Formalisation of informal collectors under a dual-recycling channel: A game theoretic approach

Abstract

Formalisation of informal collectors is beneficial for economical, environmental and social sustainability. Through dividing collectors and recyclers, a benchmark model consists of competitive dual formal and informal channels is established to quantitatively analyse the possibility of formalising informal collectors and study the formalisation extent. This study comprehensively compares the effects of respective subsidy or punishment targeting at collectors or recyclers in the extended policy model. The subsidy delay used to represent the response speed of the subsidy system is first included. This study indicates the influences of different factors on formalisation activity, including bargaining power, reluctance of informal collectors and recycling cost of formal channels. The policy model concluded that the subsidy on informal collectors or formal recyclers (punishment on informal collectors or informal recyclers) presents no difference regarding the formalisation extent. Based on numerical data, we studied the formalisation extent for the context of China and visualised the effects of different policies. The decremental effect of subsidy and the incremental effect of punishment are concluded in a formalisation activity. This study fills the gap of a quantitative study on formalisation activity and the results will comprehend the promotion of the formalisation of informal collectors.

Keywords

Waste electrical and electronic equipment collection informal collection formalisation dual-channel bargaining power

Introduction

As one of the fastest growing waste streams, waste electrical and electronic equipment (WEEE) attracts huge concern worldwide because of its potential value, environmental pollution and human safety risk (if not properly managed) (Oguchi et al., 2011; Robinson, 2009; Tsydenova and Bengtsson, 2011; Xue et al., 2012). Being aware of these, developed countries have been establishing a formal collection channel and adopted advanced recycling methodology to deal with WEEE. However, a formal collection and recycling channel is still in its infancy in most developing countries. Specific to China, informal private trades dominate more than 80% of WEEE so far (Chi et al., 2014; Tang and Wang, 2014). Most of informal collectors send the collected WEEE to informal recyclers, where the dated and environmentally unfriendly technologies are applied and poor working and living conditions are offered. Owing to these, informal recycling activities were long criticised as associated with environmental pollution and damage to workers’ health (Medina, 2000; Wilson et al., 2006).

Unlike informal recyclers, informal collectors generate little pollution to the environment. Informal collectors mainly act as gathering WEEE and carrying out simple dismantling activities. These activities are helpful and beneficial for waste collection and reduction. Several studies have pointed out that informal collectors can significantly contribute to the reduction of landfill volume and cost of the whole waste management systems (Wilson et al., 2006, 2012). Moreover, these activities can generate working opportunities for the low-income group (Linzner and Lange, 2013).

Considering the benefits of informal collectors and harmfulness of informal recyclers, one constructive proposal that we claim is to incorporate informal collectors into the formal collection and recycling channel, while expelling informal recyclers from the market. Expelling informal recyclers can reduce environmental pollution through eliminating the low-end backward equipment and technology. Incorporating informal collectors into the formal channel can benefit the income stability and social identity of informal collectors on the one hand. On the other, it can increase the collection rate with a minimised overall collection cost, which is much cheaper than expelling informal collectors through strict policy or through fierce market competition (Campos, 2014; Li and Tee, 2012). It has been concluded that incorporating the informal collectors (waste pickers activities) into the formal waste recovery system (instead of either ignoring or prohibiting their participation) is beneficial for economical, environmental and social sustainability (Besiou et al., 2012).

Even though there exists a lot of benefits, incorporation or formalisation of informal collectors is not an automatic process; it depends on the competition between formal and informal recyclers directly. Stated thus, this study is conducted to quantitatively study the possibility of formalising informal collectors and analyse the effects of different policies on promoting the formalisation activity by considering the channel competition.

The remainder of this article is organised as follows. A literature review is provided, followed by model assumptions and notations. The following sections come up with the details of the benchmark model and the policy model. The influences of different factors and the effects of different policies are analysed in these sections. Thereafter, the formalisation extent for the context of China is studied and the effects of different policies are visualised based on numerical data. Finally, we summarise our main conclusions.

Literature review

Qualitative study of formalising informal channels has been conducted previously (Serrona et al., 2014; Velis et al., 2012). By using an analytical framework and tool named ‘InteRa’, the integration of the informal recycling sector has been studied in Pakistan and Madagascar (Andrianisa et al., 2017; Masood and Barlow, 2013). Quantitative study of formalising informal channels is rare. Based on system dynamics methodology, Ghisolfi et al. (2017) modelled the formalisation of waste pickers in Brazil and concluded that the formalisation of waste pickers cooperatives is not yet enough and dependent on their bargaining power. Their study mainly focuses on measuring the impact of legal incentives and the bargaining power obtained by the volume of collected waste on the effective formalisation of waste pickers, regardless of the negative effect of informal recyclers. Comparing these, this study is the first trail to quantitatively analyse the possibility of formalising informal collectors and study the formalisation extent by considering the competition between formal and informal channels.

