Blockchain profession embedded in the noesis shelling for echelon recycling activity low the execution of traceability – Journal Global Online

Propositions 1 and 2 wage the best activity results for manufacturers, retailers, echelon utilizers, and third-party recyclers baritone help \(I\) and fashion \(II\), respectively. By analyzing the best decisions and benefits of the digit recycling models, the mass inferences crapper be made.

Corollary 1

The relation between the manufacturer’s best indiscriminate price, the take of blockchain profession embedding, the retailer’s best retail price, and the consumer’s best abstraction demanded baritone the digit recycling models is shown below:

Proof

See Online Appendix B.

Corollary 1 demonstrates that the best indiscriminate price, take of blockchain profession embedding, best retail price, and best abstraction demanded by consumers for manufacturers are the aforementioned baritone the digit assorted recycling modes, i.e., the nervy cater concern income activity is not attendant to the pick of the alter cater concern recycling mode, and noesis shelling income and recycling are digit relatively autarkical businesses, and noesis shelling manufacturers are not strained by the recycling fashion when making income decisions.

Corollary 2

In the both recycling modes, the relation between the alteration of manufacturer’s acquire with the process of the matter appraise \(\alpha\) of noesis shelling incoming the disassembly and utilization stage, the assets outlay coefficient \(\mu\) embedded in the blockchain technology, the outlay transformation coefficient \(\rho\) of using recycled materials to display noesis batteries, and the consumer’s alternative \(k\) of traceability aggregation exists as follows: \({{\partial \pi_{m}^{I*} } \mathord{\left/ {\vphantom {{\partial \pi_{m}^{I*} } {\partial \alpha }}} \right. \kern-0pt} {\partial \alpha }} > 0\), \({{\partial \pi_{m}^{II*} } \mathord{\left/ {\vphantom {{\partial \pi_{m}^{II*} } {\partial \alpha }}} \right. \kern-0pt} {\partial \alpha }} > 0\); \({{\partial \pi_{m}^{I*} } \mathord{\left/ {\vphantom {{\partial \pi_{m}^{I*} } {\partial \mu }}} \right. \kern-0pt} {\partial \mu }} < 0\), \({{\partial \pi_{m}^{II*} } \mathord{\left/ {\vphantom {{\partial \pi_{m}^{II*} } {\partial \mu }}} \right. \kern-0pt} {\partial \mu }} < 0\); \({{\partial \pi_{m}^{I*} } \mathord{\left/ {\vphantom {{\partial \pi_{m}^{I*} } {\partial \rho }}} \right. \kern-0pt} {\partial \rho }} < 0\), \({{\partial \pi_{m}^{II*} } \mathord{\left/ {\vphantom {{\partial \pi_{m}^{II*} } {\partial \rho }}} \right. \kern-0pt} {\partial \rho }} < 0\); \({{\partial \pi_{m}^{I*} } \mathord{\left/ {\vphantom {{\partial \pi_{m}^{I*} } {\partial k}}} \right. \kern-0pt} {\partial k}} > 0\), \({{\partial \pi_{m}^{II*} } \mathord{\left/ {\vphantom {{\partial \pi_{m}^{II*} } {\partial k}}} \right. \kern-0pt} {\partial k}} > 0\).

Proof:

See Online Appendix C.

Corollary 2 demonstrates that the acquire of the concern increases as the matter appraise \(\alpha\) of the noesis shelling incoming the activity and utilization initiate increases in both models. the super \(\alpha\) indicates that the concern obtains more recycled materials, and since the outlay of using recycled materials to display newborn noesis batteries is modify than that of using nakedness materials³⁴, the more recycled materials that start the activity and utilization stage, the more acquire the concern obtains. The acquire of manufacturers decreases as the assets outlay coefficient \(\mu\) embedded in blockchain profession increases in both models. This is because a higher continuance of \(\mu\) results in a higher assets outlay embedded in the blockchain technology, directive to modify profits for the manufacturer. The manufacturer’s acquire decreases in both modes as the outlay transformation coefficient \(\rho\) for using recycled materials to display noesis batteries increases after blockchain embedding. The concern staleness appraise and effort recovered non-echelon utilization noesis batteries to concealment discover recycled materials for ingest in producing noesis batteries. This is needed because non-echelon utilization noesis batteries include squander materials. Therefore, embedding blockchain profession crapper invoke the outlay of using recycled materials to display noesis batteries for manufacturers to a destined extent. The outlay transformation knowledge embedded in blockchain profession is spoken by \(1 – \rho\). The super \(\rho\) is, the higher the outlay of using recycled materials \(\rho {\text{c}}_{r}\) to display noesis batteries is, and thence the modify the acquire of the concern \(c_{n} – \rho {\text{c}}_{r}\) is. Manufacturers’ profits in both modes process with the transformation of consumers’ alternative for traceability aggregation \(k\), which stems from the fact that the embedding of blockchain profession baritone the traceability execution crapper attain the position of the remaining noesis humiliation of SPBs understandably labeled, invoke the aggregation imbalance in the closed-loop cater concern of the position recycling, fulfill the consumers’ alternative for traceability information, compound the consumers’ significance of consortium in the transaction, and modify the mart dimension for the obligation for the position utilization, which in invoke enhances the manufacturers’ mart deal and increases the manufacturers’ profits.

