Optimal production and carbon emission reduction level under cap-and-trade and low carbon subsidy policies

Accepted Manuscript Optimal production and carbon emission reduction level under cap-and-trade and low carbon subsidy policies

Kaiying Cao, Xiaoping Xu, Qiang Wu, Quanpeng Zhang PII:

S0959-6526(17)31708-0

DOI:

10.1016/j.jclepro.2017.07.251

Reference:

JCLP 10254

To appear in:

Journal of Cleaner Production

Received Date:

31 March 2016

Revised Date:

30 July 2017

Accepted Date:

31 July 2017

Please cite this article as: Kaiying Cao, Xiaoping Xu, Qiang Wu, Quanpeng Zhang, Optimal production and carbon emission reduction level under cap-and-trade and low carbon subsidy policies, Journal of Cleaner Production (2017), doi: 10.1016/j.jclepro.2017.07.251

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

1

Optimal production and carbon emission reduction level under cap-

2

and-trade and low carbon subsidy policies

3

Kaiying Caoa, Xiaoping Xub,*, Qiang Wuc, Quanpeng Zhangd a

4 5 6

999 Xuefu Road, Nanchang 330031, PR China b Management

7

Research Center, China Electronics Technology Group Corporation, No. 38

Research Institute, 199 Xiangzhang Avenue, Hefei, Anhui 230088, PR China c

8

School of Management, University of Science and Technology of China,

9 10

96 Jinzhai Road, Hefei, Anhui 230026, PR China d Capital

Operation Center, Beijing Tianheng Development Group CO., LTD, 31 Fuwai Street,

11 12

School of Management, Nanchang University,

Xicheng District, Beijing 100037, PR China *Corresponding

author ((+86)-551- 63607949; [email protected])

13 14 15 16 17 18 19 20 21 22 23 1

ACCEPTED MANUSCRIPT 24

Optimal production and carbon emission reduction level under cap-

25

and-trade and low carbon subsidy policies

26

Abstract: In recent years, massive carbon emissions have caused serious global

27

environmental damage such as a worsening greenhouse effect and thick haze. To curb

28

carbon emissions as well as maintain sustainable economic development, governments

29

promote the development of low carbon economy by issuing multiple policies among

30

which the cap-and-trade policy (CTP) and low carbon subsidy policy (LCSP) are

31

widely adopted. Moreover, manufacturers are increasingly adopting carbon emission

32

reduction technology to produce greener products considering related government

33

policies and rising environmental awareness among consumers. To give policy-making

34

insights to governments as well as production and carbon emission reduction decision-

35

making insights to manufacturers, this paper investigates the impacts of CTP and LCSP

36

on the production and carbon emission reduction level of a manufacturer, and explores

37

which policy is better for society. The results show that the carbon emission reduction

38

level increases as the carbon trading price increases, whereas it is independent of the

39

unit low carbon subsidy. Interestingly, the carbon trading price does not always have a

40

negative effect on the manufacturer’s profit, and the cap does not always produce a

41

positive effect on the manufacturer’s profit. More importantly, we find that LCSP is

42

more beneficial to society when the environmental damage coefficient is less than a

43

threshold, but otherwise CTP is more beneficial.

44

Keywords: cap-and-trade policy; low carbon subsidy policy; carbon emission

45

reduction level; social welfare 2

ACCEPTED MANUSCRIPT

46

1. Introduction

47

Rapid economic development brings huge amounts of carbon emissions, which is the

48

main reason for global warming. To curb carbon emissions, the cap-and-trade policy

49

(CTP) has been recommended by many senior scholars such as Hua et al. (2011) and

50

Du et al. (2016) and implemented in many parts of the world. Under CTP, the

51

manufacturing firms are firstly allocated some free emission credits from the

52

government and they can trade (i.e., buy or sell) the emission credits with each other in

53

the carbon trading market. The European Union Emissions Trading Scheme is the world

54

largest carbon trading market, covering almost 50% of the total carbon emissions in

55

European Union (Hintermann, 2010). Meanwhile, in order to promote the development

56

of low carbon economy, the government also tries some creative stimulus solutions,

57

such as the low carbon subsidy policy (LCSP). That is, the government adopts a policy

58

that motivates manufacturers through giving incentives to produce green products. The

59

United States, for example, has provided $2.4 billion of loans for electric vehicle

60

corporations and $2 billion for 30 factories producing batteries and other new energy

61

vehicles (Gong et al., 2013). Hence, both CTP and LCSP can significantly affect the

62

manufacturer’s production decisions and improve environmental standards.

63

Under CTP, the carbon emission credits are essential resources for the

64

manufacturer’s annual production. Under LCSP, the manufacturers can obtain more

65

subsidies by improving the carbon emission reduction level. Hence, both CTP and

66

LCSP can stimulate the manufacturer to produce cleaner products by adopting green

67

technologies. In addition, the consumers are increasingly motivated and encouraged to 3

ACCEPTED MANUSCRIPT 68

buy green products such as the energy-saving equipment. A purchasing survey related

69

to household electronic and electrical equipment in Ningbo (Zhejiang province, China),

70

revealed that 70% to 80% of the locals prefer to buy environmental friendly products

71

(Huang et al., 2006). After implementing the green production technologies, the

72

manufacturers need to figure out optimized production and the related carbon emission

73

reduction level under CTP and LCSP. Meanwhile, the local government should decide

74

which policy should be implemented to maximize the social welfare.

75

Despite the importance of the policy choice between CTP and LCSP to the

76

government as well as the production and reduction strategies under the two policies to

77

manufacturers, there is no previous work to investigate the above challenges of

78

manufacturers and governments. To fill this gap, this paper meets those challenges.

79

This paper considers a manufacturer producing and then selling green products directly

80

under CTP and LCSP. We explore and analyze the optimal production strategy and the

81

carbon emission reduction level decisions for the manufacturer under CTP and LCSP.

82

The government optimal decisions for the cap and unit low carbon subsidy under the

83

two policies will also be examined. In addition, we compare the optimal social welfare

84

results for the two policies and propose some managerial insights.

85

The paper is organized as follows. Section 2 reviews the related literature. In Section

86

3, the key problems and scientific issues are described in detail. The results under the

87

two policies are shown in Section 4. The optimal cap and unit low carbon subsidy are

88

presented in Section 5. Section 6 compares the social welfare under the two policies.