Channel management considering the competition is a classic theme in reverse supply chain management research. Qiu and Huang (2007) modelled both manufacturer and seller collect products and act as leader and follower in a closed-loop supply chain, respectively. Ma et al. (2016) focused on dual-channel consisting of a traditional and an Internet-based channel. In the study of Huang et al. (2013), the retailer and a third party competitively collecting used products in the reverse supply chain was analysed. Hong et al. (2014) introduced a model consisting of manufacturers, importers and sellers, and recyclers, which compete in both consuming and recycling markets.

The competition between formal and informal channels was modelled by Liu et al. (2016) and Li et al. (2017). In the study of Liu et al. (2016), a quality-based price competition model for the WEEE recycling market in a dual-channel environment comprising both formal and informal sectors is established. The equilibrium acquisition prices and effects of government subsidy in the two channels are examined under four competitive scenarios. Li et al. (2017) modelled a dual-channel collection supply chain in which consumer preference to collection channels is considered. Three governance mechanisms set by both governments and formal collectors are introduced and analysed. Our research differs from these articles by focusing on the formalisation possibility and extent of informal collectors. Besides dividing collectors and recyclers, the bargaining power between formal and informal recyclers on selling recycled materials is involved.

In order to promote proper recycling activities, different policies have been recommended and the effects of these policies have been analysed. Mitra and Webster (2008) explored the impact of subsidy on the recycling market and pointed out that subsidies should also flow partly to manufacturers owing to the harmfulness of the manufacturer’s profit when only compensating recyclers. The effectiveness of an incentive mechanism on motivating recyclers to enhance the quantity recycled has been studied by Wang and Da (2010). Both Liu et al. (2016) and Li et al. (2017) involved the subsidy on the formal channel. This study not only focused on the effect of both subsidy and punishment, but also specify the subsidy and punishment target, namely collectors or recyclers. And a comprehensive comparison of the effects along with the varying targets is analysed. Considering the tedious application process of subsidy in China (Cao et al., 2016), the subsidy delay (time between applying and receiving the subsidy) used to represent the response speed of the subsidy system is first included in this study.

Our research features innovation points as follows. (1) To the best of our knowledge, our study is the first to quantitatively analyse the possibility of formalising informal collectors and study the formalisation extent by considering the channel competition. (2) Both the subsidy and punishment on formal (informal) collectors or recyclers are included and the effects of these policies are analysed and compared. In addition, this study also includes the bargaining power between different recyclers on selling recycled materials and introduces the subsidy delay to represent the response speed of subsidy system.

Model assumptions and notations

In this study, we consider a dual-channel model consisting of formal and informal collection and recycling activities simultaneously (Figure 1).

Table 1 lists the notations used in this study. In the rest of this article, some assumptions are made.

Table 1.

Notations.

Parameter	Definition
v	Reluctance of sending WEEE to formal recyclers, 0 < v < 1.
α	Collected quantity of same kind WEEE by informal collectors, 0 ⩽ α ⩽ 1.
β	Bargaining power of the informal recycler, 0 ⩽ β ⩽ 1.
θ	Unit collection price of informal collectors when the collected quantity is α, 0 ⩽ θ.
$c_{1}$	Unit minimum recycling cost.
$c_{2}$	Unit additional cost of the formal recyclers.
P	Unit sale price of recycled materials from the formal recyclers.
$X_{i c}$	Unit punishment on informal collectors when they send WEEE to informal recyclers.
$X_{i r}$	Unit punishment on informal recyclers.
$S_{i c}$	Unit subsidy to informal collectors when they send WEEE to formal recyclers.
$S_{f r}$	Unit subsidy to formal recyclers.^a
R	Subsidy delay (owing to time delay of paying the subsidy to formal recyclers, represented as discount rate).
$P_{i}$	Unit payoff to informal collectors paid by informal recyclers.
$P_{f}$	Unit payoff to informal collectors paid by formal recyclers.
$q_{i}$	Quantity of WEEE recycled by informal recyclers.
$q_{f}$	Quantity of WEEE recycled by formal recyclers.
$q_{i f}$	WEEE sent from informal collectors to formal recyclers.

WEEE: waste electrical and electronic equipment.

Note that if the subsidy for formal recyclers only targets the WEEE from informal collectors, formal recyclers will never accept the WEEE from formal collectors. Even if they do accept these WEEE, they will cheat and claim that these WEEE are from informal collectors to gain the subsidy. Therefore, the target of this subsidy is the total quantity of WEEE recycled by formal recyclers.

Assumption 1. The total amount of the same kind of WEEE that can be collected by formal and informal collectors is 1.

