However, no loss of both manufacturer’s benefit and social copying existing WEEE-type legislation may not lead welfare? to improved welfare outcomes, as different regions of the world may face different cost structures, environmental consciousness levels, and competition MODEL ASSUMPTIONS (Atasu et al., 2009) For example, now there is no Consider an electrical and electronic equipment requirement about minimum recycling rate in China, (EEE) CLSC consisting of manufacturers, retailers and nor punishment for not completing The Administrative consumers (as shown in Figure 1) New products are Provisions on the Collection of the Fund for Disposing produced by manufacturers and sold by retailers Waste Electrical and Electronic Products only Manufacturers are also in charge of the processing and provided the limit value and target value for different reuse of WEEE, which are collected from consumers types of WEEE recycling rate It also stipulated that a by retailers The government encourages the recycling certain processing fee should be levied in accordance of WEEE by subsidizing manufacturers with the amounts of production enterprises, import production, imports of electrical and electronic p w manufacturers retailers bm consumers br products separately Also it will subsidize the recycling enterprises in accordance with the real finished amounts of WEEE, nor the finished recovery or recycling rate The subsidized objects are limited to Figure The structure of EEE CLSC To facilitate problem formulation, we make the following assumptions (1) The unit production cost of the original appliances is denoted by cm , and the unit cost of MODEL FOMULATION We introduce the Cobweb theory to characterize the game: When the government sets up a subsidy criterion producing remanufactured products by the components s1 , manufacturers will choose his recycling rate u1 , cr , which generates a new subsidy criterion s2 It will the lead to a new recycling rate u2 determined by remanufactured cost per unit when the recycling rate of manufacturer Then again and again, the continuous WEEE adjustment will finally reach to an equilibrium state sn and parts with cr of cm WEEE u (cm equals g) to is denoted , where 100% Both by g is original and and un , as shown in Figure remanufactured products are selling at a same price The unit processing fee for WEEE is denoted by ch , which is a quadratic function of recycling rate u , i.e ch e fu , where e and f are both nonnegative constants Unit subsidy s (2) Manufacturers' strategy s2 u2 s4 We denote the wholesale price by w and the (3) selling price by p (4) u4 sn s5 The selling amount of the appliances D p u3 s3 has a linear relationship with the selling price p , i.e D p a bp , where a and b are both nonnegative constants (5) Government's strategy u1 s1 un The price of collecting a unit WEEE from Recycling Rate u consumers is denoted by br , while the transaction Figure The Cobweb model price of per unit paid by manufacturers to retailers is 3.1 Stage game between the government and denoted by bm manufacturers (6) The collecting amounts G br proportional i.e G br to the transaction of WEEE is , stage game, which reflects the interactions among the are both government, manufacturers and retailers In fact, the D p process can be constructed as a three phase game with Government charges a certain processing fee the following decision-making orders: The first stage is c dbr , where price c and d nonnegative constants and restricted by G br (7) br for per unit of WEEE, which is denoted by h (8) Each game in the repeated game process is called a set for environmental policy making The government Government subsidy fees for manufacturers will take the maximization of social welfare as a goal, recycling of per WEEE are denoted by s It is determining the recycling subsidy criterion s of stipulated that manufacturers’ processing rate of WEEE, which is given to manufacturers In the second WEEE should not be lower than the lowest recycling stage, manufacturers will maximize its own profits in rate u ( u ) accordance with the subsidy criterion to determine the (9) The environmental cost for consuming per wholesale price w, the transaction price paid to appliance is denoted by C , as the environmental retailers bm and the recycling rate u In the final stage, benefits from collecting and processing per unit can be retailers will determine the selling price p of the denoted by V appliances and the collecting price br under a given w and bm , to make its own profits maximum We assume that the decisions are made with perfect information and backward induction can be used to solve the problem We solve retailers’ optimal operation decision in the third stage first The total cost of purchasing appliances from manufacturer is denoted by D p w , while the total revenue is D p p The total processing fees paid to the consumers are denoted by G br br , while the total transaction fees are G br bm Retailers try to ( u R p ,br G br bm br D p ) cm g 2f (7) Eq (3), and obtain 3a bcm bh p* 4b (8) fu ucm ug s e br (1) p w * c 2d By putting Eq (5) into Eq (2), putting Eq (6) into maximize its own profits, that is max fu ucm ug s e bm 3c 4d (9) Finally, we solve the optimal economy policy of the From the first-order conditions R p 0, R br 0, we can get that determines the recycling subsidy for the purpose of a bw 2b dbm c 2d p br government in the first stage The government (2) (3) encouraging manufacturers to promote the recycling rate of WEEE and achieving the maximum social welfare Social welfare is equals to the sum of Then move to manufacturers’ optimal production decision in the second stage The total cost of D p customer surplus denoted by 2b , manufacturer’s , retailer’s profits denoted by producing remanufactured products by the components and parts of WEEE is denoted by G br cr The total profits denoted by production cost of the original ones is denoted by by D p h , subsidy fees from government denoted by D p G br cm stands D p h for the R , processing fees charged by government denoted G br s , the environmental cost for consuming new appliances processing fees charged by the government The total revenue of manufacturer is D p w , while the total transaction fees are G br bm and the total processing fees of WEEE are G br ch G br s stands for the G br s bm cm D p w cm h ch cr = ( D p )2 2b +D p M , and bm w* ( M u the G br p cm V br +cm cr ch (10) C By putting Eqs (5)-(9) into Eq (10) According to (4) the first-order condition By combining Eqs (2) and (3) with Eq (4) According to the first-order conditions and D p C M R +D p h 2b G br s D p C G br V s characterized by M by ( D p )2 max Manufacturers’ maximizing its own profits can be w,bm ,u denoted environmental benefits of collecting and processing WEEE denoted by G br V , that is recycling subsidy fees provided by the government max M M w 0, , we can get that s cm g 4f c d s , we can get that e +2V (11) By putting Eqs (7) and (11) into Eqs (6) and (9) respectively, we can obtain a bcm bh 2b ) bm cm g 4f e +V (12) br = cm g c 2d 8f e V + 2 (13) The equilibrium solution is achieved in the situation when the government, manufacturers and retailers set their goals to maximize their own profits respectively To improve the processing enthusiasm of manufacturer, the government subsidies should be no less than the loss when performing the lowest recycling rate, i.e However, it will be usually affected by some cm s constraints in practice, such as the lowest recycling rate * M M The recycling subsidy fees can be g u cm 4f fu g (16) u of WEEE in China as mentioned above That is to On the contrary, when setting up a certain subsidy say, manufacturers must set his recycling rate above u criterion s , the upper bound of recycling rate achieving so as to engage in WEEE recycling business, as well as at no loss of manufacturer’s profits is enjoy government subsidies cm u g + fs 2f 3.2 Manufacturers’ response strategy to the (17) It seems that the government should give incentive government’s subsidy criterion 3.2.1 The upper bound of recycling rate at no loss of to manufacturers to collect and process at the upper manufacturers’ profits bound of recycling rate Is it a reasonable practice? When there is no recycling subsidy from the government, the profits of manufacturer is Under this circumstance, we can get the social welfare as follows characterized by max w,bm ,u d G br M bm cm D p w cm ch his ( 14) h condition 'M u u* cm g 2f profits 3d From the g 16 f a bcm u* cm (15) e bh a 7bcm bh 8bC (18) production decision at the recycling rate u* to maximize his profits Social welfare can be denoted by g e+ recycling rate u If u cm d g c d D p w cm h + 16 f * u , the optimal decision of cm 3d g c 4d e V 2 c + 4d 16 f a bcm bh a 7bcm * ds cm cm g w cm h e fu g 16 f ds cm be denoted by c d bh 8bC (19) Using Eqs (18) and (19), we can obtain that subsidies Otherwise, the profits of manufacturer can e 32b manufacturer will not be affected by government s u 2 4f D p s Without subsidies, manufacturers will make the , we can obtain that it is required for manufacturers to process at the lowest d e V 32b When the government provides recycling subsidies, M c 4d c + 4d first-order The profit of manufacturer is d + 16 f cm * * M g cr Manufacturers will choose the recycling rate to maximize cm ch + cr c 4d e c d The profits of manufacturer should be nonnegative, i.e bm cm ch cr Thus, we can get * , as social welfare is linear decreasing with the s u cm government subsidy Remark When the government providing a s u cm g certain recycling subsidy, if manufacturers performs at = the upper bound of recycling rate on the premise of achieving no loss of his own profits, the social welfare g 4f fu + e e fu + c d c d + V s c + d e + cm g 4f + c d e V (21) It needs to be analyzed through simulation on is linear decreasing with the unit recycling subsidy of WEEE and lower than that without government cm g account of being unable to get a closed-form expression subsidy It is because that when adding the unit recycling subsidy of WEEE, the upper bound of recycling rate at 3.2.3 Government’s response strategy to the manufacturers’ recycling rate Government regulation policies are characterized by no loss of manufacturers’ profit will increase as well (from Eq (17)) If performing at this rate, it will add processing and remanufacturing cost to manufacturers’ operation, decreasing social welfare (from Eq (10)) Thus, it will make no benefit to social welfare when relative stability and adaptable readjustment when necessary If manufacturers’ recycling rate is not up to the expectation of the government, the government will adjust WEEE recycling subsidy criteria: when the recycling rate is low, he should improve the unit pursuing the maximum of recycling rate How to choose a right recycling rate? It is reasonable to maximize the recycling rate at no loss of WEEE recycling subsidy fee to encourage WEEE recycling Conversely, he should reduce the subsidy fee to a proper level to reduce the burden of government social welfare 3.2.2 The WEEE recycling rate on the condition of no loss of social welfare Assume u '' as the recycling rate chosen by manufacturers with a certain subsidy fee s The social That is to say, the unit WEEE recycling subsidy fee of next stage si has a negatively correlation with manufacturers’ recycling rate at this stage ui Assume a linear relationship, namely si welfare can be