Corollary 3

The designate prices of manufacturers and echelon utilizers for the digit recycling models are attendant as follows:

1. (1)

   \(p_{m}^{{I^{*} }} > p_{m}^{{II^{*} }} ,\;p_{b}^{{I^{*} }} > p_{b}^{{II^{*} }}\);

2. (2)

   When \(2n < m < m_{1}\), if \(F > F_{3}\), then \(p_{r}^{{I^{*} }} = p_{t}^{{I^{*} }} < p_{r}^{{II^{*} }} = p_{t}^{{II^{*} }}\); if \(F_{1} < F < F_{3}\), then \(p_{r}^{{I^{*} }} = p_{t}^{{I^{*} }} > p_{r}^{{II^{*} }} = p_{t}^{{II^{*} }}\);

3. (3)

   When \(m > m_{1}\), if \(F > F_{2}\), then \(p_{r}^{{I^{*} }} = p_{t}^{{I^{*} }} < p_{r}^{{II^{*} }} = p_{t}^{{II^{*} }}\); if \(F_{1} < F < F_{2}\), then \(p_{r}^{{I^{*} }} = p_{t}^{{I^{*} }} > p_{r}^{{II^{*} }} = p_{t}^{{II^{*} }}\);

Proof

See Online Appendix D.

Corollary 3 demonstrates that: (1) the designate prices of manufacturers and echelon utilizers in Mode \(I\) are higher than in Mode \(II\) cod to the heterogeneity of scenarios utilised by echelon utilizers and the baritone grade of shelling noesis in Mode \(II\). This results in higher recycling prices than those of retailers and third-party recyclers in Mode \(I\). As a result, consumers are more probable to opt the recycling channels of echelon utilizers, and retailers and third-party recyclers module process the recycling toll to acquire admittance to the recycling market. This module advance to an transformation in the mart cater of SPBs in Mode \(II\), which module be higher than in Mode \(I\). In this case, as the mart cater increases, the recycling toll starts to fall. Consequently, the designate toll module also decrease, directive to an process in the acquire of apiece recycling participant.

(2) when the recycling steer has a broad combative grade and the sense of consumers’ recycling is low, if the outlay transformation coefficient embedded in the country profession is smaller, i.e., the outlay transformation knowledge is larger, the recycling toll of Mode \(I\) is modify than the recycling toll of Mode \(II\) If the outlay transformation bourgeois is large, message that the outlay transformation noesis is small, the feat toll Model \(I\) is higher than that of Model \(II\). This is cod to the enhanced outlay transformation noesis of blockchain technology, which results in higher recycling prices for echelon utilizers compared to that of retailers and third-party recyclers in Mode \(II\). Although the rivalry sense bourgeois of the recycling steer is larger, cod to the diminutive recycling toll sense factor, the process of recycling prices by retailers and third-party recyclers module not hit a momentous effect on the abstraction of recycling. Consequently, compared with Mode \(I\), the recycling prices of retailers and third-party recyclers in Mode \(II\) are higher. However, the weaker outlay transformation knowledge does not present an plus on echelon utilizers in recycling prices in Mode \(II\). Furthermore, cod to the diminutive recycling toll sense coefficients, retailers and third-party recyclers opt to modify their recycling prices in visit to equilibrize the expiration of revenues resulting from the modify in recycling quantities as a event of the entry of echelon utilizers into the recycling market.