Generally, three direct destinations for WEEE are collected by either formal or informal collectors directly (including all kinds of collection activities, such as door-to-door collection, retailer collection), disposed together with municipal solid waste directly and hibernated at home. The hibernation is a temporary activity and the hibernated WEEE will finally flow to the other two destinations. Therefore, only the WEEE in the former two destinations are treated as ‘the WEEE can be collected’ in this study. Because of the potential value, the directly disposed quantity of WEEE is small. Moreover, even being disposed of directly, the WEEE can always be collected indirectly by waste-pickers, one kind of informal collectors.

Assumption 2. Collectors make their decisions based on the last period payoff paid by recyclers. And the recyclers decide current payoff based on the completed collection activities in current period.

Given the last period payoff paid by recyclers, there must be a set collection price and collected quantity as an optimal solution for either formal or informal collectors. Given the collection price of informal collectors as θ (0 ⩽ θ) and the collection price of formal collectors, the corresponding collected quantity of same kind of WEEE as α and ( $1 - α$ ) for informal and formal collectors can be determined according to Assumption 1. It is noteworthy that the collection prices vary among informal collectors. For instance, different door-to-door collectors may offer different collection prices to consumers. Besides, the collection prices between a door-to-door collector and waste pickers may vary a lot, since the waste pickers pay zero apart from labour efforts. In this study, the collection prices of informal collectors are assumed continuous and evenly distributed.

Based on the completed current collection activities, the amount of WEEE collected by both formal and informal collectors are determined. According to the known collected quantity, the formal and informal recyclers will compete with each other in order to maximise their profit.

Assumption 3. Informal collectors have incentives to send the collected WEEE to formal recyclers.

Informal collectors are always treated as pure profit-seekers. Compared with formal recyclers, informal recyclers would pay informal collectors more to gain their WEEE. Under such conditions, the informal collector prefers to send WEEE to informal recyclers. However, the payoff by informal recyclers is highly relevant to the quantity and quality of WEEE, which is uncertain and influenced by the up-front, such as the attitude and behaviour of consumers. Hence, the revenue of informal collectors is uncertain and risky if they choose to do business with informal recyclers. Besides, informal collectors and informal recyclers are always regarded as dirty, unregulated and environmental troublemakers (Ezeah et al., 2013; Wilson et al., 2006). Relevant practitioners often feel inferior to others owing to a lack of social identity. In contrast, if being formalised, the revenue risk of informal collectors can be reduced and the social identity of them can be improved even though the direct unit payoff is relatively low. For instance, the formal recycler can provide a minimum salary to informal collectors to reduce their income risk and uncertainty once being formalised. Considering these, this study assumes that informal collectors have incentives to send the collected WEEE to formal recyclers to a certain extent.

Assume the reluctance of sending WEEE to formal recyclers as v, and v is a discounted rate of the collection price θ. Given the payoff paid by formal and informal recyclers as $P_{f}$ and $P_{i}$ , the utility of informal collectors can be denoted as $U_{f (θ)} = P_{f} - v θ$ or $U_{i (θ)} = P_{i} - θ$ when sending WEEE to formal or informal recyclers.

Considering informal collectors only trade with some economic gains, it can be concluded that the informal collector will send WEEE to formal recyclers only if the following condition is satisfied ${θ | U_{f (θ)} \geq U_{i (θ)}, U_{f (θ)} \geq 0, (P_{f} - θ) \geq 0}$ . Likewise, they will choose informal recyclers as a destination when the utility satisfies ${θ | U_{i (θ)} \geq U_{f (θ)}, U_{i (θ)} \geq 0}$ .

Accordingly, when

P_{f} > \frac{P_{i}}{2 - v}

the informal collector who offers a collection price among

[\frac{P_{i} - P_{f}}{1 - v}, P_{f}]

will choose formal recyclers as their destination, while the informal collector who offers a collection price among

[0, \frac{P_{i} - P_{f}}{1 - v}]

prefers sending WEEE to informal recyclers. When

v P_{i} < P_{f} \leq \frac{P_{i}}{2 - v}

and $P_{f} v P_{i}$ , the informal collector will never consider formal recyclers as their destination while the informal collector offers a collection price among

[0, \frac{P_{i} - P_{f}}{1 - v}]

and [ $0, P_{i}$ ] will choose informal recyclers.

Assumption 4. Formal collectors will only send the collected WEEE to formal recyclers. Informal collectors have two choices, either sending the collected WEEE to formal or informal recyclers. And both of them will clean up the stock of all the collected WEEE in each period.