89

The last section concludes the paper, and the future research directions are also 4

ACCEPTED MANUSCRIPT 90

proposed. All the proofs in this paper are shown in the Appendix section.

91

2. Literature review

92

An abundance of investigations concerning the cap-and-trade and low carbon

93

subsidy policies, in different aspects, can be found in the open literature resources. The

94

ones which are highly related to this work can be divided into three categories: (1) a

95

firm’s optimal operational decisions under CTP; (2) a firm’s optimal operational

96

decisions under LCSP; (3) comparison of a firm’s operational decisions under the

97

different environmental policies.

98

2.1. A firm’s operational decisions under CTP

99

Dobos (2005) studies the optimal production-inventory strategies for a company

100

under the cap-and-trade policy regulation, and finds that the optimal production

101

quantities are reduced after applying the emission trading policy. Benjaafar et al. (2013)

102

analyzes the optimal production decisions covering multiple periods under carbon tax,

103

cap-and-trade policy, and carbon offsets, and the results show that the cap allocated by

104

government has no effect on the firm’s optimal decisions. To extend the study of

105

Benjaafar et al. (2013) by allowing different emissions trading prices, Gong and Zhou

106

(2013) establish the structural properties of the optimal cost functions and find that the

107

allocated cap influences the firm’s production decisions. To take into account an

108

emission-dependent supply chain, Du et al. (2013) analyze the impact of cap-and-trade

109

policy on such a chain and find the allocated cap has a significant effect on the optimal

110

production decisions for the supply chain. Xu et al. (2017a) investigate the problems of 5

ACCEPTED MANUSCRIPT 111

production and pricing with two substitutable and complementary products in a Make-

112

To-Order supply chain under cap-and-trade policy, and the results show that the cap-

113

and-trade regulation may not induce the manufacturers to produce cleaner products. In

114

follow-up work, Xu et al. (2017b) study the production and carbon emission reduction

115

level in a Make-To-Order supply chain under cap-and-trade regulation, and find that

116

both wholesale price and cost sharing contracts can coordinate the supply chain.

117

The above literature, with the exception of Xu et al. (2017b), does not consider the

118

effect of the carbon emission reduction level, which plays a key role in the firm’s

119

operational decisions. Moreover, unlike previous works, our work focuses on

120

comparison of the CTP and LCSP, and takes social welfare into account. Since it is

121

necessary for the government to choose among the different environmental policies, we

122

apply a Stackelberg game to compare the social welfare benefits under CTP and LCSP,

123

and present some managerial insights based on the results.

124

2.2. A firm’s operational decision under LCSP

125

Considerable attention has been devoted to investigating the effect of subsidy policy

126

on green technology or new energy, as exemplified by Lin and Jiang (2011) and Cohen

127

et al. (2015). Here we focus on the literature of the operational decisions under subsidy

128

policy. Moraga-González and Viaene (2005) explore the pricing decisions of two

129

competitive firms under subsidy policy. The results show that the government can

130

improve the social welfare by subsidizing domestic low-quality production. In order to

131

extend the reference of the newsvendor model, Zhang (2014) investigates the optimal 6

ACCEPTED MANUSCRIPT 132

production decisions with a governmental subsidy policy, and determines that the

133

subsidies are significant factors affecting the optimal production quantity. By

134

combining system dynamics with real option models, Jeon et al. (2015) optimize

135

financial subsidies and investments for renewable energy technologies, and find that

136

their model can help governments to optimize their subsidy allocation.

137

Similar to the situation described in subsection 2.1, no paper considers the carbon

138

emission reduction level under LCSP. Moreover, the social welfare functions in

139

previous research have not considered the negative influence of carbon emission on the

140

social welfare. Since carbon emissions can influence the social welfare, it is necessary

141

to consider their negative effect in the social welfare function. In our work, we consider

142

the firm’s production and carbon emission reduction level decisions under CTP and

143

LCSP, and compare the social welfare benefits under the two policies, which makes the

144

problem much more complex.

145

2.3. Comparison of a firm’s operational decisions under different environmental

146

policies

147

Many published papers compare different environmental policies considering

148

various aspects such as the total carbon emissions, social welfare, and so on. The studies

149

mainly focus on (i) the comparison of carbon tax policy and subsidy policy; (ii) the

150

comparison of cap-and-trade and carbon tax policies.

151

By modelling household relocation choice behaviors and consumption behaviors,

152

Yin et al. (2016) study the effect of three environmental policies on energy 7

ACCEPTED MANUSCRIPT 153

consumption. They find that the combination of subsidy and tax policies can move 2.2%

154

of households to the city center area. Zhao et al. (2015) study the effect of carbon tax

155

and government subsidy on the efficiency improvement, and find that the two policies

156

have a positive impact on the efficiency improvement. By considering environmentally

157

aware consumers, Bansal and Gangopadhyay (2003) investigate the optimal pricing

158

decisions under the uniform policy and discriminative policy. They find that the

159

discriminative subsidy policy can increase the social welfare and the discriminative tax

160

policy can reduce social welfare. When considering variable cleanup cost, Bansal

161

(2008) studies the optimal pricing decisions under carbon tax and low carbon subsidy

162

policies. He discovers that the optimal policy depends on the value of the environmental

163

damage coefficient. Galinato and Yoder (2010) investigate the optimal revenue under

164

carbon tax and subsidy policies, and find that both types can enhance social welfare.

165

Lim and Kim (2012) introduce Research and Development into the CGE (Computable

166

General Equilibrium) model to simulate the technology progress. They find that the

167

combination of the subsidy policy and carbon tax policy can increase GDP without

168

increasing carbon emissions.

