# Competing Reverse Channels' Performance with Sustainable Recycle Innovation Input
## 5 Comparison and Insights
### Numerical Analysis
#### 5.2.1 Impact of Marginal Demand Coefficient for Recycling Innovation Inputs
We further compare the individual players' profits in the two models. In Figure 10, the manufacturer's profits are in the following order, \(\Pi_{M}^{Hs*}>\Pi_{M}^{BE*}\). The reason for larger profit of the manufacturer in model \(H\) is the increased social welfare brought about by the increased investment in recycling innovation. Due to the externality of innovation investment, the recycling volume of collector 2 without innovation investment will also be improved to a certain extent. For example, the social awareness of environmental recycling is enhanced, and manufacturers can purchase second-hand products or waste materials from collector 2 at a lower price. Then the manufacturers' profits could be further improved, and also the manufacturers are more willing to sell new products to consumers at lower retail prices. Figure 8: The influences of \(K\) on the collection effort \(\tau\). Figure 9: The influences of \(K\) on the total profit of the supply chain \(\Pi_{T}\). The collectors' profits cannot be established. In Figure 11, collector 1 incurs the highest profit in the hybrid system with innovation input. With the increase of \(K\), it means that the positive external influence brought by innovation investment increases, and the profit of the collector increases with the increase of \(K\). Even if collector 2 does not invest in innovation investment, his profit is slowly increasing with the increase of \(K\), which is mainly due to the positive external response brought by the innovation input. It can also be said that the innovation input brings social welfare. When the \(K\) is low, it means that the collector is in the initial stage of investment and innovation investment, and the profits' relationship between each collector is as follows: \(\Pi_{\mathrm{C1}}^{H*}>\Pi_{\mathrm{C2}}^{H*}>\Pi_{\mathrm{C}}^{BE*}\). Correspondingly, the collection rate relationship among various collectors can be observed: \(\tau_{1}^{H*}>\tau_{2}^{H*}>\tau^{BE*}\), which means that it is difficult for recycling companies to invest in innovation in the recycling market at first. The conclusions are drawn that the third-party recycling channel is the most unfavorable. Because it often bears a huge amount of innovation input costs when it does not achieve sufficient recycling to make a profit. However, the amount of waste items in society is getting higher and higher. Recycling must also be specialized. The establishment of recycling enterprises is  
Figure 11: The influences of \(K\) on the collector’s profit \(\Pi_{\mathrm{C}}\). Figure 10: The influences of \(K\) on the manufacturer’s profit \(\Pi_{M}\). an inevitable trend. Of course, it will require the joint assistance of the government, manufacturing enterprises, and remanufacturing enterprises. When the \(K\) increases, it means that the collector has entered the development stage of investment and recycling innovative inputs, the market environment for innovative inputs is relatively good, and people also prefer recycling channels that contain innovative inputs. We observe that the sorting of the profit size of collectors has changed, \(\Pi_{\text{C1}}^{H*}>\Pi_{\text{C}}^{BE*}>\Pi_{\text{C2}}^{H*}\). The corresponding recovery rate also changes as follows. \(\tau_{1}^{H*}>\tau^{BE*}>\tau_{2}^{H*}\). In Figure 12, we study the two collectors' profits with innovation input and determine regions where its profit is highest relative to \(K\). In the same value of \(K\), \(\Pi_{\text{C}}^{H*}>\Pi_{\text{C}}^{BE*}\). When model \(BE\) and model \(H\) are in the different \(K\) levels, we assume \(K_{g}(g=BE,H)\), subscript \(g\) represents the value of \(K\) under model \(BE\) and model \(H\) respectively, which also shows the different market environment responses to innovation input. As the relative \(K_{H}\) increases, we find that case 2 is more profitable for the collector 1 in model \(H\). We find, at higher relative level of \(K_{BE}\), case 1 is more profitable than case 2 for the collector in the model \(BE\).