WANG Mingjing()， ZHUANG Meiling()， LIU Jing( )

College of Fashion Design and Engineering， Qingdao University， Qingdao 266000， China

Abstract： In the global environment of pursuing resource regeneration and green environmental protection， more and more wasted clothing need to be solved. In order to make full use of the wasted clothing and save land and soil resources， an idea of wasted clothing’s recycling and remanufacturing is put forward. In the new idea a pricing game model is established basing on Stacklberg differential game theory between traditional and remanufactured clothing. In this model， the differences in consumers’ willingness to pay and the government’s subsidies are considered. Government’s optimal subsidy are obtained which ensure not only the interests of manufacturers but also environmental reputation and maximum social benefits. The study is helpful to push the wasted clothing’s recycling and remanufacturing plan. It makes some index more precise quantification as government’s subsidy， manufacturers and the social benefits. Government and manufactures can make the detailed cooperation plan reference to it.

Key words： wasted clothing； recycling and remanufacturing； pricing game model； government subsidy； Stacklberg differential game theory

Introduction

With the exhaustion of material resources and the deterioration of natural environment， the issue of resources and environment has become a topic of common concern all over the world from the beginning of the 21st century. However， a lot of wasted clothing have not been properly utilized， which have wasted resources and polluted the environment. Globally， thirty million tons of clothing are discarded each year， with a combined utilization rate of less than 5%， most of which are buried or burned directly[1-2]. The widespread use of chemical fibers has made many clothing unable to degrade in the natural environment， so the clothing is extremely harmful to the soil environment after burying[3]. In addition， clothing containing chemical fibers has produced a large number of toxic gases during the combustion process， which has resulted in serious air pollution[4]. Relevant studies have shown that reasonable classification and recycling of 1 ton of wasted clothing can reduce carbon dioxide emissions by 10 tons compared with incineration[5-6]. Therefore， the recycling of wasted clothing has received extensive attention in the society.

Throughout the Chinese market， consumers’ willingness to pay for remanufactured garments is low. One reason is that most consumers are not sure of hygiene and quality for wasted clothing’s recycling and remanufacturing process. Another reason is the consumption concept of consumers， who mind wearing second-hand clothing[7]. In addition， the higher production cost has made remanufactured garments at a competitive disadvantage in the market. However， the environmental pollution and resource waste caused by more and more wasted clothing have made the recycling of resources become very urgent[8]. Therefore， the government’s encouragement of policies and funds is particularly important for the remanufactured garments. At present， the impact of government subsidies on the recycling and remanufacturing of closed loop supply chain has become the focus of research. Mitra[9]proposed a two-cycle model to study the effects of government subsidies on remanufactured products. The study found that when manufacturers and remanufacturers compete， the subsidy can incentivize remanufacturing activity. Zhu and Dou[10]studied the impact of government subsidies related to product greenness level on supply chain under the difference of consumers’ willingness to pay. Wang and Da[11]studied the decision-making problems of electronic products remanufacturers. The research proposed an optimal model for manufacturers with or without recycling and remanufacturing cost advantages. Xuetal.[12]established a supply chain model of duopoly manufacturers and retailers. The optimal pricing strategy of low carbon products and ordinary products was obtained by comparing the decentralized model of non-government subsidy and government subsidy. Xie[13]studied the differences between ordinary and green products in the green supply chain， and the impact of the differences on overall benefits and the social environment.

Previous literatures mostly regarded government subsidies as a fixed parameter in the game model， assuming that the cost of remanufactured products was lower， and ignoring the problem of consumer preference. Due to the limitation of recycling technology of wasted clothing， the cost of recycling and remanufacturing clothing is higher and the acceptance of consumers is lower， but this is a problem must be solved under the general trend. At present， the cost for remanufactured garments is high but it is favorable and necessary for long-term social and environmental benefits. So it needs our government to give subsidies to promote and support remanufactures interests for remanufactured garments. Related model and research for remanufacturies are less. In this research such factors as government subsidies, product competition and consumer preferences for traditional and remanufactured garment are analyzed.

Based on the deficiency of the current research literature， a Stackelberg game model for two production lines of the same garment manufacturer was constructed[14]. The purpose is to explore the effect of government subsidy on remanufactured garments and total social income (SI).