169

Some papers compare carbon tax and cap-and-trade regulations based on macro

170

analysis, such as literature survey and opinion pieces analysis (Harrison and Smith,

171

2009), advantage and disadvantage analysis (Avi-Yonah and Uhlmann, 2009),

172

empirical data analysis (Carl and Fedor, 2016). Meanwhile, there are also some studies

173

which compare carbon tax and cap-and-trade policies in a micro aspect. Wittneben

174

(2009) compares six aspects of cap-and-trade and carbon tax regulations, and finds that 8

ACCEPTED MANUSCRIPT 175

carbon tax regulation is a quicker and cheaper way to control carbon emissions. Based

176

on the traditional Economic Order Quantity (EOQ) model, He et al. (2015) study the

177

optimal lot-sizing problem under cap-and-trade and carbon tax policies and compare

178

the total carbon emissions under the two policies. Zhang and Xu (2013) investigate the

179

optimal production decision considering multiple products under cap-and-trade and

180

carbon tax policies. In that work, they find that there is no policy always having an

181

advantage in curbing carbon emissions. Xu et al. (2015) explore the optimal production

182

and pricing decisions under cap-and-trade and carbon tax policies, and they find that

183

social welfare under carbon tax policy is no less than that under cap-and-trade policy.

184

Li et al. (2017) investigate production and transportation outsourcing strategies in two

185

cases: one under cap-and-trade policy and the other under joint cap-and-trade and tax

186

policy, and find that joint policy is better than single policy to curb carbon emissions.

187

The differences between our paper and previous works are presented as follows. Our

188

paper is among the first papers to investigate the impacts of CTP and LCSP on

189

production and reduction strategies of firms who produce and sell products directly.

190

Moreover, we explore the optimal decisions of the government under CTP and LCSP,

191

respectively, and compare the social welfare consequences under CTP and LCSP to

192

present the optimal policy. In practice, our results serve for firms to determine optimal

193

production and reduction strategies under CTP and LCSP as well as providing insights

194

for the government to issue optimal policy.

195

3. Model formulation and notation

9

ACCEPTED MANUSCRIPT 196

We consider a single manufacturer selling green products directly. To promote the

197

development of low carbon economy, the government has two policies: one is cap-and-

198

trade policy (CTP) and the other is low carbon subsidy policy (LCSP). Under CTP, the

199

government allocates a cap (i.e., limited number of carbon emission permits) to the

200

manufacturer, and the manufacturer can trade (i.e., buy or sell) emission credits in the

201

carbon trading market according to its own situation. Under LCSP, the government

202

subsidizes the manufacturer by a specified amount per unit green product sold.

203

To clarify our model, notation is defined in Table 1.

204

Table 1

205

The major parameters and notations

206

Notation

Description

a

Initial market potential (unit/year)

p

Product price ($/unit)

e

Carbon emission reduction level (kg CO2e/unit)

k

Product price sensitivity coefficient (unit2/$/year)

m

Consumers’ sensitivity to carbon emission reduction level (unit2/kg CO2e/year)

e0

Initial unit carbon emissions (kg CO2e/unit)

h

Cost coefficient of carbon emission reduction ($ unit/kg CO2e2)

c1

Unit production cost ($/unit)

q

Production quantity ($/year)

E

Total emission, which is equal to (e0  e) q (kg CO2e/unit)

b

Carbon trading price ($/kg CO2e/unit)

C

Emission cap (kg CO2e/unit)



Unit low carbon subsidy ($/unit)

v

Environmental damage coefficient ($/kg CO2e/unit)

M

Profit of the manufacturer ($/year)

3.1. The demand function

10

ACCEPTED MANUSCRIPT 207

Following the example of earlier scholars (e.g. Luo et al., 2016), we assume that the

208

demand for green products is sensitive to the carbon emission reduction level. Thus,

209

the demand function faced by the manufacturer can be given as the following:

210

D  a  kp  me .

⑴

211

In Eq. (1), e is the carbon emission reduction level, k is the product price sensitivity

212

coefficient and the parameter m reflects the consumers’ sensitivity to carbon emission

213

reduction level (Wang et al., 2016).

214

215

Note that, we assume that the production quantity q is equal to the product demand.

3.2．The cost structure

216

The unit production cost is denoted by the parameter c1 . Following Luo et al. (2016),

217

we assume that the carbon emission reduction cost is he 2 , which also represents carbon

218

reduction investment. Note that the parameter h represents the cost coefficient of

219

carbon emission reduction.

220

As in Cachon (2014), the environmental damage cost is assumed to be increasing in

221

total emission and is expressed as vE , where v is the environmental damage coefficient

222

which translates a unit carbon emission into a monetary unit. Moreover, we assume that

223

v  0 , which means that carbon emission makes the society worse off.

224

3.3．Two policies

225

This paper investigates optimal production and carbon emission reduction level

226

decisions under CTP and LCSP, and explores the impacts of these two policies (i.e.,

227

CTP and LCSP) on the manufacturer’s optimal decisions. Moreover, the study 11

ACCEPTED MANUSCRIPT 228

determines which policy is optimal for the government by comparing social welfare

229

under these two policies.

230

Under CTP, the government allocates an emission cap C to the manufacturer. The

231

manufacturer curbs its total emission E  (e0  e)q by improving the carbon emission

232

reduction level e . If E is larger (less) than the cap C , the manufacturer will buy (sell)

233

emission credits from (into) the carbon trading market with a unit carbon trading price

234

b . Moreover, we assume that e0 q  C , that is, the cap is lower than the manufacturer’s

235

initial total carbon emissions (Du et al., 2013). The assumption is reasonable since the

236

manufacturer would not be induced to curb carbon emission unless the cap is less than

237

the initial carbon emissions, thus the government sets a low cap to stimulate the

238

manufacturer to reduce carbon emissions.

239 240 241

Under LCSP, the government subsidizes that manufacturer per unit product sold and the unit low carbon subsidy is represented by the parameter  . Note that, in our model we use superscripts C and S to represent CTP and LCSP

242

respectively.

243

3.4．The game

244

There is a Stackelberg game in our model. The government is the leader and the

245

manufacturer is the follower. The government is committed to maximizing social

246

welfare and the manufacturer pursues maximal profit. Note that we use backward

247

induction to solve the model.

248

4. The main results under CTP and LCSP 12

ACCEPTED MANUSCRIPT 249

The section is divided into two subsections, one is the optimal operational decisions

250

under CTP and other one is the optimal operational decisions under LCSP. Under each

251

policy, the manufacturer determines carbon emission reduction level and product price.

252

4.1. The optimal operational decisions under CTP

253 254 255 256 257

Based on Eq. ⑴, the manufacturer’s profit under CTP is given as following:

max CM ( p, e)  D( p  c1  he 2 )  b[(e0  e) D  C ] .