Based on the above assumptions, the total amount of WEEE received by formal and informal recyclers can be summarised as follows:

q_{f} = {\begin{matrix} α \frac{(2 - v) P_{f} - P_{i}}{P_{f} (1 - v)} + (1 - α) P_{f} > \frac{P_{i}}{2 - v} \\ 1 - α v P_{i} < P_{f} \leq \frac{P_{i}}{2 - v} \\ 1 - α P_{f} \leq v P_{i} \end{matrix}

(1)

q_{i} = {\begin{matrix} α \frac{(P_{i} - P_{f})}{P_{f} (1 - v)} P_{f} > \frac{P_{i}}{2 - v} \\ α v P_{i} < P_{f} \leq \frac{P_{i}}{2 - v} \\ α P_{f} \leq v P_{i} \end{matrix}

(2)

Assumption 5. The formal recycler will offer the same payoff to either the formal or informal collectors.

Apparently, the unequal payoff will disorder the participation of either the formal or informal collectors.

Assumption 6. A low bargaining power is assigned to informal recyclers.

Generally, the formal recycler is the one who has advanced equipment and technology, with which more pure and higher quality materials can be recycled. Upon the promotion of formal recycling from the governments’ side, the possibility and efficiency of the formal recycler to get access to sufficient cash flow can be improved. In contrast, the informal recycler is always recognised as backyard working associated with dated technology and small scale (Chi et al., 2011; Ezeah et al., 2013; Wilson et al., 2006). The higher quality of recycled materials and the sufficient cash flow providing the formal recycler a higher bargaining power on selling recycled materials.

Given the sale price of the formal recycler as P, the sale price of the informal recycler will be βP given a lower bargaining power as β. Therefore, the average benefit of the informal and formal recyclers are $B_{i} = β P - P_{i} - c_{1}$ and $B_{f} = P - P_{f} - c_{1} - c_{2}$ , where $c_{1}$ is the minimum recycling cost for each recycler and $c_{2}$ is the additional cost for formal recyclers. The additional cost mainly consists of environmental protection and waste treatment cost. The average benefit $B_{i}$ and $B_{f}$ are both no less than zero, otherwise, neither formal nor informal recyclers will conduct the recycling activity.

Combining with the quantity, the profit function of the formal and informal recyclers are as follows:

π_{f} = (\begin{array}{l} P - P_{f} \\ - c_{1} - c_{2} \end{array}) * {\begin{matrix} α \frac{(2 - v) P_{f} - P_{i}}{P_{f} (1 - v)} + (1 - α) P_{f} > \frac{P_{i}}{2 - v} \\ 1 - α v P_{i} < P_{f} \leq \frac{P_{i}}{2 - v} \\ 1 - α P_{f} \leq v P_{i} \end{matrix}

(3)

π_{i} = (β P - P_{i} - c_{1}) * {\begin{matrix} α \frac{(P_{i} - P_{f})}{P_{f} (1 - v)} P_{f} > \frac{P_{i}}{2 - v} \\ α v P_{i} < P_{f} \leq \frac{P_{i}}{2 - v} \\ α P_{f} \leq v P_{i} \end{matrix}

(4)

When

v P_{i} < P_{f} \leq \frac{P_{i}}{2 - v}

and $P_{f} \leq v P_{i}$ , informal collectors will never send the collected WEEE to formal recyclers, which means the formalisation extent is zero under such condition. Only when

P_{f} > \frac{P_{i}}{2 - v}

the informal collector chooses to send WEEE to formal recyclers, and the formalisation extent is varied accordingly. Considering the main target of this study, we will focus on the condition of

P_{f} > \frac{P_{i}}{2 - v}

in the following sections.

Benchmark model

The formal recycler is considered as the Stackelberg leader in the competition with informal recyclers. In the formal recycler Stackelberg game model, the formal recycler decides its optimal price $P_{f}$ first. Then, the informal recycler makes its pricing decision $P_{i}$ based on the optimal price $P_{f}$ . The model is formulated as follows:

{\begin{matrix} F i r s t : \max π_{f} (P_{f}) \\ T h e n : \max π_{i} (P_{i}) \\ s . t . P_{f} > \frac{P_{i}}{2 - v} \end{matrix}

(5)

Proposition 1 (Proof in Appendix A)

When

\sqrt{\frac{α (P - c_{1} - c_{2}) (β P - c_{1})}{2 (1 - v) (1 - α) + α (3 - 2 v)}} > \frac{β P - c_{1}}{3 - 2 v}

is satisfied, the optimal price is

\begin{array}{l} P_{f} = \sqrt{\frac{α (P - c_{1} - c_{2}) (β P - c_{1})}{2 (1 - v) (1 - α) + α (3 - 2 v)}}, \\ and P_{i} = \frac{β P - c_{1}}{2} + \frac{1}{2} \sqrt{\frac{α (P - c_{1} - c_{2}) (β P - c_{1})}{2 (1 - v) (1 - α) + α (3 - 2 v)}} \end{array}

the received WEEE by the formal and informal recyclers are as follows:

\begin{array}{l} q_{f} = - \frac{1}{2 (1 - v)} \sqrt{\frac{α (β P - c_{1}) [2 (1 - v) (1 - α) + α (3 - 2 v)]}{P - c_{1} - c_{2}}} \\ + \frac{α (3 - 2 v)}{2 (1 - v)} + (1 - α) \end{array}

