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Abstract
The implementation of carbon reduction policy is an important method for the firms to reduce carbon emissions.So it is of great significance to research on the firms’strategies under different carbon reduction policies.In this paper，we study the manufacturer’s wholesale price strategy and the retailer’s ordering strategy， as well as carbon emissions policy’s impact on the production and profit， under mandatory carbon emissions capacity policy， carbon emissions tax policy and cap-and-trade policy respectively.In addition， the government’s decision-making about carbon emissions policy parameters is also discussed.The conclusion builds a microeconomic foundationfor the carbon emissions policy’sdesign and development， and also verified the policy’seffectivenessand scientificity， at last achieved the “win-win”ofthe government and enterprises.
Key word：Pricing；Ordering；Carbon emission policies
INTRODUCTION
Greenhouse effect caused by carbon dioxide emissions has become the focus of global attention.Asthe development of low-carbon economy， reducing global carbon emissions is animportantstrategyto preventclimate from warming.Today， carbon emission has become a major survival and developmentthreat toglobal enterprise thatcan not be ignored.At present， the world has entered a critical period of energy saving and emission reduction： The chinesegovermment has solemnly promised to the international organizationthatcarbon dioxide emissions brought by per unit of GDP will be reducedby40%-45% in 2020than in 2005.
Different carbon emission policies，includingmandatory carbon emissions capacity， carbon emissions tax and cap-and-trade have become the key factors in effecting manufacture's pricing and retailer’s Ordering. In 2009， Wal-Mart proposed the “low carbon supermarket”in the “World Low Carbon and ecologicaleconomy Conference.” Wal-Mart has developed a variety of methods， such as energy saving and green products， reducingwaste，and improvingsupply chain's efficiency.
2. LITERATURE REVIEW
In recent years， as serious global environmental problemsare increasing， many scholars have researchedoncarbon emissions issues.Most of the present researches focused on the macroscopic level. Benjaafar， Li and Daskin（2013）study aboutlow-carbon supply chain undermandatory carbon emissions capacity policy， cap-and-trade and carbon offsets， the vendordecidingthe productionand when toreplenish in multiple cycles. （Du， Ma， Fu， Zhu，&Zhang， 2011）When considering emissions trading， constructs a supplier and rely on non-profit organization of green environmental protection as a carbon emissions rights of enterprises to form a new type of supply chain， based on the newsboy model research on Stackbergof the game process. （Lin， Anderson， and Cruz， 2012）Production and sales of environmentally friendly products the important benefit from an increase in demand from the consumer environmental awareness， environmental protection manufacturers marketing methods should be taken to guide the consumer to increase environmental protection meaning， motivate the green consumers into a green consumer. （Vipuland Sridhar， 2000） Considering the risk factors， we usethe newsvendor model under uncertain demand to get the optimal purchase quantity and price decision， in order to achievemaximum expected utility.Song and Leng（2012）found the firm’s optimal production and corresponding expected profit under different carbon emissions policies. 3. MODEL DESCRIPTIONS AND ASSUMPTION
This paper considers a two-stage supply chain which is composed of a manufacturer and a retailer， manufacturer dominating. In this supply chain， we study how the manufacturer prices the products and how much the retailer ordersgoods. Weassumes that the manufacturer is independent ofthe retailer，and their information issymmetrical， their risks are neutral.The cost of each product is〖 C〗_s， the retailer faces a stochastic market demandx， and the priceP is an exogenous variable.If the productionQ exceeds the demand， the remaining products will be sold at a price ofV. On the contrary， if the demand exceeds the production， the manufacturer will pay C_μas ‘shortage cost’， P>C_s>V>C_μ.
Under Policy 1-mandatory carbon emissionscapacity （a mandatorycapacity on the amount of carbon emitted by each firm）， the carbon quotaisA， each product produces e unit carbon emissions， Q_0means the mandatory capacity of the production that results incarbonemissions，〖 Q〗_0=A/e.Under Policy 2-carbon emissions tax （tax imposed to each firm on theamount of carbon emissions），the carbon emissions tax foreach product is t. Under Policy 3-cap-and-trade policy， the trading price of unit carbon emissionisi.