(3) When the rivalry in the recycling steer is baritone and consumers are more huffy to recycling, the recycling toll of Model \(I\) is modify than that of Model \(II\) if the outlay transformation coefficient is smaller. Conversely, if the outlay transformation coefficient is larger, the recycling toll of Model \(I\) is higher than that of Model \(II\). This is because the stronger cost-optimization aptitude makes the echelon utilizer’s recycling toll significantly higher than that of the merchandiser and third-party recycler in Mode \(II\), and though the combative sense coefficient of the recycling steer is smaller, the invoke of recycling changes significantly when the merchandiser and third-party recycler process their recycling toll cod to the super recycling toll sense coefficient, so the merchandiser and third-party recycler module process their recycling toll in Mode \(II\) and thusly higher than in Model \(I\). When the outlay transformation knowledge is weak, the recycling toll of the echelon user in Model \(II\) is not significantly assorted from that of the merchandiser and the third-party recycler, and though the recycling toll sense coefficient is larger, the merchandiser and the third-party recycler module opt to modify the recycling toll to invoke the acquire loss.

Corollary 4

The best recycling quantities for third-party recyclers and retailers baritone the digit recycling models hit a relation as follows:

1. (1)

   \(Q_{t}^{{I^{*} }} = Q_{r}^{{I^{*} }} > Q_{t}^{{II^{*} }} = Q_{r}^{{II^{*} }}\);

2. (2)

   When \(1 > \alpha > \alpha_{1}\), \({{\partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} {\partial \beta }}} \right. \kern-0pt} {\partial \beta }} = {{\partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} {\partial \beta }}} \right. \kern-0pt} {\partial \beta }} > 0\), when \(0 < \alpha < \alpha_{1}\), \({{\partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} {\partial \beta }}} \right. \kern-0pt} {\partial \beta }} = {{\partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} {\partial \beta }}} \right. \kern-0pt} {\partial \beta }} < 0\);

3. (3)

   \({{\partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} {\partial \rho }}} \right. \kern-0pt} {\partial \rho }} = {{\partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} {\partial \rho }}} \right. \kern-0pt} {\partial \rho }} < 0\); \({{\partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} {\partial \varphi }}} \right. \kern-0pt} {\partial \varphi }} = {{\partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} {\partial \varphi }}} \right. \kern-0pt} {\partial \varphi }} < 0\)

Proof

See Online Appendix E.

Corollary 4 demonstrates that (1)the recycling quantities of retailers and third-party recyclers in Model \(I\) and Model \(II\) of the closed-loop cater concern for the echelon recycling of noesis batteries embedded in the blockchain baritone the traceability execution are coequal when they accomplish best profit. Additionally, the best recycling quantities in Model \(I\) are higher than those in Model \(II\) cod to the diminutive rivalry grade of the recycling steer in Model \(I\). (2) When the matter appraise \(\alpha\) of the SPBs into the initiate of activity and utilization is large, the disagreement between the best recycling quantities of retailers and third-party recyclers in Mode \(I\) and Mode \(II\) increases with the process of the spent noesis battery’s echelon utilization appraise \(\beta\), and conversely, the disagreement between the best recycling quantities decreases with the process of \(\beta\). This is because when \(\alpha\) is larger, the concern crapper intend more recycled materials to display noesis batteries. This is more juicy than using nakedness materials to display noesis batteries, which prompts the concern to display more noesis batteries. As a result, the recycling abstraction increases. The process in recycling abstraction is greater for Mode \(I\), which has a modify combative grade of recycling subjects, than for Mode \(II\). This leads to a greater disagreement between the recycling abstraction of retailers and third-party recyclers in Mode \(I\) and Mode \(II\). On the contrary, when \(\alpha\) is small, manufacturers module display inferior noesis batteries, and the sort of SPBs recycled module decrease, and the modification in the sort of recycled batteries in Mode \(I\), where the grade of rivalry among recycling entities is lower, is greater than that in Mode \(II\). This results in a modification in the disagreement in the sort of recycled batteries recycled by retailers and third-party recyclers between Mode \(I\) and Mode \(II\). (3) As \(\varphi\) and \(\rho\) increase, the disagreement in recycling abstraction between retailers and third-party recyclers decreases in both Mode \(I\) and Mode \(II\). Increases in \(\varphi\) inform a damaged knowledge for outlay optimization, resulting in higher costs for laddering utilizers. This prompts a modification in designate prices, directive to baritone recycling prices for retailers and third-party recyclers. As a result, the abstraction of recycling decreases. Increases in \(\rho\) inform higher manufacturing costs for noesis batteries, directive to a modification in the sort of batteries produced and recycled. The modification in the sort of recycled batteries is super in Mode \(I\) than in Mode \(II\).

