Supply Chain Pricing Decisions under Corporation Social Responsibility

The multiple push from the government, the public and non-governmental organizations has increased CSR awareness and makes CSR behavior of cooperators an issue. Considering the impact of sales efforts on demand, making the supply chain which dominated and undertakes the sales effort by retailers as the research object, This paper compares three models of the node enterprise pricing decisions in three CSR commitment models, studies the impact of CSR participation and sales efforts on member profits and social welfare. The study found that the three models can improve social welfare, sales efforts can reduce prices and increase sales; There is a big profit gap and different pricing strategies between M mode and R mode; The social welfare is the large st under MR model, However, there is a threshold for CSR engagement in this model, the supply chain profit shows a downward trend beyond the threshold. Keywords— Corporate social responsibility (CRS), supply chain, pricing decisions, Stackelberg game, sales efforts.

is affected by the price and the retailer's sales efforts.
represent market demand, who lesale price, retailer's profit per unit product, selling price, and retailer's sales effo rt, respectively.
Assumed that the seller's cost of selling effort is

The case of R taking on CSR(R model)
According to the definition of social welfare in economics: social welfare is equal to the sum of retailer surplus (retailer profit) and consumer surplus, Consumer surplus is the difference between the actual market price and the maximu m price of which consumers are willing to pay for a product. In this case, the profit function of manufacturer and retailer is respectively: In which, 0 1 r  refers to the degree of social responsibility, The larger r is, the greater the degree of social responsibility it takes.
In R mode, the solution result is shown in equation (2)： is negatively correlated with r. Proof: Equation 3 shows that: Under R's social responsibility, R stimulates consumer demand and expands product demand by lowering selling price and improving sales efforts . In R mode, the manufacturers is in a subordinate position，meanwhile it is not constrained by the sense of social responsibility. Therefore, when the market demand expands, the manufacturer will increase the wholesale price without restriction in order to maximize its own profit. The imp lementation of a series of measures, such as raising the wholesale price, reducing the cost of sales efforts and lowering the selling price, will great ly reduce t he unit product profit of retailers. Theorem 2： , , , is positively related to r, R r  is negatively correlated with r; Proof: Equation 4 shows that: With the increasing awareness of social responsibility of leading retailers, the price reduction and sales efforts of retailers not only provide social welfare, but also imp rove the overall profit of all members of the system. Altho ugh the retailer sacrifices some of its own pure profits, all members benefit fro m it, which is in line with the lead ing party with a sense of social responsibility to pay attention to its stakeholders. Furthermo re, the stronger the retailer's awareness of social responsibility, the more obvious the improvement of the stakeholders' and the system's overall profit.

The case of M taking on CSR(M model)
In this case, the profit function of manufacturer and retailer is respectively: The game process is as follows: Firstly, R determines the degree of sales effort, then M determines the wholesale price, and the solution is: Equation 7 shows that: Under the social responsibility of M, manufacturers will lower the wholesale price and retailers will increase their sales efforts, so as to increase the sales volume of supply chain products. For dominant retailers, without the constraint of social responsibility, R will not reduce the profit per unit product, but increase the net profit per unit prod uct due to Equation8 shows that: With the increasing social responsibility of manufacturers, the sales efforts of retailers can imp rove social welfare, retailers' profits and the overall profit o f the supply chain. However, for the manufacturer itself, when the degree of social responsibility is small, it is beneficial to its net profit. However, when the coefficient of social responsibility excee ds 0.5, some of its profit will suffer, which will greatly reduce the manufacturer's enthusiasm to assume social responsibility.

The case of MR taking on CSR(MR model)
Under shared social responsibility and centralized pricing: Theorem 5 shows that: In the M R model, the retailer will reduce the profit of per unit product and increase the level of sales efforts, and the manufacturer will reduce the wholesale price. That is, Concessions fro m both will be great ly reduced and the sales volume of the product will be increased.
In the MR model, When the social welfare is the largest and the overall profit of the supply chain is the best, the CSR threshold is 2/3. With the enhancement of social responsibility, CSR behaviors of members will sacrifice part of their own interests to maximize social welfare.

pattern comparison and analysis
Theorem 7： , , , , w Theorem 7 shows that: Under the three modes, In the MR model, the selling price is the lowest, the sales effort is the strongest and the product sales volume is the largest. This is because manufacturers and retailers at the same time make profits to consumers in the MR model,, that is, M reduces the wholesale price and R reduces the profit per unit product, which makes the selling price of products drop sharply and the sales volume rise rapidly.

International Journal of Advanced Engineering, Management and Science (IJAEMS)
[ has higher profit and greater social welfare, but M has lower profit.

IV. SIMULATION ANALYSIS
Assuming 500 5 2 q p e    ， 3   ，the simulation results in the three models are shown in the table: It can be seen from Table 1 that: (1) the co mmon ground of the three models is that with the increase of CSR degree of members, the selling price o f products decreases, R's sales efforts increase, and product sales volume increases greatly. In M R mode, the selling price is the lowest, R has the strongest sales effort and the sales volume is the largest. In the R model, with the increase of R's participation in CSR, social welfare, manufacturer profit and supply chain all increase, but the profits of retailer decrease. When the retailer's level of responsibility is relat ively small, the retailer's profit is higher than the manufacturer's. When CSR exceeds the threshold, retailers' pro fits are lower than manufacturers'.
3) In the MR model, as MR's involvement in CSR increases, social welfare increases, while supply chain profit decreases. In a word, with the increase of CSR, the social welfare of three modes all increases, d the net profit of the underwriters declines.
This proves theorems 1, 3, 5, 7. (1) the co rrelation between the p rofit of each member, social welfare and the degree of social responsibility r, which verifies the correctness of conclusions 2, 4 and 6; (2) For M profit, SC profit and social welfare, R mode is better than M mode, wh ile for R profit, M mode is better.
These verify the correctness of conclusion 8; (3)Fro m the perspective of supply chain profit, when members participate less in CSR, the MR mode is better, and when the participation degree of social responsibility exceeds the threshold, the M mode is the best, which verifies the correctness of conclusion 8.

V. CONCLUSION
This paper takes the supply chain dominated by retailers and considering sales efforts as the research object, analyzes and studies the pricing decisions of various responsible parties and CSR members under the participation degree of CSR, and discusses the influence of R's sales efforts and CSR behaviors on the supply chain.
The following conclusions are drawn: (1) In all three cases, the retailer's sales efforts reduce prices and increase the sales volume. The mo re CSR is involved, the influence of retailers' sales efforts on selling price and sales volume is more significant.
(2) In all three cases, the participation of CSR bearers is greater, social welfare is higher, but bear's profits has downward trend.
(3) CSR model and CSR part icipation level are closely related to supply chain pricing decisions.
This paper only discusses the influence of different CSR models on the profit of supply chain members and social welfare under the R leading and considering the sales efforts, and considers the production or sales cost, government guidance and other factors, wh ich is the next research direction.