This paper analyzes and discusses the influence of different carbon policy on manufacturer’spricing and retailer’s ordering.
4. MODELFORMULATIONS
4.1Retailer’ Sorderingstrategy
The retailer faces a stochastic market demand， the quantity of order is made according to the wholesale priceW.For the retailer， no matter which policy the government adopts， the ordering decisionis based on the wholesale price. Without carbon policy， letthe optimal wholesale prices W^*， the optimal order quantity is Q_r^*.Under different policy， the optimal wholesale price is W_c^*、W_t^*、W_rc^*， and the optimal order quantity is Q_c^*、Q_t^*、Q_rc^*，respectively.
Under the stochastic demand， the manufacturer’s profit is as formula （1）：
π_r={█（Px+（Q-x）V-QW， x≤Q@PQ-QW-（x-Q） C_μ，x>Q）┤，（1）
Then we can get the retailer’s profit as formula （2）：
E（π_r ）=（P-W+C_μ ）-（P-V+C_μ ） ∫_0^Q?〖F（x）dx-μC_μ 〗，（2）
Due to the manufacturer dominates，the retailer’s decision is the optimal order quantity Q_r^*according to the manufacturer's wholesale price. According to formula （2）， we can get that （?^2 E（π_r ））/（?Q）^2 <0，so E（π_r ） is a strictly concave function. If we set ?E（π_r ）/?Q=0，we can get the optimal order quantity Q_r^* as formula （3）： Q_r^*=F^（-1） （（P-W+C_μ）/（P-V+C_μ ）），（3）
Thetailer’s wholesale price varies according to the type of carbon policy， so under different carbon policies， the retailer’s order quantity varies， too.
4.2Manufacturer’s Wholesale Price Strategy
4.2.1Manufacturer’s Wholesale Price Strategy Without Carbon Policy
The information of the manufacturer and the retailer is symmetrical， as the dominant party， the manufacturercan predict the retailer's ordering strategy to determine the optimal wholesale price， so the profit of the manufacturer is as formula （4）：
π_m （Q_r^* ）=（W-C_s ） Q_r^*，（4）
According to formula （3） and （4）， we can get the manufacturer’s expected profit as formula （5）：
E（π_m ）=（W-C_s ） F^（-1） （（P-W+C_μ）/（P-V+C_μ ）） ，（5）
And the optimal wholesale price W^* meet formula （6）：
〖W^*=Q〗_r^* （P-V+C_μ ）f（F（Q_r^* ） ）+C_s，（6）
According to formula （3） and （4）， we can get the retailer’s optimal order quantity as formula （7）：
Q_r^*=F^（-1） （（P-W^*+C_μ）/（P-V+C_μ ）），（7）
4.2.2 Manufacturer’s Wholesale Price Strategy Under Carbon Policy
Under different carbon policies， the manufacturer’s wholesale price strategies differ from each other. Now let us discuss manufacturer’s wholesale price strategy under each carbon policy respectively.
4.2.3 Manufacturer's wholesale price strategy under Policy 1- mandatory carbon emissions capacity
Under Policy 1- mandatory carbon emissions capacity， the profit of the manufacturer is as formula （8）：
〖E（π_m ）〗_c=（W_c-C_s ） Q_c^*，（8）
According to formula （3） and （8）， the profit of the retailer is as formula （9）：
{█（〖E（π_m ）〗_c=（W_c-C_s ） F^（-1） （（P-W_c+C_μ）/（P-V+C_μ ））@s.t. Q_c^*=F^（-1） （（P-W_c+C_μ）/（P-V+C_μ ））≤Q_0 ）┤，（9）
According to formula （9）， we can get the following conclusion：
1）IfW_c2， the optimal wholesale price is W_c1=P+C_μ-F（Q_0 ）（P-V+C_μ ）.
2）If Q_0≥Q_c^*， W_c2≥W_c1， the optimal wholesale price meet the equationW_c2= Q_r^* （P-V+C_μ ）f（F（Q_r^* ） ）+C_s.
