Green Supply Chain Decisions with Corporate Social Responsibility in Mind under Government Subsidies

: Taking a green supply chain consisting of a green product manufacturer and a dominant retailer as the research object, three different government subsidy scenarios are proposed in the case of retailer social responsibility and manufacturer social responsibility, namely, manufacturer subsidy, retailer subsidy and consumer subsidy. and then discuss the influence of government subsidies on supply chain decision making and corporate social responsibility under different circumstances.


Introduction
At the same time of the rapid development of the world economy, the problems of environmental pollution and resource scarcity have become increasingly prominent. Therefore, the green and sustainable development has aroused more and more people's attention. In this context, more and more enterprises are realizing that if they want to enhance their market competitiveness, they must carry out green technology innovation, while taking into account their consumer, environmental and social responsibilities. The government also vigorously supports the development of green industry and has introduced many subsidy strategies. Therefore, it is of great significance to study the subsidy strategy of green supply chain. In recent years, the issue of green supply chain has aroused a lot of scholars' extensive research, and a lot of achievements have been made in the issues related to corporate social responsibility. Yue H et al. [1]studied the social responsibility behavior of lithium-ion battery enterprises and verified that the total profit of closed-loop supply chain would increase in the presence of corporate social responsibility. LI et al. [2]respectively constructed a two-stage closed-loop supply chain model under centralized and decentralized decision-making in which manufacturers and retailers bear social responsibilities separately. It is found that social welfare is greater when manufacturers and retailers jointly fulfill social responsibilities. In terms of government subsidy strategy, many scholars have also done in-depth research. HAN et al. [3]made a comparative analysis of the influence of retailers' fairness concerns on supply chain decision-making under two conditions: no government subsidies and government subsidies. It is found that government subsidies are beneficial to increase supply chain profits and have a coordinating effect on the influence of retailers' equity concerns on product pricing and greenness decisions. Jian X A et al. [4]investigated the pricing of governmentsubsidized green products and the optimal strategy of green investment. The study showed that the government's subsidy behavior to manufacturers could motivate manufacturers to invest in a higher level of green technology. To sum up, only a few scholars have studied both corporate social responsibility and government subsidies. In addition, most of these studies consider situations where manufacturers dominate the supply chain. Based on this, this paper constructs a single channel green supply chain consisting of a green product manufacturer and a dominant retailer on the basis of the existing literature. Considering the situation of retailers fulfilling their social responsibilities, this paper explores the influence of government subsidies on the level of retailers' social responsibilities and supply chain decisions.

Problem description and model hypothesis 2.1 Problem description
This paper is based on the green supply chain consisting of a single manufacturer and retailer, manufacturer and retailer Stackelberg game, retailer is the leader, manufacturer is the follower. At the same time, considering the impact of retailers and manufacturers to fulfill CSR, and considering three kinds of government subsidies, namely subsidies to manufacturers, subsidies to retailers and subsidies to consumers, to analyze the effects of different subsidy situations. Table 1 shows the meanings of related symbols.

Model hypothesis
Based on the above conditions, the assumptions of this paper are as follows: Hypothesis1.Manufacturers and retailers are "economic men" and risk neutral.
Hypothesis2.In order to ensure the profitability of supply chain members, the parameters of the supply chain system shall meet the following requirements: c w p   .
Hypothesis3.The R&D investment of green products is 2 / 2 ug [5]and the R&D investment is a one-time investment that is fully borne by the manufacturer. Hypothesis4.The market demand of green products is affected by the price, the greenness of products and the amount of retailers' social responsibility. The demand

Situation of Government subsidies to manufacturers
To represent the subsidy coefficient of unit product based on greenness, the government subsidy expenditure of unit product is sg [7].The decision sequence of supply chain is retail price p and social responsibility performance h . The manufacturer then determines the wholesale price w, greenness of the product g and the amount of social responsibility n to be fulfilled according to the retailer.  The results of Conclusion 1 show that when the government's greenness subsidy coefficient s increases, the greenness of products will increase. Due to consumers' preference for green products, the improvement of product greenness will increase the market demand, and the manufacturer will also increase its wholesale price. At the same time, the sales volume and retail price of retailers will increase correspondingly, and at the same time gain more profits. In this way, retailers will also take the initiative to improve their social responsibility performance.

Situation of government subsidies to retailers
We use  to represent the unit subsidy coefficient of government subsidies for retailers to fulfill their social responsibilities. At this time, the profit functions of manufacturers and retailers are respectively: The following equilibrium solution is obtained: The proof procedure is consistent with conclusion 1, which is omitted here. The results show that when the government directly subsidizes retailers, it will more directly reduce the cost burden of retailers to fulfill their social responsibilities, so that retailers are more motivated to shoulder the corresponding social responsibilities.

The situation of government subsidies to consumers
In order to stimulate green consumption, the government will also provide subsidies to consumers as appropriate. Suppose that the amount of government subsidy for unit green product price is k , that is, the actual purchase price of the consumer is p k  [8],

Conclusion
The research results show that: first, compared with the situation where the government does not provide subsidies, no matter what kind of subsidies the government adopts, the greenness of products, the amount of retailers' social responsibility fulfillment, the amount of manufacturers' social responsibility fulfillment, the profits of manufacturers and retailers can increase. Second, from the perspective of manufacturers and retailers, when the government unit subsidy expenditure is the same, the government subsidy to manufacturers will make manufacturers and retailers gain higher earnings. Therefore, both manufacturers and retailers tend to prefer the government to provide manufacturers with unit greenness subsidy. Third, for the government, when the subsidy expenditure of government units is the same, government subsidies to manufacturers will stimulate manufacturers to increase investment in green technology, thus improving the greenness of products. Government subsidies to retailers will more effectively encourage retailers to improve the level of social responsibility. Therefore, the government can choose different subsidy methods according to different situation.