(6)

q_{i} = \frac{1}{2 (1 - v)} \sqrt{\frac{α (β P - c_{1}) [\begin{array}{l} 2 (1 - v) (1 - α) \\ + α (3 - 2 v) \end{array}]}{P - c_{1} - c_{2}}} - \frac{α}{2 (1 - v)}

(7)

\begin{array}{l} q_{i f} = - \frac{1}{2 (1 - v)} \sqrt{\frac{α (β P - c_{1}) [\begin{array}{l} 2 (1 - v) \\ (1 - α) + α (3 - 2 v) \end{array}]}{P - c_{1} - c_{2}}} \\ + \frac{α (3 - 2 v)}{2 (1 - v)} \end{array}

(8)

Corollary 1. A high bargaining power of informal recyclers acts as an obstacle for the formalisation activity.

Proof of Corollary 1

\frac{\partial q_{f}}{\partial β} < 0, \frac{\partial q_{i f}}{\partial β} < 0, \frac{\partial q_{i}}{\partial β} > 0

The partial differential results indicate that the WEEE recycled by formal recyclers decreases as the bargaining power of informal recyclers increases.

In order to promote the formalisation activity, it is important to comprehend and restrict the bargaining power of the informal recycler. On one hand, the government can regulate the recycling materials market directly by introducing a recycled material label. Only the recycled materials with the label can be freely traded in the market. On the other hand, the development of alliances between the formal recycler and the market can be promoted from the government perspective. A recycled material label and a strong alliance may decrease the bargaining power of informal recyclers through influencing their sales convenience.

Corollary 2. Formalisation extent of the informal collector decreases as the increasing additional cost of formal recyclers.

Proof of Corollary 2

It can be derived that

\frac{\partial q_{i f}}{\partial c_{2}} < 0, \frac{\partial q_{f}}{\partial c_{2}} < 0, \frac{\partial q_{i}}{\partial c_{2}} < 0

The additional cost mainly consists of environmental protection and waste treatment cost. In terms of policy, a cost sharing system can be a possible countermeasure. The government can undertake the additional cost directly or share the cost through subsidy or tax reduction. In terms of technology, more cost-efficient technologies should be developed and adopted by formal recycling activity. By perfecting the management system and adopting advanced technology, it is anticipated that a higher formalisation extent of informal collectors can be achieved owing to the decreased additional cost.

Corollary 3. A high sale price enlarges the payoff to informal collectors

(\frac{\partial P_{f}}{\partial P} > 0, \frac{\partial P_{i}}{\partial P} > 0)

while a high minimum recycling cost has the opposite influence

(\frac{\partial P_{f}}{\partial c_{1}} < 0, \frac{\partial P_{i}}{\partial c_{1}} < 0)

For the collectors, a high sale price and a low minimum recycling cost are preferred. However, the quantity of WEEE recycled by either formal or informal recyclers is uncertain.

Corollary 4. Increasing the WEEE collected by the informal collector (α) (increasing the reluctance of sending WEEE to formal recyclers v) will enlarge the payoff paid by both the formal and informal recyclers. And the change of payoff paid by the formal recycler is twice the one paid by the informal recycler.

Proof of Corollary 4

It can be derived that

\begin{array}{l} \frac{\partial P_{f}}{\partial α} > 0, \frac{\partial P_{i}}{\partial α} > 0, and \frac{\partial P_{f}}{\partial α} = 2 \frac{\partial P_{i}}{\partial α}; \\ \frac{\partial P_{f}}{\partial v} > 0, \frac{\partial P_{i}}{\partial v} > 0, and \frac{\partial P_{f}}{\partial v} = 2 \frac{\partial P_{i}}{\partial v} . \end{array}

However, it is unclear whether

\frac{\partial q_{i f}}{\partial α}, \frac{\partial q_{f}}{\partial α}, \frac{\partial q_{i}}{\partial α}, \frac{\partial q_{i f}}{\partial v}, \frac{\partial q_{f}}{\partial v} or \frac{\partial q_{i}}{\partial v}

is bigger than zero or not.