Proposition1：Under mandatory carbon emissions capacity， when the manufacturer’s carbon emissions less than the carbon quota A， the policy has nothing to do with the optimal wholesale price and profit of the manufacturer. On the contrary， the manufacturer's optimal wholesale price will be increased andthe manufacturer'sprofit will decrease. The retailers' profit is a monotone increasing function of the orderquantity，it will decrease with the decrease oforder quantity. Proof：
① When the carbon emissions emit from the manufacturer's optimal production less than the carbon quota A，〖 Q〗_0≥Q_r^*， then Q_c^*=Q_r^*， and the optimal wholesale is W_c2= Q_r^* （P-V+C_μ ）f（F（Q_r^* ） ）+C_s=W^*， 〖E（π_m ）〗_c=E（π_m ）.
②When the carbon emissions emit from the manufacturer's optimal production more than the carbon quota A，〖 W〗_c1=P+C_μ-F（Q_0 ）（P-V+C_μ ）. What is more， F（Q_0 ） is a monotone increasing function of Q_0， Q_0P+C_μ-F（Q_r^* ）（P-V+C_μ ）. That is， the optimal wholesale price will increase.
The unconditional maximum value must be greater than or equal to the maximum value under certain conditions， so when the carbon quota less than the carbon emissions produced by the optimal production， the manufacturer’s profit will decrease.From the formula （2） we can know that d（E（π_r ） ）/dQ>0， so the retailer’s profitE（π_r ） is a monotone increasing function of the order quantityQ. It will decrease with the decrease of order quantity.
End.
4.2. 3 Manufacturer's Wholesale Price Strategy Under Policy 2- Carbonemissions Tax Policy
Under carbon emissions tax policy， the manufacturer’s profit is as formula（10）：
π_m （Q_t^* ）=（W_t-C_s-t） Q_t^*.（10）
From formula （3） and （10），we can get：
π_m （Q_t^* ）=（W_t-C_s-t） F^（-1） （（P-W_t+C_μ）/（P-V+C_μ ））.（11）
From formula （11）， we can know that the manufacturer can make out the optimal wholesale price 〖W_t〗^*， and it meet the formula（12）：
〖W_t〗^*=Q_t^* （P-V+C_μ ）f（F（Q_t^* ） ）+C_s+t.（12）
According to formula （11） and （12）， the optimal order quantity can be concluded as formula （13） ：
Q_t^*=F^（-1） （（P-〖W_t〗^*+C_μ）/（P-V+C_μ ））.（13）
Proposition 2： Under carbon emissions tax policy， the wholesale price will increase， the order quantity will decrease， the profit of the manufacturer and the retailer will decrease.
Proof：Under carbon emissions tax policy， the existence of carbon tax is equivalent totheaddition of the cost of production， so the retailer’s optimal order quantity will drop， which means Q_t^*W〗^*.Comparing the manufacturer’s profit under carbon emissions tax policy with that without carbon policy， we can find：
π_m （Q_t^* ）-E（π_m ）=（P-C_s+C_μ ）（Q_t^*-Q_r^* ）-tQ_t^*- （P-V+C_μ ）[F（Q_t^* ） Q_t^*-F（Q_r^* ） Q_r^* ]， where （P-C_s+C_μ ）>0， Q_t^* Then it can be easily found that π_m （Q_t^* ）-E（π_m ）<0， which means the manufacturer’sprofit will drop down under carbon emissions tax.
As proposition 1， the retailers' profit is a monotone increasing function of the order quantity， so under carbon emissions tax policy， Q_t^* End.
4.2.4 Manufacturer's wholesale price strategy under Policy 3- cap-and-trade
Under cap-and-trade policy， if the carbon quota A is equal or greater than〖 Q〗_r^*， the policy will have nothing to do with the carbon emissions. So the necessary condition that the policy works is Q_0=A/e The manufacturer’s profit can be expressed as formula （14）：
π_m （Q_i ）=（W_rc-C_s ） Q_i-i（Q_i-Q_0 ）.（14）
According to formula （3） and （14）， it can be found that
π_m （Q_i ）=（W_rc-C_s-i） F^（-1） （（P-W_rc+C_μ）/（P-V+C_μ ））+〖iQ〗_0.