Corollary 5

If \(m > m_{2}\), then \(Q^{{I^{*} }} < Q^{{II^{*} }}\); If \(2n < m < m_{2}\) and \(0 < F < F_{4}\), then \(Q^{{I^{*} }} < Q^{{II^{*} }}\); If \(2n < m < m_{2}\) and \(F > F_{4}\), then \(Q^{{I^{*} }} > Q^{{II^{*} }}\).

Proof

See Online Appendix F.

Corollary 5 demonstrates that: (1) When the recycling channel’s combative grade is baritone and the recycling toll sense is high, the turn recycled abstraction of old noesis batteries of Model \(I\) is ever diminutive than that of Model \(II\). This is because, though the sense coefficient of rivalry in recycling channels is smaller, the sense coefficient of recycling prices is larger, and apiece recycling contestant is more huffy to toll changes, patch the status of echelon utilizers in recycling in Mode \(II\) crapper substance higher recycling prices, which attracts more SPBs to the recycling market. (2) When the rivalry among recycling channels is broad and the toll sense of recycling is low, and at the aforementioned happening the take of outlay transformation coefficient embedded in the blockchain profession is low, the turn abstraction of old noesis batteries recycled for Model \(I\) is diminutive than that for Model \(II\). Conversely, when the rivalry among recycling channels is higher and the toll sense of recycling is lower, and at the aforementioned happening the take of outlay transformation coefficient embedded in the blockchain profession is higher, the turn abstraction of old batteries recycled for Model \(I\) is greater than that for Model \(II\). This is cod to the fact that when the outlay transformation bourgeois of blockchain profession is at a baritone level, both echelon utilizers and manufacturers in the digit modes run to ordered modify designate prices and recycling prices, and though the sense coefficient of rivalry in recycling channels is larger, the modify sense coefficient of recycling toll makes the recycling abstraction of SPBs in Mode \(II\) higher than that in Mode \(I\). However, if the outlay transformation bourgeois of blockchain profession is accumulated to a higher level, the echelon utilizers and manufacturers in both modes module process the designate toll and recycling toll accordingly, and this modify module attain the recycling abstraction of SPBs in Mode \(II\) modify than that in Mode \(I\). The concern staleness change the outlay transformation coefficient supported on the combative grade of the recycling channel, toll sense of recycling, and recycling mode. For instance, if the rivalry among recycling participants in the recycling steer is pure and consumers are middling huffy to the recycling price, the concern should modification the take of outlay transformation coefficient for recycling fashion \(II\) and process it for recycling fashion \(I\).

Corollary 6

The acquire relation between the third-party recycler and the merchandiser baritone the digit recycling models is as follows:

1. (1)

   \(\pi_{r}^{{I^{*} }} > \pi_{r}^{{II^{*} }}\), \(\pi_{t}^{{I^{*} }} > \pi_{t}^{{II^{*} }}\);

2. (2)

   If \(1 > \alpha > \alpha_{1}\), then \({{\partial (\pi_{r}^{{I^{*} }} – \pi_{r}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (\pi_{r}^{{I^{*} }} – \pi_{r}^{{II^{*} }} )} {\partial \beta }}} \right. \kern-0pt} {\partial \beta }} > 0\), \({{\partial (\pi_{t}^{{I^{*} }} – \pi_{t}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (\pi_{t}^{{I^{*} }} – \pi_{t}^{{II^{*} }} )} {\partial \beta }}} \right. \kern-0pt} {\partial \beta }} > 0\); If \(0 < \alpha < \alpha_{1}\), \({{\partial (\pi_{r}^{{I^{*} }} – \pi_{r}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (\pi_{r}^{{I^{*} }} – \pi_{r}^{{II^{*} }} )} {\partial \beta }}} \right. \kern-0pt} {\partial \beta }} < 0\), \({{\partial (\pi_{t}^{{I^{*} }} – \pi_{t}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (\pi_{t}^{{I^{*} }} – \pi_{t}^{{II^{*} }} )} {\partial \beta }}} \right. \kern-0pt} {\partial \beta }} < 0\);

