Trade in Used Durables and Recycling Policies∗
Keisaku Higashida†
September 10, 2013
Abstract
Assuming that durable goods can be used for two periods, we examine the
effects of recycling policies on prices and consumption quantities of both new and
used goods, the quantity of recycling, the amount of waste disposed of into landfills.
Taking into consideration three recycling policies, a disposal fee, a recycling subsidy,
and a sales tax on new goods, we also consider what kind of combination of recycling
policies is the most effective. We demonstrate that the effect of a disposal fee is
different from that of a recycling subsidy in particular on the consumption quantity
of used goods: the former increases the quantity, while the latter decreases it.
Therefore, the optimal combination is the disposal fee and the sales tax on new
goods. Moreover, we find that the superiority of the combination holds when used
goods are internationally traded as far as recycling policies of importing countries
and an export quota function well as intended. However, when those policies do not
function effectively, it may be that the recycling subsidy should be adopted instead
of the disposal fee.
Keywords: Disposal fee, recycling subsidy, trade in used goods, used durables.
JEL Code: F13, F18, Q53.
∗
We would like to thank Rüdiger Pethig, Jota Ishikawa, Taiji Furusawa, Akira Hibiki, Naoto Jinji, and
all participants of the Summer Workshop on Economic Theory 2012 at Otaru University of Commerce,
the 13th conference of Association of Public Economic Theory at Lisbon, and the seminars at National
Institute for Environmental Studies and Kyoto University. We gratefully acknowledge financial support
from Japan Society for the Promotion of Science (JSPS) under Grant-in-Aid for Scientific Research (B)
23330087.
†
School of Economics, Kwansei Gakuin University, 1-155, Ichiban-cho, Uegahara, Nishinomiya, Hyogo
662-8501, Japan. Email: keisaku@kwansei.ac.jp
1
1
Introduction
Consumers buy and sell used durable goods, such as vehicles and computers, in their daily
lives. Dealers of used goods buy them from consumers, and decide whether they sell them
to consumers for secondhand use or to recyclers for dismantling, recycling, and disposing.
When recyclers dismantle used goods, they can extract resources and used parts from
which they make profits. Thus, even if used goods are not broken and can be used as
secondhand, they are sometimes dismantled. In other words, consumers of used durables
and recyclers compete for used durables supplied by other consumers.
The first purpose of this paper is to examine the effects of recycling policies on prices
and consumption quantities of both new and used durable goods, the quantity of recycled
durables, the amount of waste disposed of into landfills, in the presence of the market of
used goods. Moreover, we consider what kind of combination of recycling policies is the
most effective in terms of welfare.
One important trend in terms of economics on used durables is that the transboundary movement of used goods from developed to developing countries has increased substantially in the last few decades.1 Importantly, imported used goods frequently contain
hazardous substances, and upon dismantling and recycling in importing/developing countries, often account for serious environmental pollution. The reasons are as follows. First,
in developing countries, the recycling sector is informal and usually unskilled-labor intensive. Persons engaged in recycling in developing countries prefer pecuniary gains to
environmental protection and generally have little understanding of the toxicity of hazardous substances. Therefore, they extract materials to acquire income without taking
due care of the environment. Second, in some developing countries, environmental and
recycling policies have not been enforced yet. Or, even if they are implemented, they do
not function well as intended because of imperfect monitoring and corruption.
1
See Wong et al. (2007), Ray (2008), Shinkuma and Huong (2009), Kellenberg (2010), Ichinose et al.
(2013), and Higashida and Managi (2013), among others, for real-world situations concerning the trade
in used goods and wastes.
2
The second purpose of this paper is to examine the effects of recycling policies when
used durable goods are internationally traded. We also compare the effective combination
of recycling policies in the presence of trade in used goods with that in the absence of the
trade.