Then the optimal wholesale price 〖W_rc〗^*can be concluded as formula （15）：
〖W_rc〗^*=Q_i^* （P-V+C_μ ）f（F（Q_i^* ） ）+C_s+i.（15）
From formula （3） and （15）， the optimal order quantity is as formula （16）：
Q_i=F^（-1） （（P-〖W_i〗^*+C_μ）/（P-V+C_μ ））.（16）
Proposition 3： Under cap-and-trade policy， the wholesale price will rise， the production and order quantity will decrease， and the retailer’s profit will decrease too.
Proof： Under cap-and-trade policy， the manufacturer will buy more carbon emissions permits from carbon emissions market. That is equivalent to the increase of each commodity’s cost. So the optimal order quantity and the production will decrease.
According to formula （15）， the wholesale price is an inverse function of the order quantity， so the wholesale price will rise.
As proposition 1， retailer’s profit is a monotone increasing function of the order quantity， and Q_i End.
Proposition 4： Under cap-and-trade policy， the manufacturer’s profit is decided by the carbon quota A. Let A_0=（e（W^*-C_s ） Q_r^*-e（〖W_rc〗^*-C_s ） Q_i）/i+〖eQ〗_i， if A>A_0 ， the manufacturer’s profit will increase， if A Proof： According to formula （4） and （14）， π_m （Q_i ）=（〖W_rc〗^*-C_s ） Q_i-i（Q_i-A/e）， π_m （Q_r^* ）=（W-C_s ） Q_r^*. When π_m （Q_i ）=π_m （Q_r^* ）， A=（e（W^*-C_s ） Q_r^*-e（W_rc-C_s ） Q_i）/i+〖eQ〗_i.
So if A>A_0， π_m （Q_i ）>π_m （Q_r^* ）， the manufacturer’s profit will increase， if A CONCLUSIONS AND FUTURE RESEARCH
In this paper， we studied the manufacturer’spricingstrategyand retailer’sordering strategy whenconsidering mandatory carbon emissions capacity policy， carbon emissions tax policyandcap-and-trade policyrespectively，based on the classic newsvendor mode， with the two-stage supply chain of one manufacturerand one retailer （manufacturerdominates）as the object.Comparing with the situation without carbon emissionspolicy， it could be concluded as follows：（1）Under mandatory carbon emissions capacity policy， when the limit production （the production according to the carbon quota）ismorethan the optimal production， the manufacturer'swholesale price，the retailer'sorderingquantityand their profitswill not be affected. The retailer’sordering quantitydependson thewholesale price. On the contrary， when the limit production isless than the optimal production， the manufacturer’swholesale pricewill be increased， the retailer’s ordering quantity will bedecreased， and each member's profitwilldecline. The manufacturer'swholesaleand profit depend on thecarbon quota.（2）Under carbon emissions tax policy， the manufacturer's wholesale price will be increased， the retailer'sorderingquantity will bedecreased， and their profits will decline， the retailer's ordering quantitydependssonthe carbon emissions tax. （3） Under cap-and-trade policy，the retailer’s orderingquantityand profit will bedecreased， andthe manufacturer's wholesale price will beincreased.The manufacturer'sprofitdependson the carbon quota and the carbon emission's price. The retailer’s ordering quantitydependson the sale price of carbon emissions.
Underthree different carbon emissions policies， the manufacturer’s pricing strategyand the retailer’s ordering strategyaredifferent.From the perspective of supply chain， the research on the strategies of each node company of thesupply chainunder different carbon emissions policiesbuilt a micro-foundationfor thedesign and formulation ofcarbon emissions policies. By studding thecompanies’ strategies，carbon policies’sscientificityand effectiveness was validated， and achieved “win-win”.In the future， it will be ofgreate significance to studyfrom the perspectiveof multiple retailers and multiple manufacturers. REFERENCES
Benjaafar， S.， Li， Y.， &Daskin， M. （2013）.Carbon footprint and the management of supply chains： Insights from simple models.IEEE Transactions on Automation Science and Engineering， 10（1），99-116.