⑵

( p ,e )

On the right side of the equation, the first term is the sales profit of the manufacturer, and the second term is the carbon trading cost or revenue. The optimal decisions and profits under CTP are shown in Theorem 1.

258

Theorem 1. Under CTP, the optimal product price, carbon emission reduction level,

259

production quantity, and profit are given as follows:

260

(a) When 0  C  C , 



261

p C  [3m 2  4hk (kc1  kbe0  a )  kb(2m  kb)] (8hk 2 ) , eC  (m  kb) (2kh) ,

262

q C  [m 2  4hk (kc1  kbe0  a )  kb(2m  kb)] (8hk ) ,

263

CM  bC  [m 2  4hk (kc1  kbe0  a )  kb(2m  kb)]2 (64h 2 k 3 ) ;

264





(b) when C  C , 





265

p C  (ae0  C ) (ke0 )  (m 2  bkm) (2hk 2 ) , eC  (m  kb) (2kh) , q C  C e0 ,

266

CM  C[m 2 e0  4hk (kc1e0  C  ae0 )  kb(2me0  bke0 )] (4hk 2 e0 2 ) ,

267

where C  e0 [m 2  4hk (kc1  kbe0  a )  kb(2m  kb)] (8hk ) .



268

Theorem 1 shows that the emission trading decisions of the manufacturer depend on

269

the size of the cap. When the allocated cap is less than a threshold, the manufacturer 13

ACCEPTED MANUSCRIPT 270

buys emission credits from the carbon trading market and the purchasing amount is

271

equal to the difference between the total emissions and the cap. When the allocated cap

272

is larger than the threshold, the manufacturer sells surplus emission credits to the carbon

273

trading market, and the sale amount is equal to the difference between the cap and the

274

total emissions. When the allocated cap is equal to the threshold, the manufacturer

275

neither buys nor sells emission credits.

276

Theorem 1 also shows that the optimal production quantity firstly remains constant

277

and then increases as the cap increases. The result is rather intuitive. The optimal

278

production quantity remains constant as the cap increases, because the manufacturer

279

determines the optimal production quantity without considering the cap when the cap

280

is less than a threshold. The optimal production quantity increases as the cap increases,

281

because the manufacturer determines the optimal production quantity at the point of a

282

certain restrictive condition when the cap is larger than the threshold. Please note that

283

the threshold is equal to C and the point of the restrictive condition is C e0 .

284

Theorem 1 indicates that the optimal carbon emission reduction level and the product

285

price increase as the carbon trading price increases. This pattern occurs due to the

286

manufacturer’s motivation in improving the carbon emission reduction level and

287

reducing the total carbon emissions. The manufacturer also should raise the product

288

price to deal with the increase of carbon emission reduction cost.

289

Proposition 1.

290

(1) The impact of the cap on the manufacturer’s optimal profit is as follows:

291

  (a) When 0  C  C , CM is increasing in C ; 14

ACCEPTED MANUSCRIPT 292 293 294

  (b) when C  C , CM is decreasing in C ,

 where C  e0 [m 2  4hk (kc1  a )  kb(2m  kb)] (8hk ) . (2) The impact of the carbon trading price on the manufacturer’s optimal profit is as

295

follows:

296

  (a) When 0  C  C , CM is decreasing in b ;

297

  (b) when C  C , CM is increasing in b ,

298

 where C  [e0  (m  kb) (2hk )][m 2  4hk (kc1  kbe0  a )  kb(2m  kb)] (8hk ) .

299

Proposition 1(1) shows that the manufacturer’s profit firstly increases and then

300

decreases as the cap increases. When the cap is less than a threshold, as the cap

301

increases, the manufacturer makes no changes and although its sales profit remains

302

constant, the manufacturer’s profit increases due to the increase of carbon trading

303

revenue. When the cap is larger than the threshold, as the cap increases, the

304

manufacturer’s profit decreases due to the decrease of product price.

305

Proposition 1(2) shows that the manufacturer’s profit firstly decreases and then

306

increases as the carbon trading price increases. When the cap is less than the

307

manufacturer’s emissions, it must buy emissions credits from the carbon trading

308

market, thus the manufacturer’s profit decreases as the carbon trading price increases.

309

When the cap is larger than the manufacturer’s emissions, it can earn some carbon

310

trading revenue by selling surplus emissions credits, thus the manufacturer’s profit

311

increases as the carbon trading price increases.

312

4.2. The optimal operational decisions under LCSP

15

ACCEPTED MANUSCRIPT 313

Based on Eq. ⑴, the objective function of the manufacturer under LCSP is given as

314

follows:

315

max  SM ( p, e)  D( p    c1  he 2 ) .

316 317

⑶

( p ,e )

Theorem 2. Under LCSP, the optimal retail price, carbon emission reduction level, production quantity, and profit are given as follows: 



318

p S  [3m 2  4hk (kc1  a  k  )] (8hk 2 ) , e S  m (2kh) ,

319

q S  [m 2  4hk (kc1  k   a )] (8hk ) ,  SM  [m 2  4hk (k   a  kc1 )]2 (64h 2 k 3 ) .

320

Theorem 2 states that the optimal carbon emission reduction level increases as the

321

consumers’ sensitivity to carbon emission reduction level increases. The link occurs

322

because the manufacturer should improve the carbon emission reduction level to

323

stimulate more consumers to purchase products, a conclusion which is similar to Liu et

324

al. (2012).





325

Theorem 2 also says that the optimal product price increases as the consumers’

326

sensitivity to carbon emission reduction level increases. The optimal carbon emission

327

reduction level increases as the consumers’ sensitivity to carbon emission reduction

328

level increases, thus the manufacturer should raise the product price due to the increase

329

of carbon emission reduction cost.

330 331 332 333 334

Theorem 2 shows that as the low carbon subsidy increases, the optimal product price decreases and the optimal production quantity increases. This result is rather intuitive. It also implies that LCSP can motivate the manufacturer to produce more green products. Theorem 2 indicates that the manufacturer’s profit increases as the consumers’ 16

ACCEPTED MANUSCRIPT 335

sensitivity to carbon emission reduction level increases. Therefore, the manufacturer

336

has the motivation to improve the consumers’ sensitivity to carbon emission reduction

337

level.