To achieve our goal, there are four features of this paper. First, we apply the model
of vertical quality differentiation to the situation in which both new and used durable
goods are consumed. Clerides and Hadjiyiannis (2008) examined trade in used durables
and demonstrated that a quality standard can be a kind of trade-related policies: the
government may use it to protect the profits of domestic firms at the sacrifice of foreign
firms.2 We extend their analysis by introducing a recycling sector. When new goods had
been used for one period, they can be sold to consumers again or recyclers. In other
words, even if a durable good can be used for another period, it may be dismantled
because recyclers can make profits by extracting resources/used parts from the good and
selling them to resource buyers.
Second, following the existing literature, we consider three kinds of recycling policies:
disposal fee, recycling subsidy, and sales tax on new durable goods.3 Several studies have
been analyzing the optimal combination of recycling policies (Dinan, 1993, Fullerton
and Kinnaman, 1995, Ino, 2011). Those existing literature found that when markets
are perfectly competitive, a disposal fee and a combination of a recycling subsidy and a
consumption tax have the same effect, and both types of policies can maximize welfare if
they are set equal to the social marginal cost. However, when there are some additional
factors, such as illegal disposal, the latter policy may be superior to the former one.
Third, when we take into consideration trade in used durable goods, we consider situations in which recycling policies in importing countries and/or trade restriction do not
function effectively as intended. Copeland (1991) analyzed this situation in the frame2
In the literature of trade and the environment, there are many studies which use this type of model.
See Moraga-González and Padrón-Fumero (2002) and Toshimitsu (2008) among others.
3
When we do not consider the existence of consumption of used goods, the sales tax is equivalent to
the consumption tax.
3
work of general equilibrium, and demonstrated that environmental tax should be lower
than the social marginal cost. However, he did not take into consideration consumption
of used goods, and focused on trade in wastes. Kinnaman and Yokoo (2011) examined
the global optimal policies when used goods are exported from developed to developing
countries, and those used goods generate environmental damage in developing countries.
They also obtained results similar to those of Copeland (1991). However, they did not
consider a situation in which both new and used goods are consumed in both countries.
Moreover, we consider that new goods are supplied by a monopolist.4
Fourth, we mainly consider environmental damage from waste disposal. However, as an
extension, we also consider environmental damage from consumption activities. In reality,
when observing durables such as vehicles, pollution is emitted when they are used. Even
if consumption itself does not emit any pollution, the supply of electricity for consumption
of durables may generate environmental costs.
The main results are as follows. In the case of closed economy, when environmental
damage is generated by disposal of waste into landfills, the combination of a disposal
fee and a sales tax on new goods superior to the combination of a recycling subsidy and
a sales tax on new goods. The reason is that a disposal fee discourages the recycling
activities while a recycling subsidy encourages them. Then, a disposal fee decreases the
demand for used goods by recyclers and the price of used goods decreases, which leads
to an increase in consumption of used goods. Then, to achieve a certain recycling rate
and a certain amount of waste disposal, the consumption quantity of durable goods under
the former policy combination is greater than that under the latter. On the other hand,
when environmental damage is also generated by consumption, the superiority of policy
combination may be reversed.
Even if used goods are internationally traded, recycling policies in both exporting and
importing countries function effectively, the superiority the combination of a disposal fee
4
Bernard (2010) demonstrated that a stricter environmental standard in developed countries decreases
the ratio of reusable parts extracted from used durables and increases the illegal export of used durables
and wastes.
4
and a sales tax on new goods holds in terms of world welfare. Even if recycling policies in
importing countries do not work well as intended, the same result for exporting countries
holds as far as an export quota function effectively. However, neither recycling policies in
importing countries nor an export quota work as intended, the combination of a recycling
subsidy and a sales tax on new goods may be desirable.
The structure of the paper is as follows. Section 2 describes the model. Section 3
examines the effects of recycling policies on prices, quantities, environmental damage,
and welfare in a closed economy. We also compare the combinations of recycling policies
to achieve greater welfare. Section 4 introduces trade in used goods and considers the
optimal combinations of recycling policies. Section 5 investigates a situation in which
environmental damages are generated not only from waste disposal but also from consumption activities. Section 6 provides concluding remarks.
2
The Model
Consider a durable good which can be used for two periods. In the first period, the good
is new whose quality level is qn . On the other hand, the good becomes old in the second
period. It can be either consumed as used or dismantled as wastes. When the used good
is consumed in the second period, it has a quality level of qs , where qn > qs .