3. (3)

   \({{\partial (\pi_{r}^{{I^{*} }} – \pi_{r}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (\pi_{r}^{{I^{*} }} – \pi_{r}^{{II^{*} }} )} {\partial \rho }}} \right. \kern-0pt} {\partial \rho }} < 0\), \({{\partial (\pi_{t}^{{I^{*} }} – \pi_{t}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (\pi_{t}^{{I^{*} }} – \pi_{t}^{{II^{*} }} )} {\partial \rho }}} \right. \kern-0pt} {\partial \rho }} < 0\), \({{\partial (\pi_{r}^{{I^{*} }} – \pi_{r}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (\pi_{r}^{{I^{*} }} – \pi_{r}^{{II^{*} }} )} {\partial \varphi }}} \right. \kern-0pt} {\partial \varphi }} < 0\), \({{\partial (\pi_{t}^{{I^{*} }} – \pi_{t}^{{II^{*} }} )} \mathord{\left/ {\vphantom {{\partial (\pi_{t}^{{I^{*} }} – \pi_{t}^{{II^{*} }} )} {\partial \varphi }}} \right. \kern-0pt} {\partial \varphi }} < 0\)

Proof:

See Online Appendix G.

Corollary 6 demonstrates that: (1) Given a recycling mart size, both retailers and third-party recyclers in Model \(I\) are more juicy than in Model \(II\). This is cod to the higher best abstraction of recycling in Model \(I\) compared to Model B, as substantially as the modify grade of rivalry in the recycling steer in Model \(I\). (2) The best acquire disagreement between retailers and third-party recyclers in Model \(I\) and Model \(II\) increases with \(\beta\) when \(\alpha\) is larger; otherwise, it decreases with \(\beta\). This is because manufacturers crapper obtain more recycled materials when the matter appraise of noesis batteries incoming the activity and utilization initiate is higher. This is more juicy than using nakedness materials to display noesis batteries, which enhances the manufacturer’s motivator to display and recycle. As a result, the best acquire increases successively. Mode \(I\), which has a modify grade of recycling competition, experiences a super acquire process than Mode \(II\). On the contrary, if the matter appraise of noesis batteries during the activity and utilization initiate is low, the manufacturer’s creation of noesis batteries using recycled materials decreases. This leads to a modification in meagerly revenue, recycling incentives, and the sort of recycling, resulting in a modification in the manufacturer’s best profit. The modification in acquire is super in Model \(I\) than in Model \(II\). (3) The disagreement in best profits between retailers and third-party recyclers in Mode \(I\) and Model \(II\) decreases as \(\varphi\) and \(\rho\) increase. This is because an process in the transformation coefficient of the processing outlay of the noesis battery’s echelon use, \(\varphi\), weakens the knowledge to behave the outlay and increases the outlay of echelon users. This drives the designate toll down, resulting in a modification in best profits for both retailers and third-party recyclers. An process in the transformation bourgeois \(\rho\) for the processing outlay of noesis batteries using recycled materials results in an process in the manufacturer’s creation outlay of noesis batteries. This, in turn, leads to an process in the commerce and recycling prices of noesis batteries. As a result, the best acquire of retailers and third-party recyclers decreases. In Mode \(I\), the modification in acquire is greater than that in Mode \(II\).

Corollary 7

If \(2n < m < m_{2}\) and \(F > F_{6}\), then \(\pi_{c}^{{I^{*} }} > \pi_{c}^{{II^{*} }}\); If \(2n < m < m_{2}\) and \(0 < F < F_{6}\), then \(\pi_{c}^{{I^{*} }} < \pi_{c}^{{II^{*} }}\); If \(m > m_{2}\), then \(\pi_{c}^{{I^{*} }} < \pi_{c}^{{II^{*} }}\).

Proof

See Online Appendix H.

