Propositions 1 and a couple of present the optimum resolution outcomes for producers, retailers, echelon utilizers, and thirdparty recyclers beneath mannequin (I) and mode (II), respectively. By analyzing the optimum selections and advantages of the 2 recycling fashions, the next inferences will be made.
Corollary 1
The connection between the producer’s optimum wholesale value, the extent of blockchain knowhow embedding, the retailer’s optimum retail value, and the buyer’s optimum amount demanded beneath the 2 recycling fashions is proven under:
$$w^{{I^{*} }} = w^{{II^{*} }} ,;t^{{I^{*} }} = t^{{II^{*} }} ,;p^{{I^{*} }} = p^{{II^{*} }} ,;D^{{I^{*} }} = D^{{II^{*} }}$$
Proof
See Online Appendix B.
Corollary 1 demonstrates that the optimum wholesale value, stage of blockchain knowhow embedding, optimum retail value, and optimum amount demanded by customers for producers are the identical beneath the 2 completely different recycling modes, i.e., the ahead provide chain gross sales resolution just isn’t associated to the selection of the reverse provide chain recycling mode, and energy battery gross sales and recycling are two comparatively unbiased companies, and energy battery producers are usually not affected by the recycling mode when making gross sales selections.
Corollary 2
Within the each recycling modes, the connection between the variation of producer’s revenue with the rise of the residual fee (alpha) of energy battery getting into the disassembly and utilization stage, the funding value coefficient (mu) embedded within the blockchain knowhow, the associated fee optimization coefficient (rho) of utilizing recycled supplies to provide energy batteries, and the buyer’s desire (ok) of traceability data exists as follows: ({{partial pi_{m}^{I*} } mathord{left/ {vphantom {{partial pi_{m}^{I*} } {partial alpha }}} proper. kern0pt} {partial alpha }} > 0), ({{partial pi_{m}^{II*} } mathord{left/ {vphantom {{partial pi_{m}^{II*} } {partial alpha }}} proper. kern0pt} {partial alpha }} > 0); ({{partial pi_{m}^{I*} } mathord{left/ {vphantom {{partial pi_{m}^{I*} } {partial mu }}} proper. kern0pt} {partial mu }} < 0), ({{partial pi_{m}^{II*} } mathord{left/ {vphantom {{partial pi_{m}^{II*} } {partial mu }}} proper. kern0pt} {partial mu }} < 0); ({{partial pi_{m}^{I*} } mathord{left/ {vphantom {{partial pi_{m}^{I*} } {partial rho }}} proper. kern0pt} {partial rho }} < 0), ({{partial pi_{m}^{II*} } mathord{left/ {vphantom {{partial pi_{m}^{II*} } {partial rho }}} proper. kern0pt} {partial rho }} < 0); ({{partial pi_{m}^{I*} } mathord{left/ {vphantom {{partial pi_{m}^{I*} } {partial ok}}} proper. kern0pt} {partial ok}} > 0), ({{partial pi_{m}^{II*} } mathord{left/ {vphantom {{partial pi_{m}^{II*} } {partial ok}}} proper. kern0pt} {partial ok}} > 0).
Proof:
See Online Appendix C.
Corollary 2 demonstrates that the revenue of the producer will increase because the residual fee (alpha) of the ability battery getting into the dismantling and utilization stage will increase in each fashions. the bigger (alpha) signifies that the producer obtains extra recycled supplies, and since the price of utilizing recycled supplies to provide new energy batteries is decrease than that of utilizing uncooked supplies^{34}, the extra recycled supplies that enter the dismantling and utilization stage, the extra revenue the producer obtains. The revenue of producers decreases because the funding value coefficient (mu) embedded in blockchain knowhow will increase in each fashions. It’s because the next worth of (mu) leads to the next funding value embedded within the blockchain knowhow, resulting in decrease income for the producer. The producer’s revenue decreases in each modes as the associated fee optimization coefficient (rho) for utilizing recycled supplies to provide energy batteries will increase after blockchain embedding. The producer should consider and check recovered nonechelon utilization energy batteries to display screen out recycled supplies to be used in producing energy batteries. That is obligatory as a result of nonechelon utilization energy batteries include waste supplies. Subsequently, embedding blockchain knowhow can cut back the price of utilizing recycled supplies to provide energy batteries for producers to a sure extent. The price optimization capacity embedded in blockchain knowhow is expressed by (1 – rho). The bigger (rho) is, the upper the price of utilizing recycled supplies (rho {textual content{c}}_{r}) to provide energy batteries is, and subsequently the decrease the revenue of the producer (c_{n} – rho {textual content{c}}_{r}) is. Producers’ income in each modes enhance with the enhancement of customers’ desire for traceability data (ok), which stems from the truth that the embedding of blockchain knowhow beneath the traceability mechanism could make the gradient of the remaining capability degradation of SPBs clearly labeled, cut back the data asymmetry within the closedloop provide chain of the gradient recycling, fulfill the customers’ desire for traceability data, improve the customers’ sense of belief within the transaction, and develop the market breadth for the demand for the gradient utilization, which in flip enhances the producers’ market share and will increase the producers’ income.