338

5. The government decisions

339

As the leader, the government takes the manufacturer’s reaction functions into

340

account. Therefore, the government determines the cap under CTP and decides the unit

341

low carbon subsidy under LCSP.

342

5.1. The optimal decisions of the government under CTP

343

The government determines the cap to maximize social welfare after considering the

344

manufacturer’s reaction functions. We define  MS as the manufacturer’s sales profit,

345

i.e.,  MS =(a  kp  me)( p  c1  he 2 ) . Similar to Yenipazarli (2016), the social welfare

346

is defined as the sum of the manufacturer’s sales profit and the consumer surplus less

347

the environmental damage cost. Thus, the social welfare function is the following:

348

max SW (C )   C

(C )

qC

0











( p  p C )d q  CMS v(e0  eC )q C .

⑷

349

On the right side of the equation, the first two terms are the consumer surplus and

350

the manufacturer’s optimal sales profit, respectively, and the last term is the

351

environmental damage cost which is calculated by multiplying the environmental

352

damage coefficient by the carbon emissions.

353

Theorem 3. The optimal cap and social welfare are

354

C   e0 [m 2  k 2b 2  2kv(m  bk )  4hk (kc1  a  kve0 )] (4hk ) , 17

ACCEPTED MANUSCRIPT 

355

SW C  [m 2  k 2b 2  4hk (kc1  kve0  a )  2kv(m  kb)]2 (32k 3 h 2 ) .

356

Theorem 3 shows that the optimal cap and social welfare firstly increase and then

357

decrease as the carbon trading price increases. From Theorem 1, we can see that the

358

optimal carbon emission reduction level increases as the carbon trading price increases,

359

then the unit carbon emission reduction cost increases and the unit environmental

360

damage decreases. When the carbon trading price is less than a threshold, as it increases,

361

the increase of the social welfare from the decreased environmental damage cost is

362

larger than the decrease of the social welfare from the increased carbon emission

363

reduction cost, thus the government should improve the cap to stimulate the

364

manufacturer to produce more products. When the carbon trading price is larger than

365

the threshold, as it increases, the increase of the social welfare from the decreased

366

environmental damage cost is less than the decrease of the social welfare from the

367

increased carbon emission reduction cost, thus the government should decrease the cap

368

to curb carbon emissions.

369

5.2. The optimal decisions of the government under LCSP

370

Using the analysis in this section, the government can determine a unit low carbon

371

subsidy to maximize social welfare after considering the manufacturer’s reaction

372

functions. The social welfare function is the following:

373

max SW (  )  

374 375

S

( )

qS

0













( p  p S )d q   SM   q S  v(e0  e S )q S .

On the right side of the equation, the first term



qS

0



⑸ 

( p  p S )d q is the consumer 



surplus, the second term  SM is the manufacturer’s profit, the third term   q S is the 18

ACCEPTED MANUSCRIPT 



376

government expenditure, and the last term v(e0  e S )q S is the environmental damage

377

cost.

378

Theorem 4: The optimal unit low carbon subsidy and social welfare are

379

   [m 2  4kmv  4hk (kc1  a  2kve0 )] (4hk 2 ) ,

380

SW S  [m 2  2kmv  4hk (kc1  kve0  a )]2 (32k 3 h 2 ) .

381

Theorem 4 implies that the optimal unit low carbon subsidy decreases as the initial

382

unit carbon emissions increases. This phenomenon makes sense because if the product

383

has higher initial unit carbon emissions, the government should reduce the unit low

384

carbon subsidy to stimulate the manufacturer to decrease the production quantity.



385

Theorem 4 also implies that the optimal unit low carbon subsidy decreases as the

386

environmental damage coefficient increases. This happens because the government

387

reduces the unit low carbon subsidy to demotivate the manufacturer to produce

388

products, and thus control the total emissions.

389

Theorem 4 indicates that both the optimal unit low carbon subsidy and social welfare

390

increase as the consumers’ sensitivity to carbon emission reduction level increases. It

391

is known that consumers’ willingness-to-pay increases as the consumers’ sensitivity to

392

carbon emission reduction level increases. The government should improve the unit

393

low carbon subsidy to motivate the manufacturer to produce more products with less

394

unit carbon emissions, which can obviously increase the social welfare. Therefore,

395

government has the motivation to improve the consumers’ sensitivity to carbon

396

emission reduction level.

397

6. The optimal policy 19

ACCEPTED MANUSCRIPT 398

In this section, we compare the social welfare benefits under CTP and LCSP, and the

399

optimal policy is presented.

400

Theorem 5. The size relationship between two social welfare benefits is as follows:

401

(a) When b 2  v , SW C  SW S ;

402

(b) when b 2  v , SW C  SW S .









403

Theorem 5 (a) says that the social welfare under CTP is better than that under LCSP

404

when the environmental damage coefficient is larger than a threshold. From Theorem

405

1 and Theorem 2, it is easy to find that the total emissions under CTP is lower than that

406

under LCSP. Therefore, the government should choose CTP to control the total

407

emissions when the environmental damage coefficient is larger than the threshold.

408

Theorem 5 (b) says that the social welfare under CTP is lower than that under LCSP

409

when the environmental damage coefficient is less than the threshold. From Theorem

410

1 and Theorem 2, it is easy to find that the production quantity under LCSP is larger

411

than that under CTP. Therefore, the government should choose LCSP to stimulate the

412

manufacturer to produce more products when the environmental damage coefficient is

413

less than the threshold.

414

To illustrate Theorem 5 intuitively, we consider the following numerical example.

415

We set a  10 unit/year, b  1 $/kg CO2e/unit, k  1 unit2/$/year, c1  3 $/unit, h  1 $

416

unit/kg CO2e2, e0  1 kg CO2e/unit, m  0.5 unit2/kg CO2e/year, and the value of v is allowed

417

to vary between 0 and 1. Then, the social welfare under two policies with respect to v

418

is depicted in Fig. 1.