Increasing the collected quantity of WEEE enlarges the market share of the informal collector. To attract informal collectors, the formal and informal recyclers have to compete with each other fiercely. Such competition will enlarge the economic burden of the formal recycler, and damage the sustainable development of formal reverse logistics. It is noteworthy that the quantity of WEEE recycled by the formal recycler is not yet clear. This result gives a hint to the formal collection and the recycling industry, even though the formalisation of informal collectors is a good choice, informal collectors should not be the only one in the market. Moderate competition, in other words, a certain number of formal collectors are necessary to reduce the economic burden.

To reduce the reluctance of sending WEEE to formal recyclers, propaganda and education will play a big role. Most of the studies have pointed out the importance of propaganda and education in waste management from the public awareness perspective (Cao et al., 2016; Qu et al., 2013; Sun et al., 2015). In terms of the specific propaganda and education content, it can specify the stabilised revenue and improved social identity for informal collectors if being formalised. In addition, it will be more convincing if the local or central government can actively and openly support and endorse the formalisation.

Subsidy and punishment policy model

In order to promote the formalisation of informal collectors, several policies are proposed and discussed. They are the punishment of informal collectors based on the quantity of WEEE sent to informal recyclers, punishment on informal recyclers based on the recycled quantity, subsidy to informal collectors based on the quantity of WEEE sent to formal recyclers, and subsidy to formal recyclers based on the recycled quantity.

Similar to the ‘Benchmark model’ section, we only focus on the condition when the informal collectors sending WEEE to formal recyclers.

The summarised optimal results are as follows:

P_{f}^{'} = \sqrt{\frac{\begin{array}{l} α (P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c}) \\ (β P - c_{1} - X_{i c} - X_{i r}) \end{array}}{2 (1 - v) (1 - α) + α (3 - 2 v)}} - S_{i c}

(9)

and

P_{i}^{'} = \frac{1}{2} \sqrt{\frac{\begin{array}{l} α (P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c}) \\ (β P - c_{1} - X_{i c} - X_{i r}) \end{array}}{2 (1 - v) (1 - α) + α (3 - 2 v)}} + \frac{β P - c_{1} + X_{i c} - X_{i r}}{2}

(10)

Meanwhile,

\begin{array}{l} q_{f}^{'} = - \frac{1}{2 (1 - v)} \sqrt{\frac{\begin{array}{l} α (β P - c_{1} - X_{i c} - X_{i r}) \\ [2 (1 - v) (1 - α) + α (3 - 2 v)] \end{array}}{P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c}}} \\ + \frac{α (3 - 2 v)}{2 (1 - v)} + (1 - α) \end{array}

(11)

q_{i}^{'} = \frac{1}{2 (1 - v)} \sqrt{\frac{\begin{array}{l} α (β P - c_{1} - X_{i c} - X_{i r}) \\ [2 (1 - v) (1 - α) + α (3 - 2 v)] \end{array}}{P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c}}} - \frac{α}{2 (1 - v)}

(12)

q_{i f}^{'} = - \frac{1}{2 (1 - v)} \sqrt{\frac{\begin{array}{l} α (β P - c_{1} - X_{i c} - X_{i r}) \\ [2 (1 - v) (1 - α) + α (3 - 2 v)] \end{array}}{P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c}}} + \frac{α (3 - 2 v)}{2 (1 - v)}

(13)

where the condition of

\sqrt{\frac{\begin{array}{l} α (P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c}) \\ (β P - c_{1} - X_{i c} - X_{i r}) \end{array}}{2 (1 - v) (1 - α) + α (3 - 2 v)}} > \frac{β P - c_{1} - X_{i c} - X_{i r}}{3 - 2 v}

should be satisfied.

In other words

\begin{array}{l} β^{'} < \frac{α {(3 - 2 v)}^{2} (P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c})}{P [2 (1 - v) (1 - α) + α (3 - 2 v)]} + \frac{c_{1} + X_{i c} + X_{i r}}{P} \\ v' < \frac{3}{2} - \frac{(β P - c_{1} - X_{i c} - X_{i r}) +}{4 α (P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c})} - \\ \frac{\sqrt{\begin{array}{l} {(β P - c_{1} - X_{i c} - X_{i r})}^{2} - 4 α (1 - α) \\ (P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c}) (β P - c_{1} - X_{i c} - X_{i r}) \end{array}}}{4 α (P - c_{1} - c_{2} + \frac{S_{f r}}{R} + S_{i c})} \end{array}

should be satisfied.

The total profit of the formal and informal recyclers are:

{π^{'}}_{f} = (P - P_{f}^{'} - c_{1} - c_{2} + \frac{S_{f r}}{R}) * {q^{'}}_{f}

(14)

π_{i}^{'} = (β P - P_{i}' - c_{1} - X_{i r}) * q_{i}^{'}

(15)

Note that the upper comma is used to distinguish the results of this section with the ‘Benchmark model’ section.

Corollary 5. Both subsidy and punishment policies are conducive to provide a low threshold for the achievement of formalisation.

