# 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  
First, we mainly focus on the investigation of \(K\), the marginal demand coefficient for recycling innovation inputs, on the performances of the supply chain. The related parameters are assumed that \(\alpha=500\), \(\beta=30\), \(H=1000\), \(R=0.1\). The value of \(K\) is varied from 0.01 to 1.2. It's noticed that \(K\) has an increasing effect on price, collection effort, innovation input, the profitability of each player, and the total supply chain profits. In Figure 5, as \(K\) increases, the transfer prices, \(b_{1}^{H*}\) and \(b^{BE*}\) have a climbing trend, while \(b_{2}^{H*}\) stays unchanged, the gap between these two and \(b_{2}^{H*}\) is growing. It means that recyclers expect higher recycling subsidies when they invest in recycling innovations, namely the transfer price of \(b\) compensated by the manufacturer. From Figure 6, considering second scenario, as manufacturer's share of revenue increases, the products quality of the manufacturer increases and the products quality of the packaging company goes down. When \(K<0.6\), the growth of \(p\) is flat. When \(K\) is greater than 0.6, the growth rate of product selling price goes up but the relationship of \(p^{Hs}<p^{BE*}\) still remains. As shown in Figure 7, by increasing \(K\), the innovation input \(e^{H*}\) and \(e^{BE*}\) also increase, and the rate of growth is getting higher. At the same \(K\) level, the innovation input incentive of model \(H\) is slightly greater than that of model \(BE\). In other words, \(e^{H*}\) is slightly higher than \(e^{BE*}\) at a comparable \(K\) level. However, when model \(BE\) is at a high level of \(K\), the innovation input can exceed that of the model \(H\). Figure 5: The influences of \(K\) on the transfer price \(b\). Figure 8 shows even though collector 2 does not invest in innovation, its collection rate increases slowly with the increase of \(K\), mainly because of the positive externality brought by innovation input, that is, the social welfare brought by innovation input. When \(K\) is low, it means that the collector is in the initial stage of investment collection innovation, \(\tau_{1}^{H*}\) is close to \(\tau_{2}^{H*}\), it is difficult to see the changes that innovation investment will bring to the collection rate in the short term. Surprisingly, both \(\tau_{1}^{H*}\) and \(\tau_{2}^{H*}\) are higher than \(\tau^{Be*}\), we find that when \(K\) is at a low level, collector 2 charges the manufacturer a lower transfer price, which saves more cost for the manufacturer to recycle. The manufacturer's preference also encourages collector 2 to maintain a higher collection rate level. And \(e^{H*}\) is slightly higher than \(e^{Be*}\), it makes \(\tau_{1}^{H*}\) higher than \(\tau^{Be*}\). However, when \(K\) gradually increases, it means that the collectors have entered the development stage of investment and recovery of innovative investment, and the positive impact of recycling innovative investment is becoming more and more obvious. \(\tau_{1}^{H*}\) and \(\tau^{Be*}\) grow rapidly with the increase of \(K\), and \(\tau^{Be*}\) will soon exceed \(\tau_{2}^{H*}\). Therefore, the increasing trends for \(\tau_{1}^{H*}\) and \(\tau^{Be*}\) are similar. We compare collector 2's performance under the cases with (without) innovation input and can find that the marginal demand coefficient \(K\) has significant influence on \(\tau\) with innovation input. Figure 6: The influences of \(K\) on the retail price \(p\). Figure 7: The influences of \(K\) on the innovation input \(e\). Comparison of total supply chain profits shows the following relationship: \(\Pi_{T}^{H*}>\Pi_{T}^{BE*}\). Interestingly, the supply chain profit is higher in the hybrid system with two collectors in comparison to the basic centralized channel vertical Stackelberg equilibrium in Figure 9. Thus, competition of collectors through the investment of innovation input is advantageous for the supply chain.