Du， S.， Ma F.， Fu Z.， Zhu L.， &Zhang J.（2011）. Game-theoretic Analysis for An Emission-dependent Supply Chain in a ‘cap-and-trade’ System. Annals of Operations Research， DOI： 10.1007/s10479-011-0964-6
Lin， Z.G.， Anderson， T. D.， &Cruz， J. M. （2012）. Consumer environmental awareness and competiton in two-stage supply chains. European Journal of Operations Research，218（3），602-613.
Song， J.，&Leng， M.（2012）. Analysis of the single-period problem under carbon emissions policies， Handbook of Newsvendor Problems：International Series in Operations Research & Management Science. Springer， New York， 297-313.
Vipul， A.， &Sridha，r S. （2000）.Impact of uncertainty and risk aversion on price and order quantity in the nessvendor problem.Manufaturing& Service Operations Management， 2（4）， 410-423.
The implementation of carbon reduction policy is an important method for the firms to reduce carbon emissions.So it is of great significance to research on the firms’strategies under different carbon reduction policies.In this paper，we study the manufacturer’s wholesale price strategy and the retailer’s ordering strategy， as well as carbon emissions policy’s impact on the production and profit， under mandatory carbon emissions capacity policy， carbon emissions tax policy and cap-and-trade policy respectively.In addition， the government’s decision-making about carbon emissions policy parameters is also discussed.The conclusion builds a microeconomic foundationfor the carbon emissions policy’sdesign and development， and also verified the policy’seffectivenessand scientificity， at last achieved the “win-win”ofthe government and enterprises.
Key word：Pricing；Ordering；Carbon emission policies
INTRODUCTION
Greenhouse effect caused by carbon dioxide emissions has become the focus of global attention.Asthe development of low-carbon economy， reducing global carbon emissions is animportantstrategyto preventclimate from warming.Today， carbon emission has become a major survival and developmentthreat toglobal enterprise thatcan not be ignored.At present， the world has entered a critical period of energy saving and emission reduction： The chinesegovermment has solemnly promised to the international organizationthatcarbon dioxide emissions brought by per unit of GDP will be reducedby40%-45% in 2020than in 2005.
Different carbon emission policies，includingmandatory carbon emissions capacity， carbon emissions tax and cap-and-trade have become the key factors in effecting manufacture's pricing and retailer’s Ordering. In 2009， Wal-Mart proposed the “low carbon supermarket”in the “World Low Carbon and ecologicaleconomy Conference.” Wal-Mart has developed a variety of methods， such as energy saving and green products， reducingwaste，and improvingsupply chain's efficiency.
2. LITERATURE REVIEW
In recent years， as serious global environmental problemsare increasing， many scholars have researchedoncarbon emissions issues.Most of the present researches focused on the macroscopic level. Benjaafar， Li and Daskin（2013）study aboutlow-carbon supply chain undermandatory carbon emissions capacity policy， cap-and-trade and carbon offsets， the vendordecidingthe productionand when toreplenish in multiple cycles. （Du， Ma， Fu， Zhu，&Zhang， 2011）When considering emissions trading， constructs a supplier and rely on non-profit organization of green environmental protection as a carbon emissions rights of enterprises to form a new type of supply chain， based on the newsboy model research on Stackbergof the game process. （Lin， Anderson， and Cruz， 2012）Production and sales of environmentally friendly products the important benefit from an increase in demand from the consumer environmental awareness， environmental protection manufacturers marketing methods should be taken to guide the consumer to increase environmental protection meaning， motivate the green consumers into a green consumer. （Vipuland Sridhar， 2000） Considering the risk factors， we usethe newsvendor model under uncertain demand to get the optimal purchase quantity and price decision， in order to achievemaximum expected utility.Song and Leng（2012）found the firm’s optimal production and corresponding expected profit under different carbon emissions policies. 3. MODEL DESCRIPTIONS AND ASSUMPTION
This paper considers a two-stage supply chain which is composed of a manufacturer and a retailer， manufacturer dominating. In this supply chain， we study how the manufacturer prices the products and how much the retailer ordersgoods. Weassumes that the manufacturer is independent ofthe retailer，and their information issymmetrical， their risks are neutral.The cost of each product is〖 C〗_s， the retailer faces a stochastic market demandx， and the priceP is an exogenous variable.If the productionQ exceeds the demand， the remaining products will be sold at a price ofV. On the contrary， if the demand exceeds the production， the manufacturer will pay C_μas ‘shortage cost’， P>C_s>V>C_μ.
