# Tax or Subsidy? Optimal Carbon Emission Policy: A Supply Chain Perspective
## 5 Conclusions  
In this paper, we have investigated the government policy from a supply chain perspective. Specifically, we consider a Stackelberg game with the government policy maker being the leader, and the downstream manufacturer being the follower. Given the government policy (tax or subsidy) and its corresponding scale, the manufacturer decides the greenness of the product (or equivalently the greening level of technology), taking into account consumer's consciousness regarding the greenness of the product (we assume that consumers prefer environmentally friendly products in general). In anticipation of the manufacturer's possible responses to different policies, the government policy-makers decide which policy should be taken. We find that the tax policy is preferred by the government if consumers are very sensitive to the greenness, or the cost of greening is high, or the negative impact due to carbon emission is large; otherwise the government should subsidize the firm. Figure 4: Optimal values versus \(\lambda\). These insights can be carried over to the situation when the selling price is endogenously determined by the manufacturers, illustrated by our numerical study. Based on our study, we found that the government should carefully design and implement the carbon emission reduction policy. In general, there is no one-size-fit-all panacea. The policy (tax, subsidy or mix) depends on the advancement of technology, the magnitude of the negative consequences taken by carbon emission and consumers' attitude to environment protection. To encourage the adoption of green technology, possible mechanisms should also include: Green Public Procurement (GPP), joint R&D activities and support for inter-firm cooperation in design and development of green products. In addition, our study shows that the consumers' consciousness on the environment friendliness of products could play an important role in the government policy selection. As a result, the government tool kit for carbon emission reduction should include how to cultivate the people's consciousness on green products and environment production. Several future directions are worth exploring. The demand function we consider is deterministic, which applies in a long-term horizon. However, as products are upgraded in a fast speed nowadays, it is worth considering the demand uncertainty on the decisions involved in the supply chain. The cost function in our model setting is of linear format. It is quite challenging to consider other, more general formats (e.g., convex), and to investigate the optimal government policy in depth. We primarily considered the effect of policy on the manufacturer's side. Therefore, possible extensions also include investigating the optimal policy on consumers' side. Methodology, X.X. ; validation, X.C., X.X. and L.Z. ; formal analysis, X.C. ; writing--original draft preparation, X.Y. ; writing--review and editing, L.Z. ; visualization, X.Y. ; supervision, X.X. All authors have read and agreed to the published version of the manuscript. This research was funded by National Science Foundation of China (Nos.71871114, 71471085, 71732003), the Leading Talent Program of Guangdong Province (No. 2016 LJ06D703) and the Science and Technology Development Fund, Macau SAR (File no. FDCT/027/2016/A1). The authors declare no conflict of interest. The second order conditions with respect to (w.r.t) \(\theta\) is given by \(\frac{d^{2}\pi_{(\text{fig})}(\theta)}{d\theta^{2}}=2b(t-\lambda)<0\), which implies the firm's profit function is concave in \(\theta\). Thus, according to the first order condition, we get,  
\[\theta_{(\text{fig})}=\frac{b(p-c)-(\lambda-t)(a-\gamma p)}{2b(\lambda-t)} \bigg{\{} \begin{array}{l}<0,\lambda>\Delta_{1}\\ \geq 0,t<\lambda\leq\Delta_{1}\end{array} \]  
where \(\Delta_{1}=t+\frac{b(p-c)}{(a-\gamma p)}\).