characterized by ui， i 1, 2, , n (22) Where the sensitive degree of government is denoted d s u cm 3d s u cm a bcm g g e e bh 7a 7bcm 32b c fu + d c fu + d V s by subsidy fee is denoted by They are both optimally 2 determined through simulation analysis bh 8bC (20) NUMERICAL EXAMPLE As the post-subsidizing social welfare should not be less than that before subsidizing, the critical solution goes to = * We can get the relationship between u '' and s on the condition of performing no loss of social welfare, which is and the upper bound of unit WEEE recycling Take the production, recovery and processing of refrigerators as an example We assume that a 107 , b 2.5 104 , c 105 , d 105 , e =23 0，f =1000，g =1200，h =6，cm =2300，C =40，V =0.6 The initial recycling subsidy fee of WEEE for manufacturer is that s1 =80, where , [100,150] 4.1 Determine the optimal parameters of the government response strategy According to Eqs (21) and (22), we simulate the repeated game process between the government and manufacturers in Matlab 7.0 When reaching an equilibrium, i.e ( =0.01), un un manufacturers’ recycling rate un parameter and changing with is shown as Figure Figure The repeated game process between the government and manufacturers Remark When considering the condition that the post-subsidizing social welfare should be no less than that before subsidizing, there is a nonlinear relationship between manufacturers' recycling rate and unit subsidy Figure The variation of recycling rate un with parameter and for WEEE recycling The recycling rate is fluctuating in a certain interval (here is [45%, 65%]) with the Remark Along with the increasing of the sensitive increasing of unit recycling subsidy When the game degree of government imposing on manufacturer's achieving a convergence after dynamic adjustment, it recycling rate, or adding the upper bound of unit reaches the peak of the recycling rate (here is 65.01%), WEEE that is what we need recycling subsidy (subsidy ceiling), manufacturer's recycling rate performs as an oscillation increasing trend when reaching the equilibrium in the repeated game Therefore, considering the condition CONCLUSION that the post-subsidizing social welfare should be no We establish a WEEE CLSC consisting with a less than that before subsidizing, the government manufacturer, a retailer and a consumer group under should choose a higher sensitive degree as far as the government regulation, analyzing the repeated possible, as well as the subsidy ceiling, to promote the game WEEE recycling manufacturers based on the cobweb theory The main 4.2 The repeated game process between the conclusion is summarized as follows process between the government and (1) If manufacturers perform at the upper bound of government and manufacturers When =150and =150, manufacturers' recycling recycling rate on the premise of achieving no loss of its rate under an equilibrium reaches the peak, equals to own profits, it will make no benefit to social welfare 65.01% According to Eqs (21) and (22), we can The loss of social welfare is increasing with the unit obtain a repeated game process shown in Figure recycling subsidy of WEEE It is resulted from adding processing and remanufacturing cost to manufacturers’ operation and decreasing the social welfare Therefore, it is reasonable to maximize the recycling rate at no loss of social welfare (2) Considering the condition that the economical sustainability of WEEE closed-loop supply post-subsidizing social welfare should be no less than chains with recycling: a system dynamics analysis”, that before subsidizing, higher sensitive degree and International Journal of Advanced Manufacturing subsidy ceiling should be chosen by the government in Technology, Vol.47, No.5-8, pp 475-493 the equilibrium of the repeated game to promote the Hammond, D and Beullens, P (2007) “Closed-loop supply chain network equilibrium under legislation”, European WEEE recycling Journal of Operational Research, Vol.183, No.2, pp.895-908 ACKNOWLEDGMENTS Hong, I.-H and Ke, J.-S (2011) “Determining Advanced This research was supported by National Natural Science Recycling Fees and Subsidies in “E-scrap” Reverse Foundation of China (No.71103149), National Social Supply Chains”, Journal of Environmental Management, Science Foundation of China (No.07CJY019), Program for New Century Excellent Talents in University (No.NCET-10-0706), Fund for Cultivating Academic and Technological Leaders in Sichuan Province (No.2011-441), Fundamental Research Funds for the Central Universities (No.SWJTU11CX152), and the Grant-in-Aid for Asian CORE Program "Manufacturing and Environmental Management in East Asia" of Japan Society for the Promotion of Science (JSPS) Vol.92, No.6, pp.1495-1502 Jen, S T (2007) The Optimal Economic Policy of Governmental Involvement on the Performance of Green Supply Chain, Master’s Thesis, National Chiao Tung University Li, X Q., Wu, Q M., and Zhu, D L (2011) “A Multicommodity Flow Closed- loop Supply Chain Equilibrium Model with Stochastic Demand” Systems Engineering, Vol.29, No.10, pp 51-57 Mitra, S and Webster, S (2008) “Competition in REFERENCES Aksen, D., Aras, N., and Karaarslan, A G (2009) “Design and analysis of government subsidized collection systems for incentive-dependent returns”, International Journal of Production Economics, Vol.119, No.2, pp.308-327 Atasu, 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It is reasonable to maximize the recycling rate at no loss of WEEE recycling subsidy fee to encourage WEEE recycling Conversely,... nonlinear relationship between manufacturers' recycling rate and unit subsidy Figure The variation of recycling rate un with parameter and for WEEE recycling The recycling rate is fluctuating in