Corollary 3
The switch costs of producers and echelon utilizers for the 2 recycling fashions are associated as follows:

(1)
(p_{m}^{{I^{*} }} > p_{m}^{{II^{*} }} ,;p_{b}^{{I^{*} }} > p_{b}^{{II^{*} }});

(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)
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 switch costs of producers and echelon utilizers in Mode (I) are larger than in Mode (II) because of the range of situations utilized by echelon utilizers and the low saturation of battery capability in Mode (II). This leads to larger recycling costs than these of shops and thirdparty recyclers in Mode (I). In consequence, customers are extra doubtless to decide on the recycling channels of echelon utilizers, and retailers and thirdparty recyclers will enhance the recycling value to achieve entry to the recycling market. This may result in an enchancment out there provide of SPBs in Mode (II), which will probably be larger than in Mode (I). On this case, because the market provide will increase, the recycling value begins to fall. Consequently, the switch value can even lower, resulting in a rise within the revenue of every recycling participant.
(2) when the recycling channel has a excessive aggressive depth and the sensitivity of customers’ recycling is low, if the associated fee optimization coefficient embedded within the block knowhow is smaller, i.e., the associated fee optimization capacity is bigger, the recycling value of Mode (I) is decrease than the recycling value of Mode (II) If the associated fee optimization issue is giant, which means that the associated fee optimization capability is small, the restoration value Mannequin (I) is larger than that of Mannequin (II). That is because of the enhanced value optimization capability of blockchain knowhow, which ends up in larger recycling costs for echelon utilizers in comparison with that of shops and thirdparty recyclers in Mode (II). Though the competitors sensitivity issue of the recycling channel is bigger, because of the smaller recycling value sensitivity issue, the rise of recycling costs by retailers and thirdparty recyclers is not going to have a major affect on the amount of recycling. Consequently, in contrast with Mode (I), the recycling costs of shops and thirdparty recyclers in Mode (II) are larger. Nonetheless, the weaker value optimization capacity doesn’t confer a bonus on echelon utilizers in recycling costs in Mode (II). Moreover, because of the smaller recycling value sensitivity coefficients, retailers and thirdparty recyclers select to decrease their recycling costs to be able to offset the lack of revenues ensuing from the discount in recycling portions as a consequence of the entry of echelon utilizers into the recycling market.
(3) When the competitors within the recycling channel is low and customers are extra delicate to recycling, the recycling value of Mannequin (I) is decrease than that of Mannequin (II) if the associated fee optimization coefficient is smaller. Conversely, if the associated fee optimization coefficient is bigger, the recycling value of Mannequin (I) is larger than that of Mannequin (II). It’s because the stronger costoptimization functionality makes the echelon utilizer’s recycling value considerably larger than that of the retailer and thirdparty recycler in Mode (II), and though the aggressive sensitivity coefficient of the recycling channel is smaller, the quantity of recycling adjustments considerably when the retailer and thirdparty recycler enhance their recycling value because of the bigger recycling value sensitivity coefficient, so the retailer and thirdparty recycler will enhance their recycling value in Mode (II) and thus larger than in Mannequin (I). When the associated fee optimization capacity is weak, the recycling value of the echelon utilizer in Mannequin (II) just isn’t considerably completely different from that of the retailer and the thirdparty recycler, and though the recycling value sensitivity coefficient is bigger, the retailer and the thirdparty recycler will select to decrease the recycling value to cut back the revenue loss.