20

ACCEPTED MANUSCRIPT

419 Fig. 1. The social welfare with respect to v

420 421

Fig.1 shows that the social welfare under either policy decreases as the environmental

422

damage coefficient increases. Fig.1 also exhibits that the two policies’ social welfare is

423

equal at the point v  0.5 . If the environmental damage coefficient is less than that

424

point, the social welfare under CTP is better than that under LCSP; otherwise, the social

425

welfare under CTP is worse than that under LCSP.

426

Theorem 5 implies that LCSP is the optimal policy for the government when the

427

environmental damage coefficient is less than a threshold; otherwise, CTP is the

428

optimal policy for the government. Hence, there is no single policy that always yields

429

the best social welfare.

430

7. Conclusion

431

Environmental pollution caused by carbon emissions (e.g., greenhouse effect) has

432

attracted the attention of all parts of society including governments, firms, and

433

consumers. To promote low carbon economy, governments in many countries are 21

ACCEPTED MANUSCRIPT 434

widely adopting CTP and LCSP. As of July 2015, there are 17 emissions trading

435

systems in force across four continents, covering 35 countries (ICAP report, 2015).

436

Moreover, the US government in 2009 granted a subsidy (tax credit) for consumers

437

who purchased electronic vehicles (Cohen et al., 2015), and the Chinese government

438

implemented a new energy vehicles subsidy in 2010. Though one is a tax policy and

439

the other is subsidy policy, both CTP and LCSP make society better off. To explore

440

which policy is more conducive to society as well as investigate the impact of these two

441

policies on the production and carbon emission reduction level of manufacturers, we

442

consider a manufacturer producing green products and selling them directly.

443

Theoretical models are developed to examine optimal strategies of the manufacturer

444

and the government. Some important managerial insights are concluded as follows.

445

The optimal policy: The government should issue CTP when the environmental

446

damage coefficient is larger than a certain threshold; otherwise, the government should

447

issue LCSP.

448

The optimal cap and unit low carbon subsidy: As the carbon trading price

449

increases, the government should improve the optimal cap when the carbon trading

450

price is relative small; otherwise, the government should reduce the optimal cap. As the

451

initial unit carbon emissions or the environmental damage coefficient increases, the

452

government should reduce the optimal unit low carbon subsidy, whereas the

453

government should improve the optimal subsidy as the consumers’ sensitivity to carbon

454

emission reduction level increases.

455

The optimal production and carbon emission reduction level: As the cap 22

ACCEPTED MANUSCRIPT 456

increases, the manufacturer should improve the carbon emission reduction level, but

457

should keep its production unchanged when the cap is relative small and should increase

458

its production otherwise. As the unit carbon subsidy increases, the manufacturer should

459

improve its production but should keep the optimal carbon emission reduction level

460

unchanged.

461

The manufacturer’s optimal profit: Interestingly, the results show that the cap may

462

make the manufacturer worse off, whereas the carbon trading price may make the

463

manufacturer better off. Moreover, the unit low carbon subsidy always makes the

464

manufacturer better off.

465

There is still much space for future research. Firstly, we assume that the manufacturer

466

produces products and sells them into the market directly. Thus the situation in which

467

the manufacturer sells products through an independent retailer could be considered in

468

future research. Secondly, our paper just studies one product but multi-products can

469

also be also considered. Finally, it would be interesting and valuable to explore the

470

situation in which there are two or more competing manufacturers under the two

471

policies.

472

473

References

474

Avi-Yonah, R. S., Uhlmann, D. M., 2009. Combating global climate change: Why a

475

carbon tax is a better response to global warming than cap and trade. Stanf. Environ.

476

Law J. 28, 3-50. 23

ACCEPTED MANUSCRIPT 477 478 479 480

Bansal, S., Gangopadhyay, S., 2003. Tax/subsidy policies in the presence of environmentally aware consumers. J. Environ. Econ. Manag. 45(2), 333-355. Bansal, S., 2008. Choice and design of regulatory instruments in the presence of green consumers. Resour. Energy. Econ. 30(3), 345-368.

481

Benjaafar, S., Li, Y., Daskin, M., 2013. Carbon footprint and the management of supply

482

chains: Insights from simple models. IEEE. T. Autom. Sci. Eng. 10(1), 99-116.

483

Cachon, G. P., 2014. Retail store density and the cost of greenhouse gas emissions.

484 485 486

Manage. Sci. 60(8), 1907-1925. Carl, J., Fedor, D., 2016. Tracking global carbon revenues: A survey of carbon taxes versus cap-and-trade in the real world. Energy Policy 96, 50-77.

487

Cohen, M. C., Lobel, R., Perakis, G., 2015. The impact of demand uncertainty on

488

consumer subsidies for green technology adoption. Manage. Sci. 62(5), 1235-1258.

489

Dobos, I., 2005. The effects of emission trading on production and inventories in the

490 491 492

Arrow–Karlin model. Int. J. Prod. Econ. 93, 301-308. Du, S., Tang, W., Song, M., 2016. Low-carbon production with low-carbon premium in cap-and-trade regulation. J. Clean. Prod. 134, 652-662.

493

Du, S., Zhu, L., Liang, L., Ma, F., 2013. Emission-dependent supply chain and

494

environment-policy-making in the ‘cap-and-trade’ system. Energy Policy 57, 61-

495

67.

496 497 498

Gong, X., Zhou, S. X., 2013. Optimal production planning with emissions trading. Oper. Res. 61(4), 908-924. Galinato, G. I., Yoder, J. K., 2010. An integrated tax-subsidy policy for carbon emission 24

ACCEPTED MANUSCRIPT 499 500 501 502 503

reduction. Resour. Energy. Econ. 32(3), 310-326. Gong, H., Wang, M. Q., Wang, H., 2013. New energy vehicles in China: policies, demonstration, and progress. Mitig. Adapt. Strat. Gl. 18(2), 207-228. Harrison, T., Smith, G., 2009. Cap and Trade versus a Carbon Tax. Working paper, Citizens Action Coalition of Indiana, Indianapolis, IN 46204.

504

He, P., Zhang, W., Xu, X., Bian, Y., 2015. Production lot-sizing and carbon emissions

505

under cap-and-trade and carbon tax regulations. J. Clean. Prod. 103, 241-248.

506

Hintermann, B., 2010. Allowance price drivers in the first phase of the EU ETS. J.