1 Model Description and Assumption

It is assumed that there is a garment enterprise with high brand awareness， high product price and excellent reputation. Under the general situation where the government gives subsidies to remanufactured garments， this enterprise has improved from the original single production mode to the parallel production mode. In the parallel production mode， the garment enterprise simultaneously produces both traditional and remanufactured garments. The production and sales of remanufactured garments have an advertising effect on the enterprise and benefit the long-term development of the enterprise. Due to the strong capital and advanced production equipment， there is no quality difference between the remanufactured garments and the garments produced with the new materials， and the consumers fully trust the company. On this basis， this paper constructed a supply chain consisting of garment manufacturer and consumer. When the garment manufacturer produces both traditional and remanufactured garments， the government subsidizes remanufactured garments， as shown in Fig.1.

Fig. 1 Game model of traditional and remanufactured garments in parallel production mode

Consumers have different preferences for traditional garments and remanufactured garments， so garment manufacturer adopt differentiated pricing strategies to promote remanufactured garments. Under the parallel production mode， traditional garments and remanufactured garments have the same quality， but consumers have different willingness to pay for the two kinds of garment.θis defined as consumers’ willingness to pay for the traditional garment of the unit[15]， andθsubjects to the uniform distribution on [0，1]. Consumers’ willingness to pay for single remanufactured garment isγθ.γcan be regarded as the acceptance level of consumers to remanufactured garments， andγ∈[0， 1][16]. The higher the consumer’s acceptance of remanufactured garments， the closer theγis to 1. Supposing that the selling prices of traditional garments and remanufactured garments areptandprrespectively， in order to promote remanufactured garments among consumers, we makepr

Letθ1indicate consumers’ willingness to pay when there is no difference between buying remanufactured garments and not buying products. In this case， according toγθ1-pr=0， we have

(1)

Letθ2indicate consumers’ willingness to pay when there is no difference between buying remanufactured garments and buying traditional garments. According toγθ2-pr=θ2-pt， we have

(2)

whereγ∈[0， 1] is the acceptance level of consumers to remanufactured garments；ptis the selling price of traditional garments，pris the selling price of remanufactured garments， andpr

The relationship between consumer surplusUtandUrand willingness to payθis shown in Fig.2.

Fig. 2 Schematic diagram of consumer surplus function

Setting the market size to be standardized to 1， it can be concluded from Fig.2 that the demand of consumers for traditional garmentsQtand remanufactured garmentsQrin the parallel production mode.

(3)

(4)

In the same way， consumers’ demand for traditional garments in a single modeQsis

Qs=1-pt.

(5)

It is assumed that the unit marginal cost of manufacturing traditional clothing and remanufactured garment isctandcrrespectively. Due to the high production process requirements for remanufactured garments，ct

(6)

πr=(pr-cr+b)Qr=

(7)

whereQtis the demand of consumers for traditional garments；Qris the demand of consumers for remanufactured garments；πtis the profit of traditional garments；πris the profit of remanufactured garments；bis the government subsidy for the remanufactured garment.

Set the total profit under the parallel production mode asΠp， andΠp=πt+πr. It is assumed that the total profit of the single production mode isΠs， andΠs=(pt-ct)(1-pt).

2 Model Analysis and Solution

2.1 Manufacturer’s optimal decision analysis

(8)

Substituting Eq. (8) into Eq. (6)， we have

(9)

(10)

(4-γ)b]/4(2-γ),

(11)

At this point， the optimal output and profit of the enterprise are

(2-γ)b]/(4(2-γ)(1-γ)]，

(12)

(4-3γ)b]/[4γ(2-γ)(1-γ)]，

(13)

(14)

(15)

For Eqs. (10)-(15)， the partial derivatives ofbcan be obtained respectively：

Therefore， when the government subsidies for remanufactured garments increase, the price of traditional garments and remanufactured garments will decrease； the demand for traditional garments will decrease as the demand for remanufactured garments will increase； the profit of remanufactured garments will increase， while the profit of the corresponding traditional garments will decrease. The results show that government subsidy is conducive to the promotion of remanufactured garments.

2.2 Government subsidy analysis

b>cr-(2-γ)ct-2(1-γ).