Corollary 4
The optimum recycling portions for thirdparty recyclers and retailers beneath the 2 recycling fashions have a relationship as follows:

(1)
(Q_{t}^{{I^{*} }} = Q_{r}^{{I^{*} }} > Q_{t}^{{II^{*} }} = Q_{r}^{{II^{*} }});

(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 }}} proper. kern0pt} {partial beta }} = {{partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} {partial beta }}} proper. kern0pt} {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 }}} proper. kern0pt} {partial beta }} = {{partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} {partial beta }}} proper. kern0pt} {partial beta }} < 0);

(3)
({{partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} {partial rho }}} proper. kern0pt} {partial rho }} = {{partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} {partial rho }}} proper. kern0pt} {partial rho }} < 0); ({{partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (Q_{r}^{{I^{*} }} – Q_{r}^{{II^{*} }} )} {partial varphi }}} proper. kern0pt} {partial varphi }} = {{partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (Q_{t}^{{I^{*} }} – Q_{t}^{{II^{*} }} )} {partial varphi }}} proper. kern0pt} {partial varphi }} < 0)
Proof
See Online Appendix E.
Corollary 4 demonstrates that (1)the recycling portions of shops and thirdparty recyclers in Mannequin (I) and Mannequin (II) of the closedloop provide chain for the echelon recycling of energy batteries embedded within the blockchain beneath the traceability mechanism are equal once they attain optimum revenue. Moreover, the optimum recycling portions in Mannequin (I) are larger than these in Mannequin (II) because of the smaller competitors depth of the recycling channel in Mannequin (I). (2) When the residual fee (alpha) of the SPBs into the stage of dismantling and utilization is giant, the distinction between the optimum recycling portions of shops and thirdparty recyclers in Mode (I) and Mode (II) will increase with the rise of the spent energy battery’s echelon utilization fee (beta), and conversely, the distinction between the optimum recycling portions decreases with the rise of (beta). It’s because when (alpha) is bigger, the producer can get extra recycled supplies to provide energy batteries. That is extra worthwhile than utilizing uncooked supplies to provide energy batteries, which prompts the producer to provide extra energy batteries. In consequence, the recycling amount will increase. The rise in recycling amount is bigger for Mode (I), which has a decrease aggressive depth of recycling topics, than for Mode (II). This results in a higher distinction between the recycling amount of shops and thirdparty recyclers in Mode (I) and Mode (II). Quite the opposite, when (alpha) is small, producers will produce fewer energy batteries, and the variety of SPBs recycled will lower, and the lower within the variety of recycled batteries in Mode (I), the place the depth of competitors amongst recycling entities is decrease, is bigger than that in Mode (II). This leads to a lower within the distinction within the variety of recycled batteries recycled by retailers and thirdparty recyclers between Mode (I) and Mode (II). (3) As (varphi) and (rho) enhance, the distinction in recycling amount between retailers and thirdparty recyclers decreases in each Mode (I) and Mode (II). Will increase in (varphi) point out a weakened capacity for value optimization, leading to larger prices for laddering utilizers. This prompts a lower in switch costs, resulting in decreased recycling costs for retailers and thirdparty recyclers. In consequence, the amount of recycling decreases. Will increase in (rho) point out larger manufacturing prices for energy batteries, resulting in a lower within the variety of batteries produced and recycled. The lower within the variety of recycled batteries is bigger 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 aggressive depth is low and the recycling value sensitivity is excessive, the full recycled amount of retired energy batteries of Mannequin (I) is all the time smaller than that of Mannequin (II). It’s because, though the sensitivity coefficient of competitors in recycling channels is smaller, the sensitivity coefficient of recycling costs is bigger, and every recycling participant is extra delicate to cost adjustments, whereas the participation of echelon utilizers in recycling in Mode (II) can provide larger recycling costs, which attracts extra SPBs to the recycling market. (2) When the competitors amongst recycling channels is excessive and the worth sensitivity of recycling is low, and on the similar time the extent of value optimization coefficient embedded within the blockchain knowhow is low, the full amount of retired energy batteries recycled for Mannequin (I) is smaller than that for Mannequin (II). Conversely, when the competitors amongst recycling channels is larger and the worth sensitivity of recycling is decrease, and on the similar time the extent of value optimization coefficient embedded within the blockchain knowhow is larger, the full amount of retired batteries recycled for Mannequin (I) is bigger than that for Mannequin (II). This is because of the truth that when the associated fee optimization issue of blockchain knowhow is at a low stage, each echelon utilizers and producers within the two modes are inclined to set decrease switch costs and recycling costs, and though the sensitivity coefficient of competitors in recycling channels is bigger, the decrease sensitivity coefficient of recycling value makes the recycling amount of SPBs in Mode (II) larger than that in Mode (I). Nonetheless, if the associated fee optimization issue of blockchain knowhow is elevated to the next stage, the echelon utilizers and producers in each modes will enhance the switch value and recycling value accordingly, and this variation will make the recycling amount of SPBs in Mode (II) decrease than that in Mode (I). The producer should regulate the associated fee optimization coefficient primarily based on the aggressive depth of the recycling channel, value sensitivity of recycling, and recycling mode. For example, if the competitors amongst recycling members within the recycling channel is intense and customers are reasonably delicate to the recycling value, the producer ought to lower the extent of value optimization coefficient for recycling mode (II) and enhance it for recycling mode (I).