Under Policy 1-mandatory carbon emissionscapacity （a mandatorycapacity on the amount of carbon emitted by each firm）， the carbon quotaisA， each product produces e unit carbon emissions， Q_0means the mandatory capacity of the production that results incarbonemissions，〖 Q〗_0=A/e.Under Policy 2-carbon emissions tax （tax imposed to each firm on theamount of carbon emissions），the carbon emissions tax foreach product is t. Under Policy 3-cap-and-trade policy， the trading price of unit carbon emissionisi.
This paper analyzes and discusses the influence of different carbon policy on manufacturer’spricing and retailer’s ordering.
4. MODELFORMULATIONS
4.1Retailer’ Sorderingstrategy
The retailer faces a stochastic market demand， the quantity of order is made according to the wholesale priceW.For the retailer， no matter which policy the government adopts， the ordering decisionis based on the wholesale price. Without carbon policy， letthe optimal wholesale prices W^*， the optimal order quantity is Q_r^*.Under different policy， the optimal wholesale price is W_c^*、W_t^*、W_rc^*， and the optimal order quantity is Q_c^*、Q_t^*、Q_rc^*，respectively.
Under the stochastic demand， the manufacturer’s profit is as formula （1）：
π_r={█（Px+（Q-x）V-QW， x≤Q@PQ-QW-（x-Q） C_μ，x>Q）┤，（1）
Then we can get the retailer’s profit as formula （2）：
E（π_r ）=（P-W+C_μ ）-（P-V+C_μ ） ∫_0^Q?〖F（x）dx-μC_μ 〗，（2）
Due to the manufacturer dominates，the retailer’s decision is the optimal order quantity Q_r^*according to the manufacturer's wholesale price. According to formula （2）， we can get that （?^2 E（π_r ））/（?Q）^2 <0，so E（π_r ） is a strictly concave function. If we set ?E（π_r ）/?Q=0，we can get the optimal order quantity Q_r^* as formula （3）： Q_r^*=F^（-1） （（P-W+C_μ）/（P-V+C_μ ）），（3）
Thetailer’s wholesale price varies according to the type of carbon policy， so under different carbon policies， the retailer’s order quantity varies， too.
4.2Manufacturer’s Wholesale Price Strategy
4.2.1Manufacturer’s Wholesale Price Strategy Without Carbon Policy
The information of the manufacturer and the retailer is symmetrical， as the dominant party， the manufacturercan predict the retailer's ordering strategy to determine the optimal wholesale price， so the profit of the manufacturer is as formula （4）：
π_m （Q_r^* ）=（W-C_s ） Q_r^*，（4）
According to formula （3） and （4）， we can get the manufacturer’s expected profit as formula （5）：
E（π_m ）=（W-C_s ） F^（-1） （（P-W+C_μ）/（P-V+C_μ ）） ，（5）
And the optimal wholesale price W^* meet formula （6）：
〖W^*=Q〗_r^* （P-V+C_μ ）f（F（Q_r^* ） ）+C_s，（6）
According to formula （3） and （4）， we can get the retailer’s optimal order quantity as formula （7）：
Q_r^*=F^（-1） （（P-W^*+C_μ）/（P-V+C_μ ）），（7）
4.2.2 Manufacturer’s Wholesale Price Strategy Under Carbon Policy
Under different carbon policies， the manufacturer’s wholesale price strategies differ from each other. Now let us discuss manufacturer’s wholesale price strategy under each carbon policy respectively.