A monopolist supplies the new goods with a constant marginal cost, which is denoted
by cn . We do not consider leasing by the monopolist. On the other hand, there are many
dealers of used goods, which implies that the secondhand market is perfectly competitive.
Transaction costs of used goods are assumed to be zero, and perfect information is also
assumed. However, any used good has to go through a quality inspection if it is used in
the second period: the cost of this inspection is τ .5
If a used good is dismantled after used for one period, a consumer sells it to a recycler.
There are many recyclers, which implies that the recycling market is also perfectly com5
For example, in Japan, owners of vehicles have to pass a quality and safety inspection every two
years. Another example is the revision of systems, such as the operation system of personal computers.
Users may have to install new software every several years.
5
petitive. Recyclers extract resources from the discarded good. The greater is the ratio
of extracted resources (α (0 ≤ α ≤ 1)) from one unit of discarded good, the higher is
the unit recycling cost (Cr (α)): Cr0 > 0, Cr00 > 0, Cr0 (1) = ∞). The residuals (1 − α) are
disposed of into landfills. Hereafter, we refer to α as the unit recycling rate.
2.1
Demand and Supply
There exists a continuum of heterogeneous consumers who differ in their marginal valuations, θ, of the quality of the durable goods. To simplify, we assume that the valuation
corresponding to a consumer is uniformly distributed in the market, θ ∈ [v̄ − 1, v̄]. We
may have to consider the following two situations. First, when a consumer has no durable
in stock, s/he purchases either one unit of new or used good, or no unit of the good.
Second, when a consumer had purchased a new good in the previous period, s/he has four
alternatives: discarding it and purchasing a new good, keeping it for one more period,
discarding it and purchasing a used good, discarding it and purchasing nothing. Following the assumption set by Clerides and Hadjiyiannis (2008), we avoid this complicated
purchasing decision processes. We focus on the stationary equilibrium in which the monopolist chooses a constant price path. In this case, the prices and consumption quantities
of both new and used goods and the quantity of recycling are constant in every period.
Because we assume perfect information and no transaction costs, there is no friction in
the secondhand market. Thus, the fact that a consumer has a durable good in stock in
the beginning of a period does not affect the decision on whether purchasing a new or
used good. Thus, every consumer has the same alternatives in every period: purchasing
a new good, purchasing a used good, and purchasing nothing.
Each consumer determines her/his purchasing good based on the perceived utility. The
perceived utility when purchasing a new good is:
un = θqn − (pn + tn − δps ),
6
and that when purchasing a used good is:
us = θqs − (ps + τ − δps ),
where pn , ps , and δ denote the prices of new and used goods and the discount factor,
respectively. Moreover, tn denotes the sales tax on new goods, which implies a tax on
using resources. We do not exclude the case of tn < 0, which implies a sales subsidy on
new goods. Therefore, strictly, this policy should be referred to as the sales tax-subsidy
scheme on new goods. However, for brevity of description, we refer to this policy as the
sales tax. If a consumer purchases nothing, her/his utility is zero. As will be described
later, because both dealers of used goods and recyclers compete for used goods in the
secondhand market, the price of used goods is ps even after used for two periods. This
assumption also implies that the qualities of materials in both new and used goods are
the same in terms of recyclers. The market is assumed to be partially covered, i.e., certain
consumers purchase nothing.
We derive the demand functions for both new and used goods by consumers. The index
of the marginal consumer who is indifferent between the utility given by purchasing a new
and a used goods is characterized by θ̃ = (pn + tn − ps − τ )/q̃, where q̃ = qn − qs . The
index of the marginal consumer who is indifferent between the utility given by purchasing
a used good and nothing is θ̂ = ((1 − δ)ps + τ )/qs .
Let Dn and Ds represent the demand of consumers for the new and used goods, respectively. Assuming a uniform distribution, the demand functions are denoted as follows:
pn + tn − ps − τ
,
q̃
(1)
pn + tn − ps − τ
(1 − δ)ps + τ
−
.
q̃
qs
(2)
Dn = v̄ − θ̃ = v̄ −
Ds = θ̃ − θ̂ =
The demand for each type of good decreases in its own price and increases in the price of
the other type of product.