Corollary 6
The revenue relationship between the thirdparty recycler and the retailer beneath the 2 recycling fashions is as follows:

(1)
(pi_{r}^{{I^{*} }} > pi_{r}^{{II^{*} }}), (pi_{t}^{{I^{*} }} > pi_{t}^{{II^{*} }});

(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 }}} proper. kern0pt} {partial beta }} > 0), ({{partial (pi_{t}^{{I^{*} }} – pi_{t}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (pi_{t}^{{I^{*} }} – pi_{t}^{{II^{*} }} )} {partial beta }}} proper. kern0pt} {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 }}} proper. kern0pt} {partial beta }} < 0), ({{partial (pi_{t}^{{I^{*} }} – pi_{t}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (pi_{t}^{{I^{*} }} – pi_{t}^{{II^{*} }} )} {partial beta }}} proper. kern0pt} {partial beta }} < 0);

(3)
({{partial (pi_{r}^{{I^{*} }} – pi_{r}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (pi_{r}^{{I^{*} }} – pi_{r}^{{II^{*} }} )} {partial rho }}} proper. kern0pt} {partial rho }} < 0), ({{partial (pi_{t}^{{I^{*} }} – pi_{t}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (pi_{t}^{{I^{*} }} – pi_{t}^{{II^{*} }} )} {partial rho }}} proper. kern0pt} {partial rho }} < 0), ({{partial (pi_{r}^{{I^{*} }} – pi_{r}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (pi_{r}^{{I^{*} }} – pi_{r}^{{II^{*} }} )} {partial varphi }}} proper. kern0pt} {partial varphi }} < 0), ({{partial (pi_{t}^{{I^{*} }} – pi_{t}^{{II^{*} }} )} mathord{left/ {vphantom {{partial (pi_{t}^{{I^{*} }} – pi_{t}^{{II^{*} }} )} {partial varphi }}} proper. kern0pt} {partial varphi }} < 0)
Proof:
See Online Appendix G.
Corollary 6 demonstrates that: (1) Given a recycling market dimension, each retailers and thirdparty recyclers in Mannequin (I) are extra worthwhile than in Mannequin (II). That is because of the larger optimum amount of recycling in Mannequin (I) in comparison with Mannequin B, in addition to the decrease depth of competitors within the recycling channel in Mannequin (I). (2) The optimum revenue distinction between retailers and thirdparty recyclers in Mannequin (I) and Mannequin (II) will increase with (beta) when (alpha) is bigger; in any other case, it decreases with (beta). It’s because producers can get hold of extra recycled supplies when the residual fee of energy batteries getting into the dismantling and utilization stage is larger. That is extra worthwhile than utilizing uncooked supplies to provide energy batteries, which reinforces the producer’s incentive to provide and recycle. In consequence, the optimum revenue will increase successively. Mode (I), which has a decrease depth of recycling competitors, experiences a bigger revenue enhance than Mode (II). Quite the opposite, if the residual fee of energy batteries in the course of the dismantling and utilization stage is low, the producer’s manufacturing of energy batteries utilizing recycled supplies decreases. This results in a lower in marginal income, recycling incentives, and the variety of recycling, leading to a lower within the producer’s optimum revenue. The lower in revenue is bigger in Mannequin (I) than in Mannequin (II). (3) The distinction in optimum income between retailers and thirdparty recyclers in Mode (I) and Mannequin (II) decreases as (varphi) and (rho) enhance. It’s because a rise within the optimization coefficient of the processing value of the ability battery’s echelon use, (varphi), weakens the power to optimize the associated fee and will increase the price of echelon customers. This drives the switch value down, leading to a lower in optimum income for each retailers and thirdparty recyclers. A rise within the optimization issue (rho) for the processing value of energy batteries utilizing recycled supplies leads to a rise within the producer’s manufacturing value of energy batteries. This, in flip, results in a rise within the promoting and recycling costs of energy batteries. In consequence, the optimum revenue of shops and thirdparty recyclers decreases. In Mode (I), the lower in revenue is bigger 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 revenue of Mannequin (I) is bigger than that of Mannequin (II) when the aggressive depth of the recycling channel is excessive, recycling value sensitivity is low, and the extent of value optimization issue embedded within the blockchain knowhow is low. Conversely, when the aggressive depth of the recycling channel is excessive, recycling value sensitivity is low, and the extent of value optimization issue embedded within the blockchain knowhow is excessive, the revenue of Mannequin (I) is lower than that of Mannequin (II). This is because of the truth that when the