4.2.3 Manufacturer's wholesale price strategy under Policy 1- mandatory carbon emissions capacity
Under Policy 1- mandatory carbon emissions capacity， the profit of the manufacturer is as formula （8）：
〖E（π_m ）〗_c=（W_c-C_s ） Q_c^*，（8）
According to formula （3） and （8）， the profit of the retailer is as formula （9）：
{█（〖E（π_m ）〗_c=（W_c-C_s ） F^（-1） （（P-W_c+C_μ）/（P-V+C_μ ））@s.t. Q_c^*=F^（-1） （（P-W_c+C_μ）/（P-V+C_μ ））≤Q_0 ）┤，（9）
According to formula （9）， we can get the following conclusion：
1）If
2）If Q_0≥Q_c^*， W_c2≥W_c1， the optimal wholesale price meet the equationW_c2= Q_r^* （P-V+C_μ ）f（F（Q_r^* ） ）+C_s.
Proposition1：Under mandatory carbon emissions capacity， when the manufacturer’s carbon emissions less than the carbon quota A， the policy has nothing to do with the optimal wholesale price and profit of the manufacturer. On the contrary， the manufacturer's optimal wholesale price will be increased andthe manufacturer'sprofit will decrease. The retailers' profit is a monotone increasing function of the orderquantity，it will decrease with the decrease oforder quantity. Proof：
① When the carbon emissions emit from the manufacturer's optimal production less than the carbon quota A，〖 Q〗_0≥Q_r^*， then Q_c^*=Q_r^*， and the optimal wholesale is W_c2= Q_r^* （P-V+C_μ ）f（F（Q_r^* ） ）+C_s=W^*， 〖E（π_m ）〗_c=E（π_m ）.
②When the carbon emissions emit from the manufacturer's optimal production more than the carbon quota A，〖 W〗_c1=P+C_μ-F（Q_0 ）（P-V+C_μ ）. What is more， F（Q_0 ） is a monotone increasing function of Q_0， Q_0
The unconditional maximum value must be greater than or equal to the maximum value under certain conditions， so when the carbon quota less than the carbon emissions produced by the optimal production， the manufacturer’s profit will decrease.From the formula （2） we can know that d（E（π_r ） ）/dQ>0， so the retailer’s profitE（π_r ） is a monotone increasing function of the order quantityQ. It will decrease with the decrease of order quantity.
End.
4.2. 3 Manufacturer's Wholesale Price Strategy Under Policy 2- Carbonemissions Tax Policy
Under carbon emissions tax policy， the manufacturer’s profit is as formula（10）：
π_m （Q_t^* ）=（W_t-C_s-t） Q_t^*.（10）
From formula （3） and （10），we can get：
π_m （Q_t^* ）=（W_t-C_s-t） F^（-1） （（P-W_t+C_μ）/（P-V+C_μ ））.（11）
From formula （11）， we can know that the manufacturer can make out the optimal wholesale price 〖W_t〗^*， and it meet the formula（12）：
〖W_t〗^*=Q_t^* （P-V+C_μ ）f（F（Q_t^* ） ）+C_s+t.（12）
According to formula （11） and （12）， the optimal order quantity can be concluded as formula （13） ：
Q_t^*=F^（-1） （（P-〖W_t〗^*+C_μ）/（P-V+C_μ ））.（13）
Proposition 2： Under carbon emissions tax policy， the wholesale price will increase， the order quantity will decrease， the profit of the manufacturer and the retailer will decrease.