Recyclers purchase used goods from the secondhand market and dismantle them. The
7
profit from recycling one unit of used good is represented as:
πr = α · (pr + Sr ) − (1 − α) · tw − Cr (α),
(3)
where pr , Sr , and tw denote the selling price of resource extracted from used goods, the
recycling subsidy, and the disposal fee, respectively. We refer to πr as the unit recycling
profit, and assume that pr is constant.6 The unit recycling rate (α) is determined so that
πr is maximized:
pr + Sr + tw = Cr0 .
(4)
In terms of the unit recycling rate, the recycling subsidy and the disposal fee have the
same effect. However, in terms of the profit, they have the opposite effects:
dπr /dSr = α > 0,
dπr /dtw = −(1 − α) < 0
(5)
Recyclers have to pay other kinds of costs, such as labor costs. We assume that the other
kinds of costs do not depend not on the unit recycling rate but on the total quantity of
used goods recycled in the recycling industry. Moreover, the marginal cost relating to
the other kinds of costs is assumed to be increasing in the total quantity of recycling.
Thus, the supply curve of recycling of the whole recycling industry, which is also the total
demand for used goods by all recyclers, is represented as:
Dr = A + a · (πr − ps ),
a > 0,
(6)
where A and a are parameters.7
As noted above, we focus on the stationary equilibrium in which the monopolist chooses
a constant price path. Then, in each period, the goods which had been used for two periods
are collected by recyclers at ps . Let Ds denote the quantity of collected old goods which
6
This constant price implies that the markets of materials are much greater than the market of each
product.
7
Implicitly, we assume the producer surplus of the recycling sector as follows: Πr = (πr − ps )Dr −
CR (Dr ), where CR denotes the other kinds of costs such as labor cost. The assumption of increasing
00
0
marginal cost implies CR
> 0 and CR > 0. Then, the total demand for used goods by recyclers is
0
0
determined so that CR
= πr − ps . If we assume that CR
= Dr /a − A/a, this total demand function is
obtained.
8
had been used for two periods. Moreover, part of goods which had been used only for one
period are also collected by recyclers (Dn − Ds ). We assume that Dn > Ds holds. Thus,
Ds + (Dn − Ds ) = Dn = Dr holds, which can be rewritten as:
v̄ − θ̃ = v̄ −
pn + tn − ps − τ
= A + a · (πr − ps ).
q̃
(7)
The profit of the monopolist, which is the supplier of new goods, is given by
Πn = Dn · (pn − cn ).
Taking into consideration the effect on the price of used goods, the monopolist determines
the price of new goods to maximize its profit. From (7), it is obtained that
ps =
q̃A − q̃v̄ + aq̃πr + pn + tn − τ
.
aq̃ + 1
(8)
Then, the first-order condition (FOC) is given by
pn + tn − ps − τ
p n − cn
p n − cn
∂Πn
= v̄ −
−
−
=0
∂pn
q̃
q̃
q̃(aq̃ + 1)
(9)
From (9), we obtain the equilibrium prices:
A + aq̃v̄ − atn + aτ + aπr + acn
,
2a
(10)
(2aq̃ + 1)A − aq̃v̄ + atn − aτ + a(2aq̃ + 1)πr + acn
.
2a(aq̃ + 1)
(11)
p∗n =
p∗s =
Then, substitution of these equilibrium prices into (1) and (2) yields the equilibrium
quantities of both new and used goods:
Xn∗ =
Xs∗ =
aq̃v̄ + A − atn + aτ + aπr − a cn
2(aq̃ + 1)
(aq̃ + 2)v̄ − A + atn − aτ − aπr + acn
2(aq̃ + 1)
(1 − δ)((2aq̃ + 1)A − aq̃v̄ + atn − aτ + a(2aq̃ + 1)πr + acn )
τ
−
−
2aqs (aq̃ + 1))
qs
9
(12)
(13)
2.2
Policies, Environmental Damage, and Welfare
As noted above, we consider three kinds of recycling-related policies: the disposal fee (tw ),
the recycling subsidy (Sr ), and the sales tax on new goods (tn ).
