# Competing Reverse Channels' Performance with Sustainable Recycle Innovation Input
## 5 Comparison and Insights
### Comparison of Equilibrium Outcomes  
The optimal transfer prices of different collectors in the three models satisfy the following relationships: \(b_{1}^{H*}=b^{BE*}>b_{2}^{H*}=b^{B*}\). It is apparent that the optimal transfer price is bigger when the collector has innovation input. If the manufacturer assigns a large value of \(b\), it would observe a high level of innovation input \(e\) and collection effort \(\tau\) by the collector, but at the same time, manufacturer's net savings from remanufacturing diminish. Hence, the manufacturer faces a trade off on the transfer price. Because of this, the manufacturer is more profitable in the hybrid channel. The relationship among the manufacturers' optimal selling prices is shown in Figure 4.  
We can get \(p^{BE*}=\frac{\alpha}{\beta}-\frac{2M(\alpha-\beta\epsilon_{m})}{4\beta M-4 \beta^{2}RN}\), \(p^{H*}=\frac{\alpha}{\beta}-\frac{2M(\alpha-\beta\epsilon_{m})}{4\beta M-4 \beta^{2}RN-4\beta^{2}R(\Delta-A)^{2}}\). Obviously, \(p^{B*}>p^{BE*}\). As shown in Figure 4, among the three models, the retail price in model \(BE\) is unexpectedly the highest. When the value of \(\beta\) is small, \(p^{BE*}>p^{H*}>p^{B*}\), which reflects that consumer demand is less  
Figure 4: The influences of \(\beta\) on the retail price \(p\). sensitive to price, and consumers prefer to purchase the innovation invested products. At this time, both \(p^{BE*}\) and \(p^{H*}\) have a quicker increase due to the increased cost of innovation input and consumer preference, resulting in an additional increase in retail prices. While the integrated manufacturer considers maximizing consumer utility, it also maximizes his profits. As \(\beta\) increases, \(p^{BE*}>p^{B*}>p^{H*}\). The retail price of \(p\) is relatively small in the hybrid system because the manufacturer can choose to recycle part of the used raw materials from collector 2 with a lower transfer price \(b_{2}\). We assume that the recycled raw materials recovered by the collectors 1, 2 are homogeneous. Therefore, the manufacturer in the hybrid recycling system can save more profit than that in the model \(BE\), which is not only the positive impact of recycling innovation investment, but also the social welfare. Another reason is that the manufacturer's profit in the hybrid model is higher, and some of the profits are derived from the scale effect. In general, the retail price \(p\) in the two system models with innovative inputs is not much different from the retail price \(p\) in the model without innovative inputs. It shows that innovation investment has not significantly increased retail prices, and can effectively improve channel recovery performance, while increasing consumer demand. The optimal product return rates of different collectors satisfy the following relationship: \(\tau^{H*}>\tau^{BE*}>\tau^{B*}\), \(\tau^{H*}=\tau_{1}^{H*}+\tau_{2}^{H*}\), \(\tau_{1}^{H*}>\tau_{2}^{H*}\)  
Interestingly, the total recovery rate of the mixed channel is higher than the basic centralized model, and the manufacturer's recycling compensation has a direct impact on the collection effort \(\tau\). When \(b_{1}^{H*}>b_{2}^{H*}\), for the two recyclers in the hybrid system, collector 1 has a greater recycling effort. When \(b_{1}^{H*}=b^{BE*}\), the collection rate of collector 1 is greater than the collection rate of the collector in the basic model, the main reason is that the retail price is \(p\). It is precisely because of \(p_{1}^{H*}<p^{BE*}\) that consumer demand is greater. For single-cycle issues, the greater the demand, the greater the scale of recycling generated. The optimal innovation input of collector satisfies the following relationships: \(e^{BE*}<e^{H*}\). The manufacturer's profits under three different modes are related as follows: \(\Pi_{M}^{B*}<\Pi_{M}^{BE*}<\Pi_{M}^{H*}\). Intuitively, manufacturers benefit from increased investment in recycling innovation.