Comparing $β^{'}$ and $β$ , $v^{'}$ and $v$ , we can find that both the boundary of $β^{'}$ and $v^{'}$ are expanded ( $β^{'} \geq β$ , $v^{'} \geq v$ ). $β^{'}$ or $β$ is the bargaining power of the informal recycler, $v^{'}$ or $v$ is the reluctance of sending WEEE to formal recyclers. The expanded $β^{'}$ and $v^{'}$ indicate a lower threshold for the formalisation of informal collectors. In developing countries, the environmental awareness of the whole society is low, the supervision system is in its infancy, and the education and propaganda of formal channel are not yet mature. All of these may result in a high bargaining power of informal recyclers and a high reluctance of informal collectors. As a consequence, it becomes impossible to implement the formalisation of informal collectors. However, the subsidy or punishment policies provide a lower threshold for the achievement of the formalisation activity.

Corollary 6. Both the subsidy and punishment policies can promote the formalisation of informal collectors. And there is no difference between the subsidy to informal collectors and formal recyclers (punishment on informal collectors or informal recyclers) regarding the change of recycling quantity.

Proof of Corollary 6

\begin{array}{l} \frac{\partial q_{f}^{'}}{\partial S_{i c}} = \frac{\partial q_{f}^{'}}{\partial (\frac{S_{f r}}{R})} > 0, \frac{\partial q_{f}^{'}}{\partial X_{i c}} = \frac{\partial q_{f}^{'}}{\partial X_{i r}} > 0; \\ \frac{\partial q_{i f}^{'}}{\partial S_{i c}} = \frac{\partial q_{i f}^{'}}{\partial (\frac{S_{f r}}{R})} > 0, \frac{\partial q_{i f}^{'}}{\partial X_{i c}} = \frac{\partial q_{i f}^{'}}{\partial X_{i r}} > 0; \\ \frac{\partial q_{i}^{'}}{\partial S_{i c}} = \frac{\partial q_{i}^{'}}{\partial (\frac{S_{f r}}{R})} < 0, \frac{\partial q_{i}^{'}}{\partial X_{i c}} = \frac{\partial q_{i}^{'}}{\partial X_{i r}} < 0 . \end{array}

Corollary 7. Subsidy (punishment) policy increases (decreases) the payoff paid by informal (formal) recyclers. And subsidy to formal recyclers increases the payoff paid by formal recyclers while the punishment on informal recycler decreases the payoff paid by informal recyclers. Moreover, the payoff paid by formal (informal) recyclers increases (decreases) rapidly when the subsidy (punishment) target is formal (informal) recyclers rather than informal collectors.

Proof of Corollary 7

\begin{array}{l} \frac{\partial P_{f}^{'}}{\partial X_{i c}} = \frac{\partial P_{f}^{'}}{\partial X_{i r}} < 0, \frac{\partial P_{f}^{'}}{\partial (\frac{S_{f r}}{R})} > 0, \frac{\partial P_{f}^{'}}{\partial (\frac{S_{f r}}{R})} > \frac{\partial P_{f}^{'}}{\partial S_{i c}}; \\ \frac{\partial P_{i}^{'}}{\partial S_{i c}} = \frac{\partial P_{i}^{'}}{\partial (\frac{S_{f r}}{R})} > 0, \frac{\partial P_{i}^{'}}{\partial X_{i r}} < 0, \frac{\partial P_{i}^{'}}{\partial X_{i r}} < \frac{\partial P_{i}^{'}}{\partial X_{i c}} . \end{array}

Corollary 8. Subsidy delay (represented as discount rate R) hinders the formalisation of informal collectors.

Proof of Corollary 8

After calculation

$\frac{\partial q_{i f}^{'}}{\partial R} <$ 0, $\frac{\partial q_{f}^{'}}{\partial R} <$ 0, $\frac{\partial q_{i}^{'}}{\partial R} >$ 0

Taking China for example, the Chinese government has launched a subsidy policy for formal collection and recycling activities. However, a tedious process to apply and grant the subsidy has been pointed out (Cao et al., 2016). If the formal channel plans to try to formalise informal collectors, a simplified and effective subsidy verification and grant system should be developed.

Numerical model

Regarding the collection of WEEE in China, informal collection and recycling activities are universal. In order to study the formalisation extent for the context of China and visualise the effects of different policies, the following numerical data is employed based on the situation of China. It is reported that more than 80% of WEEE collected in China still depends on informal private traders ( $α = 0.8$ ) such as street peddles (Chi et al., 2014; Tang and Wang, 2014). Meanwhile, because of the lack of pressure from the public and the government perspective, the reluctance of sending WEEE to formal recyclers is relatively high ( $v = 0.9$ ). It has been argued that the environmental protection and waste treatment cost occupies a huge proportion of the total recycling cost for formal recyclers ( $c_{2} / c_{1} = 0.75, c_{1} = 0.2, c_{2} = 0.15$ ). The sale price of the formal recycler is standardised as $P = 1$ . Considering the lack of regulation and supervision for the market of recycled materials, we consider a relatively high bargaining power of the informal recycler ( $β = 0.9$ ). It can be found that these parameters make the condition satisfied in the benchmark model and policy model.