Proof：Under carbon emissions tax policy， the existence of carbon tax is equivalent totheaddition of the cost of production， so the retailer’s optimal order quantity will drop， which means Q_t^*
π_m （Q_t^* ）-E（π_m ）=（P-C_s+C_μ ）（Q_t^*-Q_r^* ）-tQ_t^*- （P-V+C_μ ）[F（Q_t^* ） Q_t^*-F（Q_r^* ） Q_r^* ]， where （P-C_s+C_μ ）>0， Q_t^*
As proposition 1， the retailers' profit is a monotone increasing function of the order quantity， so under carbon emissions tax policy， Q_t^*
4.2.4 Manufacturer's wholesale price strategy under Policy 3- cap-and-trade
Under cap-and-trade policy， if the carbon quota A is equal or greater than〖 Q〗_r^*， the policy will have nothing to do with the carbon emissions. So the necessary condition that the policy works is Q_0=A/e
π_m （Q_i ）=（W_rc-C_s ） Q_i-i（Q_i-Q_0 ）.（14）
According to formula （3） and （14）， it can be found that
π_m （Q_i ）=（W_rc-C_s-i） F^（-1） （（P-W_rc+C_μ）/（P-V+C_μ ））+〖iQ〗_0.
Then the optimal wholesale price 〖W_rc〗^*can be concluded as formula （15）：
〖W_rc〗^*=Q_i^* （P-V+C_μ ）f（F（Q_i^* ） ）+C_s+i.（15）
From formula （3） and （15）， the optimal order quantity is as formula （16）：
Q_i=F^（-1） （（P-〖W_i〗^*+C_μ）/（P-V+C_μ ））.（16）
Proposition 3： Under cap-and-trade policy， the wholesale price will rise， the production and order quantity will decrease， and the retailer’s profit will decrease too.
Proof： Under cap-and-trade policy， the manufacturer will buy more carbon emissions permits from carbon emissions market. That is equivalent to the increase of each commodity’s cost. So the optimal order quantity and the production will decrease.
According to formula （15）， the wholesale price is an inverse function of the order quantity， so the wholesale price will rise.
As proposition 1， retailer’s profit is a monotone increasing function of the order quantity， and Q_i
Proposition 4： Under cap-and-trade policy， the manufacturer’s profit is decided by the carbon quota A. Let A_0=（e（W^*-C_s ） Q_r^*-e（〖W_rc〗^*-C_s ） Q_i）/i+〖eQ〗_i， if A>A_0 ， the manufacturer’s profit will increase， if A
In this paper， we studied the manufacturer’spricingstrategyand retailer’sordering strategy whenconsidering mandatory carbon emissions capacity policy， carbon emissions tax policyandcap-and-trade policyrespectively，based on the classic newsvendor mode， with the two-stage supply chain of one manufacturerand one retailer （manufacturerdominates）as the object.Comparing with the situation without carbon emissionspolicy， it could be concluded as follows：（1）Under mandatory carbon emissions capacity policy， when the limit production （the production according to the carbon quota）ismorethan the optimal production， the manufacturer'swholesale price，the retailer'sorderingquantityand their profitswill not be affected. The retailer’sordering quantitydependson thewholesale price. On the contrary， when the limit production isless than the optimal production， the manufacturer’swholesale pricewill be increased， the retailer’s ordering quantity will bedecreased， and each member's profitwilldecline. The manufacturer'swholesaleand profit depend on thecarbon quota.（2）Under carbon emissions tax policy， the manufacturer's wholesale price will be increased， the retailer'sorderingquantity will bedecreased， and their profits will decline， the retailer's ordering quantitydependssonthe carbon emissions tax. （3） Under cap-and-trade policy，the retailer’s orderingquantityand profit will bedecreased， andthe manufacturer's wholesale price will beincreased.The manufacturer'sprofitdependson the carbon quota and the carbon emission's price. The retailer’s ordering quantitydependson the sale price of carbon emissions.
Underthree different carbon emissions policies， the manufacturer’s pricing strategyand the retailer’s ordering strategyaredifferent.From the perspective of supply chain， the research on the strategies of each node company of thesupply chainunder different carbon emissions policiesbuilt a micro-foundationfor thedesign and formulation ofcarbon emissions policies. By studding thecompanies’ strategies，carbon policies’sscientificityand effectiveness was validated， and achieved “win-win”.In the future， it will be ofgreate significance to studyfrom the perspectiveof multiple retailers and multiple manufacturers. REFERENCES
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