Pollution is emitted when discarded goods are disposed into landfills. For example,
toxic substances may leak out from landfills. Moreover, landfills are scarce, which means
that wastes disposed into landfills generate a kind of social cost. This external cost is
represented as
Ew ((1 − α)Xr∗ ),
Ew0 > 0,
Ew00 > 0,
(14)
where Xr∗ is the amount of discarded goods recycled by recyclers. We refer to this type
of cost as environmental damage.8
Perceived consumer surplus is given by
Z
v̄
θqn −
CS =
θ̃∗
(p∗n
+ tn −
δp∗s )dθ
Z
θ̃∗
+
θ̂∗
θqs − (p∗s + τ − δp∗s )dθ,
(15)
where θ̃∗ = (p∗n + tn − p∗s − τ )/q̃, and θ̂∗ = ((1 − δ)p∗s + τ )/qs . The profit of the monopolist
is
Πn = Xn∗ · (p∗n − cn ),
(16)
and producer surplus of recyclers is given by9
Πr =
1
· (a · (πr − p∗s ) + A)2 .
2a
(17)
Moreover, the tax revenue and subsidy expenditure are given by:
T R = tw · (1 − α)Xr∗ + tn · Xn∗ ,
SE = Sr · αXr∗ .
(18)
However, we evaluate welfare objectively: that is, the gross surplus of both new and
used goods minus the cost of producing new goods, the inspection cost, the cost of recycling, and environmental damage. Note that tax and subsidy are redistribution. Recalling
8
Even if we also consider pollution emission from recycling activities in addition to environmental
damage relating to disposal, the same results are obtained. For simplicity, we describe only the latter
environmental damage explicitly.
9
Note that producer surplus of recyclers is different from the unit recycling profit.
10
that Xn∗ = Xr∗ holds, welfare is defined as
Z
v̄
Z
θ̃∗
θqn dθ +
W =
θ̃∗
θ̂∗
θqs dθ −c∗n ·Xn∗ −τ ·Xs∗ −Cr (α)·Xn∗ −CR (Xn∗ )−Ew ((1−α)Xn∗ ), (19)
where CR denotes the other kinds of cost, which is the total recycling cost except Cr · Xn∗ .
3
Recycling Policies
In this section, we begin with the investigation of the effect of each recycling policy. First,
(10), (11), (12), and (13) reveal that a change in the disposal fee influences the equilibrium
prices and quantities only through the unit recycling profit (πr ). Precisely:
dp∗n
1−α
dp∗s
(2aq̃ + 1)(1 − α)
=−
< 0,
=−
< 0,
dtw
2
dtw
2(aq̃ + 1)
a(1 − α)
(2aq̃ + 1)(1 − α)
dXs∗
=
+ (1 − δ) ·
> 0.
dtw
2(aq̃ + 1)
2qs (aq̃ + 1)
dXn∗
a(1 − α)
=−
< 0,
dtw
2(aq̃ + 1)
(20)
The intuition is as follows. An increase in the disposal fee decreases the demand for used
goods by recyclers. Thus, the price of used goods decreases. Then, some consumers shifts
their purchasing goods from new to used ones. Thus, the consumption quantity of new
goods decreases, while that of used goods increases.
The profit of the monopolist necessarily decreases, because both the price and quantity
of new goods decreases. Producer surplus of recyclers also decreases, because
(2aq̃ + 1)(1 − α)
d(πr − p∗s )
= −(1 − α) +
<0
dtw
2(aq̃ + 1)
holds (see (3), (4), and (17)). On the other hand, in general, consumer surplus may
increase or decrease because of an increase in disposal fee, although the total consumption
amount increases (d(Xn∗ +Xs∗ )/dtw > 0). The reason is as follows. The price of used goods
decreases more greatly than that of new goods does. Therefore, the real holding price of
new goods (p∗n −δp∗s ) can increase. This price effect reduces consumer surplus of consuming
new goods, while consumer surplus of consuming used goods increases. When the former
effect dominates the latter, consumer surplus decreases: the greater is δ, the more likely
this case realizes.