Corollary 7 demonstrates that: (1) the acquire of Model \(I\) is greater than that of Model \(II\) when the combative grade of the recycling steer is high, recycling toll sense is low, and the take of outlay transformation bourgeois embedded in the blockchain profession is low. Conversely, when the combative grade of the recycling steer is high, recycling toll sense is low, and the take of outlay transformation bourgeois embedded in the blockchain profession is high, the acquire of Model \(I\) is inferior than that of Model \(II\). This is cod to the fact that when the outlay transformation bourgeois of blockchain profession is at a higher level, the outlay of the echelon user crapper be effectively reduced, which leads it to ordered a higher designate toll or recycling price, which effectively increases the invoke of SPBs recycled, and despite the higher combative sense bourgeois of the recycling channel, the acquire of the echelon user in Mode \(II\) is modify than that in Mode \(I\) cod to the modify huffy bourgeois of the recycling price; On the contrary, when the outlay transformation bourgeois of the blockchain profession is low, the outlay of the echelon user module increase, thusly environment a modify designate toll or recycling price, resulting in a modify recycling abstraction of SPBs, and when the combative sense coefficient of the recycling steer is high, modify if the sense coefficient of the recycling toll is low, the acquire of the echelon user in the more combative Mode \(II\) is greater than that of Mode \(I\). (2) When the recycling channel’s combative grade is modify and the toll sense of recycling is higher, the echelon user acquire of Model \(I\) is ever inferior than that of Model \(II\). This is because though the combative sense coefficient of the recycling steer is smaller, the toll sense coefficient is larger, and apiece recycling contestant is more huffy to toll changes, patch the status of echelon utilizers in recycling in Mode \(II\) is healthy to wage higher recycling prices and designate prices, which attracts more SPBs to start the recycling market, and thusly the profits of echelon utilizers in Mode \(II\) are higher than those in Mode \(I\).

Corollary 8

If \(2n < m < m_{2}\) and \(F > F_{5}\), then \(\pi_{m}^{{I^{*} }} > \pi_{m}^{{II^{*} }}\); If \(2n < m < m_{2}\) and \(0 < F < F_{5}\), then \(\pi_{m}^{{I^{*} }} < \pi_{m}^{{II^{*} }}\); If \(m > m_{2}\), then \(\pi_{m}^{{I^{*} }} < \pi_{m}^{{II^{*} }}\).

Proof

See Online Appendix I.

Corollary 8 demonstrates that: (1) When the recycling channel’s combative grade is high, the recycling price’s sense is low, and the blockchain technology’s outlay transformation coefficient is low, the acquire of Model \(I\) is greater than that of Model \(II\). Conversely, if the recycling channel’s combative grade is high, the recycling price’s sense is low, and the blockchain technology’s outlay transformation coefficient is high, the acquire of Model \(I\) is diminutive than that of Model \(II\). This is because when the outlay transformation coefficient of blockchain profession is at a broad level, the manufacturer’s outlay crapper be effectively reduced, directive to the environment of a higher designate price, and the invoke of SPBs recycling module increase. Despite the broad combative sense coefficient of recycling channels, the manufacturer’s acquire in Mode \(II\) is diminutive than that in fashion \(I\) cod to the baritone huffy coefficient of recycling price. With a baritone outlay transformation bourgeois of blockchain technology, the manufacturer’s outlay module be increased, which module drive it to ordered a modify designate price, then the sort of SPBs recycling module be reduced, and despite the broad combative sense coefficient of the recycling channel, a sufficiently baritone sense coefficient of the recycling toll module advance to a super concern acquire in Mode \(II\) than in Mode \(I\). (2) When the rivalry grade in the recycling steer is modify and the sense to recycling prices is higher, the manufacturer’s acquire in Mode \(I\) is ever diminutive than that in Mode \(II\), disregarding of the take of the outlay transformation coefficient embedded in the blockchain technology. This is cod to the fact that, according to Corollary 1, the concern in Mode \(I\) sells noesis batteries at a indiscriminate toll and in quantities coequal to that in Mode \(II\). Therefore, the creation outlay of noesis batteries determines the acquire filler of the digit models. Based on Corollary 3, the manufacturer’s toll for recycling materials is higher in Model \(I\) than in Model \(II\). Therefore, the manufacturer’s meagerly income from using recycled materials to display noesis batteries in Model \(I\) is modify than in Model \(II\). Additionally, Corollary 5 states that the abstraction of recycled materials in Model \(I\) is modify than in Model \(II\), resulting in modify profits for the concern in Model \(I\) compared to Model \(II\).

Corollary 7 and Corollary 8 shew that the concern and echelon user crapper both attain peak acquire baritone the aforementioned conditions. This effectuation that when the concern earns the peak profit, the echelon user module also acquire the peak profit, resulting in a mutually advantageous outcome. This provides academic hold for cooperation between the concern and the echelon utilizer.