507 508 509

Environ. Econ. Manag. 59(1), 43-56. Hua, G., Cheng, T. C. E., Wang, S., 2011. Managing carbon footprints in inventory management. Int. J. Prod. Econ. 132(2), 178-185.

510

Huang, P., Zhang, X., Deng, X., 2006. Survey and analysis of public environmental

511

awareness and performance in Ningbo, China: a case study on household electrical

512

and electronic equipment. J. Clean. Prod. 14(18), 1635-1643.

513

ICAP

report

2015.

Emission

trading

worldwide.

At:

514

https://icapcarbonaction.com/images/StatusReport2015/ICAP_Report_2015_02_1

515

0_online_version.pdf (accessed July 30, 2017).

516

Jeon, C., Lee, J., Shin, J., 2015. Optimal subsidy estimation method using system

517

dynamics and the real option model: Photovoltaic technology case. Appl.

518

Energy 142, 33-43.

519

Li, J., Su, Q., Ma, L., 2017. Production and transportation outsourcing decisions in the

520

supply chain under single and multiple carbon policies. J. Clean. Prod. 141, 110925

ACCEPTED MANUSCRIPT 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537

1122. Lim, J. S., Kim, Y. G., 2012. Combining carbon tax and R&D subsidy for climate change mitigation. Energ. Econ. 34, S496-S502. Lin, B., Jiang, Z., 2011. Estimates of energy subsidies in China and impact of energy subsidy reform. Energ. Econ. 33(2), 273-283. Liu, Z. L., Anderson, T. D., Cruz, J. M., 2012. Consumer environmental awareness and competition in two-stage supply chains. Eur. J. Oper. Res. 218(3), 602-613. Luo, Z., Chen, X., Wang, X., 2016. The role of co-opetition in low carbon manufacturing. Eur. J. Oper. Res. 253(2), 392-403. Moraga-González, J. L., Viaene, J. M., 2005. Trade policy and quality leadership in transition economies. Eur. Econ. Rev. 49(2), 359-385. Wang, Q., Zhao, D., He, L., 2016. Contracting emission reduction for supply chains considering market low-carbon preference. J. Clean. Prod. 120, 72-84. Wittneben, B. B., 2009. Exxon is right: Let us re-examine our choice for a cap-andtrade system over a carbon tax. Energy Policy 37(6), 2462-2464. Xu, X., He, P., Xu, H., Zhang, P., 2017b. Supply chain coordination with green technology under cap-and-trade regulation. Int. J. Prod. Econ. 183, 433-442.

538

Xu, X., Xu, X., He, P., 2015. Joint production and pricing decisions for multiple

539

products with cap-and-trade and carbon tax regulations. J. Clean. Prod. 112, 4093-

540

4106.

541

Xu, X., Zhang, W., He, P., Xu, X., 2017a. Production and pricing problems in make-

542

to-order supply chain with cap-and-trade regulation. Omega-Int. J. Manage. S. 66, 26

ACCEPTED MANUSCRIPT 248-257.

543 544

Yenipazarli, A., 2016. Managing new and remanufactured products to mitigate

545

environmental damage under emissions regulation. Eur. J. Oper. Res. 249(1), 117-

546

130.

547

Yin, Y., Aikawa, K., Mizokami, S., 2016. Effect of housing relocation subsidy policy

548

on energy consumption: A simulation case study. Appl. Energy 168, 291-302.

549

Zhang, B., Xu, L., 2013. Multi-item production planning with carbon cap and trade mechanism. Int. J. Prod. Econ. 144(1), 118-127.

550 551

Zhang, X., 2014. Reference-dependent electric vehicle production strategy considering subsidies and consumer trade-offs. Energy Policy 67, 422-430.

552 553

Zhao, X., Yin, H., Zhao, Y., 2015. Impact of environmental regulations on the

554

efficiency and CO 2 emissions of power plants in China. Appl. Energy 149, 238-

555

247.

556

557

Appendix:

558

Proof of Theorem 1:

559 560

The objective function of the manufacturer is shown as follows: max CM ( p, e)  (a  kp  me)( p  c1  he 2  b(e0  e))  bC . ( p ,e )

561

We firstly figure out solutions without considering the assumption e0 q  C .

562

To solve the first-order condition  CM / p  a  kp  me  k ( p  c1  he2  b(e0  e))  0 and

563

 CM / e  m( p  c1  he 2  b(e0  e))  (a  kp  me)(b  2he)  0 ,

27

we get three solution groups.

ACCEPTED MANUSCRIPT 564

However, only one solution group satisfies positive demand and profit, and the

565

solution group is shown as follows:

566 567

p C [3m 2  4hk (kc1  kbe0  a )  kb(2m  kb)] / (8hk 2 ) , eC  (m  kb) / (2kh) .

It is easy to find that the second-order condition Jacobian matrix:

568

  2 CM  2  p   2 C M   ep

 2 CM    2k pe     2 CM   2m   e 2 

569

where q C  [m 2  4hk (kc1  kbe0  a)  kb(2m  kb)] / (8hk ) . Thus, we have the solution group:

  (hkq  m )  is negative definite, 2 k  2m C

2

570

p C  [3m 2  4hk (kc1  kbe0  a )  kb(2m  kb)] / (8hk 2 ) , eC  (m  kb) / (2kh) ,

571

q C  [m 2  4hk (kc1  kbe0  a )  kb(2m  kb)] / (8hk ) .

572

However, the solution group may not match our assumption e0 q  C . To solve this

573

problem, we present two scenarios to analyze it. One scenario is when e0 q C  C  0 ,

574

these solutions meet our assumption in this scenario. The other scenario is e0 q C  C ,

575

these solutions cannot meet our assumption.

576 577

Thus, under the scenario 1 when e0 q C  C  0 , the above solution group meets the 





assumption, the optimal solution is p C  p C ,eC  eC , q C  q C .

578

Otherwise, under the scenario 2 when e0 q C  C , the above solution group doesn’t

579

meet the assumption, and we find that the manufacturer can achieve maximal profit

580

when the production quantity is equal to the critical point

581

and p C  [(a  me)e0  C ] / (ke0 ) . Put them into the profit function, we can obtain the

582

profit function CM (e)  C[(ae0  mee0 ) / (ke0 )  c1  he2  be0  be] / e0  bC . As it can be easily

583

seen that the second-order condition:  2  MC /(e)2  2hc / e0  0 . Thus, we can solve the

584

first-order condition:  CM /(e)  (m / k  b  2eh)C / e0  0 to get eC  (m  kb) / (2kh) .