11
Moreover, recalling that Xn∗ = Xr∗ , from (14), environmental damage depends on (1 −
α)Xn . Equation (4) and the assumption that Cr00 > 0 reveal that an increase in the disposal
fee increases the unit recycling rate. Consequently, we obtain the following result.
Proposition 1
An increase in the disposal fee (i) decreases the prices of both new and used goods,
(ii) decreases (increases) the consumption quantity of new (used) goods, (iii) increases
consumer surplus if δ ≤ (aq̃ + 1)/(2aq̃ + 1), (iv) decreases the profit of the monopolist,
(v) decreases the producer surplus of recyclers, and (vi) decreases environmental damage.
For the effect on consumer surplus, see Appendix.
Second, similar to the disposal fee, the recycling subsidy also influences the equilibrium
prices and quantities only through the unit recycling profit. Precisely:
dp∗n
α
dp∗s
(2aq̃ + 1)α
= > 0,
=
> 0,
dSr
2
dSr
2(aq̃ + 1)
aα
aα
dXs∗
(2aq̃ + 1)α
dXn∗
=
=−
> 0,
− (1 − δ) ·
< 0. (21)
dSr
2(aq̃ + 1)
dSr
2(aq̃ + 1)
2qs (aq̃ + 1)
As noted in the previous section, an increase in the recycling subsidy increases the unit
recycling profit (πr ). Thus, the effects of the recycling subsidy on prices and quantities
contrast with those of the disposal fee. On the other hand, the effects on the unit recycling
rate work in the same direction in both cases: an increase in the disposal fee or the
recycling subsidy increases the unit recycling rate. However, because the quantity of
recycling (Xr∗ = Xn∗ ) increases, environmental damage may increase.
Proposition 2
An increase in the recycling subsidy (i) increases the prices of both new and used goods,
(ii) increases (decreases) the consumption quantity of new (used) goods, (iii) necessarily
decreases consumer surplus if δ ≤ (aq̃ + 1)/(2aq̃ + 1), (iv) increases the profit of the monopolist, (v) increases the producer surplus of recyclers, (vi) may increase environmental
damage.
See also Appendix for the effect on consumer surplus.
12
Third, we examine the sales tax on new goods. Contrary to the disposal fee and the
recycling subsidy, the sales tax on new goods directly affects the prices and quantities.
On the other hand, it does not influence the unit recycling profit. The effects are given
by
dp∗n
1
dp∗n + tn
1
dp∗s
1
= − < 0,
= >0
=
> 0,
dtn
2
dtn
2
dtn
2(aq̃ + 1)
dXn∗
a
dXs∗
a
1
=−
< 0,
=
− (1 − δ) ·
.
dtn
2(aq̃ + 1)
dtn
2(aq̃ + 1)
2qs (aq̃ + 1)
(22)
Intuitively, the sales tax on new goods decreases the consumption quantity of new goods.
Used goods are substitutes for new goods in terms of consumers. In this respect, the
consumption quantity of used goods increases. However, because the supply of new goods
decreases, the competition for used goods between consumers and recyclers becomes serious. In this respect, the consumption quantity of used goods decreases. In general,
the effect on the consumption quantity of used goods is ambiguous. Because the consumption quantity of new goods decreases, and the unit recycling rate does not change,
environmental damage necessarily decreases.
Proposition 3
An increase in the sales tax on new goods (i) increases the consumer prices of both new
and used goods (p∗n + tn and p∗s ), (ii) decreases the consumption quantity of new goods,
(iii) decreases consumer surplus, (iv) decreases the profit of the monopolist, (v) decreases
the producer surplus of recyclers, (vi) decreases environmental damage.
See Appendix for the details.
