13 Study of Formalization of Informal Collectors …
183
Proof of Corollary 2.
It is easily to derive that
∂q f
∂c 2
=
−(3−2v)
4(1−v)
< 0,
∂q i
∂c 2
=
1
4(1−v)
> 0.
Meanwhile,
∂ P f
∂c 2
= −
1
2
< 0,
∂ P i
∂c 2
= −
1
4
< 0 the payoff from the formal recycler
decreases more rapidly than from the informal recycler as the increasing additional
cost for formal recyclers and increases as the increasing sell price. The informal
collector is profit-seeker, they will choose to send the collected WEEE to informal
recyclers rather formal recyclers encountering with such payoff change.
The decreasing additional cost is necessary for the formalization extent. The
additional cost only consists of environmental protection cost and waste treatment
cost. From the technology point of view, more advanced cost-efficient technology
should be invented to optimize the cost spared to environmental protection. Besides
the technology, the share of the cost will be one possible solution. The government can
undertake the waste treatment cost for the formal recyclers directly or share the cost
through subsidy or tax reduction. It is believed that the reduction of additional cost
can be achieved through above solutions, which will result in a better formalization
extent of informal collection activities.
Corollary 3. Improving the reluctance of sending WEEE to formal recyclers will
enlarge the payoff cost of both the formal recycler and informal recycler. And the
change of payoff cost from the formal recycler is as twice as the one from the informal
recycler.
Proof of Corollary 3.
It can be derived that
∂ P f
∂v
=
β P−c 1
(3−2v)
2 > 0,
∂ P i
∂v
=
β P−c 1
2(3−2v)
2 > 0, and
∂ P f
∂v
= 2
∂ P i
∂v
.
Meanwhile, it is unclear whether
∂q f
∂v
or
∂q i
∂v
is bigger than zero or not
∂q f
∂v
=
(P−c1−c2)−(β P−c 1 )
4(1−v)
2
,
∂q i
∂v
=
4(14v
2 −35v+22)(β P−c 1 )−(3−2v)(P−c1−c2)
4(3−2v)
2 (1−v)
2
.
The formal and informal recyclers compete with each other for the WEEE. To
gather more WEEE from the consumer directly, more money should be paid to
consumers. The one who offers a higher payoff will succeed in gathering more
WEEE. Such competition will be a vicious circle, which is bad for both the formal
and informal recyclers from their economy point of view. This leads to an increased
cost for both the formal and informal recyclers, and their profit will be squeezed at
last given the constant revenue from the market. Therefore, such vicious circle will
damage the sustainable development of reverse logistics. It is noteworthy that the
change of the overall recycled amount of WEEE by either the formal or informal
recyclers is not clear.
13.4 Conclusion
Informal collection and recycling of WEEE are prevailing in many developing countries. The informal collection and recycling activities are particularly serious in China.
183
Proof of Corollary 2.
It is easily to derive that
∂q f
∂c 2
=
−(3−2v)
4(1−v)
< 0,
∂q i
∂c 2
=
1
4(1−v)
> 0.
Meanwhile,
∂ P f
∂c 2
= −
1
2
< 0,
∂ P i
∂c 2
= −
1
4
< 0 the payoff from the formal recycler
decreases more rapidly than from the informal recycler as the increasing additional
cost for formal recyclers and increases as the increasing sell price. The informal
collector is profit-seeker, they will choose to send the collected WEEE to informal
recyclers rather formal recyclers encountering with such payoff change.
The decreasing additional cost is necessary for the formalization extent. The
additional cost only consists of environmental protection cost and waste treatment
cost. From the technology point of view, more advanced cost-efficient technology
should be invented to optimize the cost spared to environmental protection. Besides
the technology, the share of the cost will be one possible solution. The government can
undertake the waste treatment cost for the formal recyclers directly or share the cost
through subsidy or tax reduction. It is believed that the reduction of additional cost
can be achieved through above solutions, which will result in a better formalization
extent of informal collection activities.
Corollary 3. Improving the reluctance of sending WEEE to formal recyclers will
enlarge the payoff cost of both the formal recycler and informal recycler. And the
change of payoff cost from the formal recycler is as twice as the one from the informal
recycler.
Proof of Corollary 3.
It can be derived that
∂ P f
∂v
=
β P−c 1
(3−2v)
2 > 0,
∂ P i
∂v
=
β P−c 1
2(3−2v)
2 > 0, and
∂ P f
∂v
= 2
∂ P i
∂v
.
Meanwhile, it is unclear whether
∂q f
∂v
or
∂q i
∂v
is bigger than zero or not
∂q f
∂v
=
(P−c1−c2)−(β P−c 1 )
4(1−v)
2
,
∂q i
∂v
=
4(14v
2 −35v+22)(β P−c 1 )−(3−2v)(P−c1−c2)
4(3−2v)
2 (1−v)
2
.
The formal and informal recyclers compete with each other for the WEEE. To
gather more WEEE from the consumer directly, more money should be paid to
consumers. The one who offers a higher payoff will succeed in gathering more
WEEE. Such competition will be a vicious circle, which is bad for both the formal
and informal recyclers from their economy point of view. This leads to an increased
cost for both the formal and informal recyclers, and their profit will be squeezed at
last given the constant revenue from the market. Therefore, such vicious circle will
damage the sustainable development of reverse logistics. It is noteworthy that the
change of the overall recycled amount of WEEE by either the formal or informal
recyclers is not clear.
13.4 Conclusion
Informal collection and recycling of WEEE are prevailing in many developing countries. The informal collection and recycling activities are particularly serious in China.