C e0



, thus we have q C  C / e0





28

ACCEPTED MANUSCRIPT 585 586

Proof of Proposition 1:

587

(a) When C  C , if C  C ,  CM /(C )  b  0 ;

588

and if C  C  C ,  CM /(C )  {[m 2  4hk (kc1  a)  kb(2m  kb)]e0  8hkC} / (4hk 2 e0 2 )  0 .

589

When C  C ,  CM /(C )  {[m 2  4hk (kc1  a)  kb(2m  kb)]e0  8hkC} / (4hk 2 e0 2 )  0 .

590

(b) When C  C ,

591

 CM /(b)  C  [e0  (m  kb) / (2hk )][m 2  4hk (kc1  kbe0  a )  kb(2m  kb)] / (8hk )  0 .

592

When C  C  C ,

593

 CM /(b)  C  [e0  (m  kb) / (2hk )][m 2  4hk (kc1  kbe0  a )  kb(2m  kb)] / (8hk )  0 .

594

When C  C ,  CM /(b)  C (2m  2kb) / (4hke0 )  0 .

595

Proof of Theorem 2:

596 597 598























The objective function of the manufacturer is max  SM ( p, e)  (a  kp  me)( p    c1  he 2 ) . ( p ,e )

Solving the first-order condition   SM /(p)  a  kp  me  k ( p    c1  he2 )  0 and

599

  SM /(e)  m( p    c1  he 2 )  2he(a  kp  me)  0 , we have three solution groups.

600

However, only one solution group satisfies positive demand and profit. The only one

601

solution group is p S  [3m 2  4hk (kc1  a  k  )] / (8hk 2 ) and e S  m / (2kh) . As it can be

602

easily seen that the second-order condition Jacobian matrix:

603

  2  SM  2  p  2 S M   ep

604 605

 2  SM    2k pe     2  SM   2m   e 2 

  (hkq  m )  is negative definite. 2 k  2m S

2

Thus, the optimal retail price, environmental improvement level and production 



quantity are p S  [3m 2  4hk (kc1  a  k  )] / (8hk 2 ) , e S  m / (2kh) and 29

ACCEPTED MANUSCRIPT 

606

q S  [m 2  4hk (kc1  k   a )] (8hk ) .

607

Proof of theorem 3:

608

Under the scenario 1, that is the situation when e0 q C  C  0 , the social welfare

609

function can be given as following:

610

SW1C  

611 612

qC

0















( p  p C )d q  CM b((e0  eC )q C  C )  v(e0  eC )q C .

In this scenario, the social welfare is not influenced by the cap. Thus, the optimal welfare of scenario 1 is 

613

614 615 616

SW1C  [m 2  k 2 b 2  4hk (kc1  kve0  a )  2kv(m  kb)]2 / (32k 3 h 2 )  [m 2  kb(3kb  2m)  4hk (kc1  kbe0  2kve0  a )  4kv(m  kb)]2 / (128k 3 h 2 ) .

Under the scenario 2, that is when e0 q C  C , the objective of government is: max SW2C (C )  

qC

0

(C )













( p  p C )d q  CM b((e0  eC )q C  C )  v(e0  eC )q C

Thus, solving the first-order condition

618

SW2C (C ) e0 (m 2  k 2 b 2  2kv(m  bk )  4hk (kc1  a  kve0 ))  4hkC  0, C 4hk 2 e0 2

619

cap is C   e0 [m 2  k 2b 2  2kv(m  bk )  4hk (kc1  a  kve0 )] / (4hk ) .

621 622

.

It is easy to verify that the second-order condition  2 SW2C / (C )2  1 / (e0 2 k )  0 .

617

620



we have the optimal

Therefore the optimal social welfare is 

SW2C  [m 2  k 2 b 2  4hk (kc1  kve0  a )  2kv(m  kb)]2 / (32k 3 h 2 ) .

At last, we compare the social welfare under two scenarios, it is easy to find that 



623

SW1C  SW2C  [m 2  kb(3kb  2m)  4hk (kc1  kbe0  2kve0  a )  4kv(m  kb)]2 / (128k 3 h 2 )  0 .

624

Thus, we have the optimal cap and the optimal social welfare:

625

C   e0 [m 2  k 2 b 2  2kv(m  bk )  4hk (kc1  a  kve0 )] / (4hk ) ,

626

SW C  [m 2  k 2 b 2  4hk (kc1  kve0  a )  2kv(m  kb)]2 / (32k 3 h 2 ) .



627 30

ACCEPTED MANUSCRIPT 628

Proof of theorem 4: Under LCSP, the social welfare function is

629 630

SW S (  )  

qS

0













( p  p S )d q   SM   q S  v(e0  e S )q S .

SW S (  ) . It can be easily seen that The objective function of the government is max ( )

631 632

the second-order condition:  2 SW S / ( )2  1 / 4  0 . Thus solving the first-order

633

condition SW S / ( )  [m 2  4kmv  4hk (kc1  a  2kve0  k  )] / (16hk )  0 , we have the

634

optimal subsidy and the optimal social welfare:

635

   [m 2  4kmv  4hk (kc1  a  2kve0 )] / (4hk 2 ) , SW S  [m 2  2kmv  4hk (kc1  kve0  a)]2 / (32k 3 h 2 )

636

.



637 638 639 640

Proof of theorem 5: The optimal social welfare under CTP is 

SW C  [m 2  k 2 b 2  4hk (kc1  kve0  a )  2kv(m  kb)]2 / (32k 3 h 2 ) .

641

The optimal social welfare under LCSP is:

642

SW S  [m 2  2kmv  4hk (kc1  kve0  a )]2 / (32k 3 h 2 ) .

643







We have SW C  SW S  [2m 2  k 2b 2  8hk (kc1  kve0  a)  2kv(2m  kb)](2v  b)b / (32kh 2 ) . 







644

Thus, when b / 2  v , SW C  SW S ; when b / 2  v , SW C  SW S ; when b / 2  v ,

645

SW C =SW S





.

646

31