associated fee optimization issue of blockchain knowhow is at the next stage, the price of the echelon utilizer will be successfully decreased, which leads it to set the next switch value or recycling value, which successfully will increase the quantity of SPBs recycled, and regardless of the upper aggressive sensitivity issue of the recycling channel, the revenue of the echelon utilizer in Mode (II) is decrease than that in Mode (I) because of the decrease delicate issue of the recycling value; Quite the opposite, when the associated fee optimization issue of the blockchain knowhow is low, the price of the echelon utilizer will enhance, thus setting a decrease switch value or recycling value, leading to a decrease recycling amount of SPBs, and when the aggressive sensitivity coefficient of the recycling channel is excessive, even when the sensitivity coefficient of the recycling value is low, the revenue of the echelon utilizer within the extra aggressive Mode (II) is bigger than that of Mode (I). (2) When the recycling channel’s aggressive depth is decrease and the worth sensitivity of recycling is larger, the echelon utilizer revenue of Mannequin (I) is all the time lower than that of Mannequin (II). It’s because though the aggressive sensitivity coefficient of the recycling channel is smaller, the worth sensitivity coefficient is bigger, and every recycling participant is extra delicate to cost adjustments, whereas the participation of echelon utilizers in recycling in Mode (II) is ready to present larger recycling costs and switch costs, which attracts extra SPBs to enter the recycling market, and thus the income of echelon utilizers in Mode (II) are larger than these 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 aggressive depth is excessive, the recycling value’s sensitivity is low, and the blockchain knowhow’s value optimization coefficient is low, the revenue of Mannequin (I) is bigger than that of Mannequin (II). Conversely, if the recycling channel’s aggressive depth is excessive, the recycling value’s sensitivity is low, and the blockchain knowhow’s value optimization coefficient is excessive, the revenue of Mannequin (I) is smaller than that of Mannequin (II). It’s because when the associated fee optimization coefficient of blockchain knowhow is at a excessive stage, the producer’s value will be successfully decreased, resulting in the setting of a better switch value, and the quantity of SPBs recycling will enhance. Regardless of the excessive aggressive sensitivity coefficient of recycling channels, the producer’s revenue in Mode (II) is smaller than that in mode (I) because of the low delicate coefficient of recycling value. With a low value optimization issue of blockchain knowhow, the producer’s value will probably be elevated, which is able to trigger it to set a decrease switch value, then the variety of SPBs recycling will probably be decreased, and regardless of the excessive aggressive sensitivity coefficient of the recycling channel, a sufficiently low sensitivity coefficient of the recycling value will result in a bigger producer revenue in Mode (II) than in Mode (I). (2) When the competitors depth within the recycling channel is decrease and the sensitivity to recycling costs is larger, the producer’s revenue in Mode (I) is all the time smaller than that in Mode (II), whatever the stage of the associated fee optimization coefficient embedded within the blockchain knowhow. This is because of the truth that, in line with Corollary 1, the producer in Mode (I) sells energy batteries at a wholesale value and in portions equal to that in Mode (II). Subsequently, the manufacturing value of energy batteries determines the revenue dimension of the 2 fashions. Primarily based on Corollary 3, the producer’s value for recycling supplies is larger in Mannequin (I) than in Mannequin (II). Subsequently, the producer’s marginal income from utilizing recycled supplies to provide energy batteries in Mannequin (I) is decrease than in Mannequin (II). Moreover, Corollary 5 states that the amount of recycled supplies in Mannequin (I) is decrease than in Mannequin (II), leading to decrease income for the producer in Mannequin (I) in comparison with Mannequin (II).
Corollary 7 and Corollary 8 exhibit that the producer and echelon utilizer can each obtain most revenue beneath the identical circumstances. Because of this when the producer earns the utmost revenue, the echelon utilizer can even earn the utmost revenue, leading to a mutually helpful end result. This supplies theoretical help for cooperation between the producer and the echelon utilizer.