(16)

It can be seen from the Eq. (16) that the minimum government subsidy to popularize remanufactured garments will increase with the increase of remanufactured garments costcrand the increase ofγ， decrease with the increase of traditional garments costct. The reason is that when the acceptance level of consumers to remanufactured garments increases， the demand for remanufactured garments increases. As the current cost of remanufactured garments is relatively high， the government subsidies need to increase. However， it is difficult to solve the problem of the high cost of remanufactured garments at present[18]. The solution to this problem is to increase investment in scientific and techological innovation for the government.

The manufacturer will only produce the remanufactured garments when the total profit in the parallel production mode is not less than that profit in the single production mode， and the profit difference in the two production modes Δ is

Δ=Πp-Πs,

(17)

whereΠpis the total profit under the parallel production mode；πsis the total profit of the single production mode.

bmin=[2γ(1-γ)-3γ(2-γ)ct+

(4-γ)cr]/(4-γ).

(18)

When the government subsidy isbmin， the prices and profits of the two garments are as follows.

(19)

pr=γct，

(20)

(21)

(22)

When the manufacturer implements the parallel production mode， the government encourages the garment enterprise to produce the remanufactured garments by subsidizing the remanufactured garments， and the government formulates the optimal subsidy policy according to the goal of maximizing the total SI. Assuming that the environmental benefit of a remanufactured garment isk, the total SI is the sum of the manufacturer’s benefit， then consumer surplus (CS) and environmental benefit， minus the government subsidy[19].

The sum of CS is

(23)

whereθis consumers’ willingness to pay for the traditional garment；γθis consumers’ willingness to pay for the remanufactured garment.

Then the total SI is

SI=πt+πr+CS+Qrk-Qrb,

(24)

wherekis the environmental benefit of a remanufactured garment.

(25)

2.3 Solution

From the above model， such summary can be obtained as follows.

remanufacturers， but also promotes remanufactured garments among consumers.

(2) When the government subsidy for remanufactured garments is

[γ(γ-2)(5γ-8)ct-(7γ2-20γ+16)cr-

2γ(1-γ)2+4γ(2-γ)(4-3γ)k]/(5γ2-20γ+16)，

the social benefits can be maximized.

3 Example Analysis

The above model is obtained through theoretical derivation， and the following numerical simulation analysis is needed to verify the correctness of the above conclusion. The production cost of traditional garments and remanufactured garments are set as basic parameters[20]. As the acceptability of remanufactured garments is not high nowadays，γtakes values in the range of [0.2， 0.6][21]. The influence of government subsidybon traditional garments and remanufactured garments is shown below.

Figures 3-4 indicate that when the government subsidies for remanufactured garments increases， the prices of traditional garments and remanufactured garments will be reduced. When consumers’ acceptance of remanufactured garments increases， the price of traditional garments will decrease， while the price of remanufactured garments will increase.

Fig. 3 Influence of b on pt

Fig. 4 Influence of b on pr

Figures 5-8 indicate that the increase of government subsidy for remanufactured garments has the same result as the increasing of consumers’ acceptance of remanufactured garments. That is， the demand for traditional garments is reduced while the demand for remanufactured garments is increased. The profit of traditional garments is reduced， but the profit of remanufactured garments increase. The results of the numerical analysis are consistent with the results of the model discussion in the previous section.

Fig. 5 Influence of b on Qt

Fig. 6 Influence of b on Qr

Fig. 7 Influence of b on πt

Fig. 8 Influence of b on πr

4 Conclusions

Above all， in this paper two kinds of profit composition of single production mode and parallel production mode are compared， and the difference of consumers’ willingness to pay is analyzed. In the parallel production mode， the differentiated pricing strategy is adopted for the traditional garments and remanufactured garments. Based on differentiated pricing strategy， a stacklberg game supply chain model is constructed. These conclusions will provide a theoretical basis for enterprise management and government decision-making.

In this research， some complex problems are simplified in model as assuming the information sharing of all parties involved in the game， and the traditional garments and remanufactured garments are produced and sold by the same manufacturer. The model will further consider more asymmetric information， different manufacturers and remanufactur conditions with third-party authorization in the future.