According to the benchmark model, it is calculated that $q_{f} = 0.359$ , $q_{i f} = 0.159$ , $q_{i} = 0.641$ , $P_{f} = 0.603$ , $P_{i} = 0.652$ , $π_{f} = 0.017$ and $π_{i} = 0.031$ . Only a small part of WEEE will be sent to formal recyclers from informal collectors ( $q_{i f} = 0.159$ ) if formalisation of informal collectors is promoted, and the total profit of the informal recycler is almost twice that of the formal recycler.

The effects of independent subsidy or punishment are analysed respectively based on the given numerical data. We discussed how much the unit subsidy or punishment level is required, respectively, to promote the formalisation to a certain level (Figure 2). The results show that if less than 0.6 WEEE recycled by formal recyclers is achieved from the current level (0.359 WEEE), the same unit subsidy or punishment level is required, in other words, the punishment and subsidy have the same efficiency. However, a higher subsidy level is required if more than 0.6 WEEE recycled by formal recyclers is achieved from the current situation (0.359 WEEE). This means that the punishment outperforms the subsidy for formalisation. As the extent of formalisation is increased, the increasing trend of the subsidy is accelerated, while the increasing trend of punishment slows down. This indicates the decremental effect of subsidy and the incremental effect of punishment on the formalisation extent. This phenomenon yet exists even changing the value of each parameter (Figure 3). Moreover, considering the tedious process of subsidy for formal recyclers, the subsidy level is increased by R-fold (Figure 2). Apparently, a simplified subsidy process for the formal recyclers may be helpful.

In addition, the total profit of the formal and informal recyclers is calculated based on the given data: $P = 1, v = 0.9, β = 0.9, α = 0.8, c_{1} = 0.2, c_{2} = 0.15$ (Figure 4). The results show that subsidy and punishment will increase (decrease) the total profit of both. And the efficiency is almost the same regarding the total profit of the informal recycler. However, the subsidy will outperform the punishment in terms of the total profit of the formal recycler. A sensitivity study regarding varying values of these parameters further proves the robustness of this conclusion (Results of sensitivity study shown in Appendix B Figure 5).

Considering the difficulty of implementation, the subsidy may be better than the punishment. More importantly, the subsidy can enlarge the total profit of the formal recycler, with which the enthusiasm of the formal recycler can be inspired and improved. However, it is noteworthy that the huge subsidy may bring a heavy financial burden on sustainable development of formal collection and recycling activities.

Conclusion

Informal collection and recycling of WEEE are prevailing in many developing countries where a formal channel is in its infancy. Formalisation of informal collectors has been concluded as beneficial for economical, environmental and social sustainability. Considering these, this study was conducted to quantitatively study the possibility of formalising informal collectors and analyse the effects of different policies on promoting the formalisation activity. It is concluded that formalisation of informal collectors is influenced by several factors, including bargaining power, reluctance of informal collectors and recycling cost of the formal channel. This study also indicates the decremental effect of subsidy and the incremental effect of punishment on promoting formalisation activity, and points out that the subsidy on informal collectors or formal recyclers (punishment on informal collectors or informal recyclers) presents no difference regarding the formalisation extent.

Accordingly, it is expected that the formalisation of informal collectors can be promoted by several possible countermeasures, including labelling the recycled material, building alliances between the formal recycler and the market, developing a cost-sharing system and launching a suitable subsidy or punishment policy. Through these countermeasures, the formalisation of informal collectors can be promoted. This study is beneficial for the development of appropriate channels for WEEE collection and recycling, especially in developing countries where informal collectors are abundant.

Footnotes

Appendix A

Appendix B

Through the numerical model, it indicates that both the subsidy and punishment will increase (decrease) the total profit of the formal (informal) recycler. And the effect extent is almost the same regarding the total profit of the informal recycler. However, the subsidy will outperform the punishment in terms of the total profit of the formal recycler. We further conducted a series of sensitivity studies to discuss the robustness of this conclusion. Through control varieties, we changed the value of each parameter and drew the figure with the results from sensitivity study (Figure 5). The sensitivity study showed the same conclusion and further proved the robustness of this conclusion.

Acknowledgements

The authors would like to express their sincere thanks to the programme of ‘Akita University New Frontier Leaders for Rare-Metals and Resources’.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Juntao Wang

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