3.1
Policy Combinations
Now let us turn to the comparison of policy combinations. First, following the literature,
we compare the disposal fee with the combination of the recycling subsidy and the sales
tax on new goods. Consider a situation in which tw = Sr = tn holds. It is obvious from
(4) that any recycling subsidy and disposal fee achieve the same unit recycling rate as far
as Sr = tw . Moreover, (20), (21), and (22) reveal that the effects of both types of policies
13
on the consumption quantity of new goods are the same: dXn∗ /dtw = dXn∗ /dSr + dXn∗ /dtn .
This equality also implies that the amounts of recycling for both types of policies are the
same. Because taxes and subsidy are redistribution, and because there is no transaction
cost for used goods, the sum of the cost of producing new goods, the cost of recycling,
and environmental damage is the same in both cases. Then, in terms of welfare except
gross surplus relating to used goods, both types of policies are equivalent.
Under this situation, let us focus on the consumption quantity of used goods. The first
and third terms of (13) are the same for both cases. The second term in the case with the
disposal fee is greater than that in the case with the combination of the recycling subsidy
and the sales tax, because both tn and πr are smaller in the former case than the latter
case. This fact reveals that the consumption quantity of used goods and, accordingly,
welfare are greater in the former case than in the latter case. As far as we focus on
situations in which tw = Sr = tn holds, the disposal fee is superior to the combination
of the recycling subsidy and the sales tax on new goods. In the literature on recycling,
one important result is that a combination of a recycling subsidy and a consumption tax
can achieve the same goal as a disposal fee if the rates of those policies are the same.
However, in the present context, both types of policies cannot have the same effect. It
should be noted that this result holds even if we consider a situation in which the new
goods market is perfectly competitive.
In general, other situations in which tw = Sr = tn does not hold should also be
considered. The merit of the combinations of the recycling subsidy and the sales tax
as compared with the disposal fee is that the former can choose the combination of the
unit recycling rate and the consumption quantity which cannot be achieved by the latter.
Consider a situation in which both types of policies achieve the same consumption quantity
of new goods and the same unit recycling rate. Then, suppose that the government
decreases both the sales tax and recycling subsidy so that the consumption quantity of
new goods does not change. In this case, because the unit recycling rate decreases, this
change cannot be created only by disposal fee. Because Xn∗ = Xr∗ holds, the social disposal
14
cost increases, while consumer surplus from consuming used goods increases.
Consider another situation: suppose that the government increases the sales tax and
recycling subsidy so that the consumption quantity of new goods does not change. In
this case, because the unit recycling rate increases, the social disposal cost decreases.
However, observing the first and second terms in (13), it is obvious that these policy
changes necessarily decrease the consumption quantity of used goods. The government
can decrease the social disposal cost without decreasing the consumption quantity of new
goods at the sacrifice of the consumers of used goods. This change cannot be achieved
only by a disposal fee.
In summary, when comparing the disposal fee with the combination of the recycling
subsidy and the sales tax on new goods, which one is superior to the other is ambiguous
generally. Then, let us introduce the third alternative: the combination of a disposal fee
and a sales tax on new goods. Compare the combination of the disposal fee and the sales
tax and the combination of the recycling subsidy and the sales tax. Consider a situation
in which tw = Sr holds, which implies that the unit recycling rates in both cases are the
same. Then, the sales tax can be chosen for each combination so that both types of policy
combinations achieve the same consumption quantity of new goods. Then, in terms of
welfare except gross surplus relating to used goods, both types of policies are equivalent.
Because the unit recycling profit (πr ) is smaller in the case with the disposal fee than
in the case with the recycling subsidy, the sales tax in the former case is lower than that
in the latter case as far as the consumption of new goods are the same (see 12).10 Then,
Equation (13) reveals that the consumption quantity of used goods is greater in the former
case than in the latter case, which implies that the combination of the disposal fee and the
sales tax is always more effective than the combination of the recycling subsidy and the
sales tax in terms of welfare. This result holds for any combination of the unit recycling
rate and the quantity of Xn∗ . Thus, we establish the following proposition.
10
When we consider the optimal policy combination, the sales tax is negative when it is used with a
disposal fee, because the negative externality from environmental damage is solved by the disposal fee.
Then, the sales tax can be used to solve the insufficient supply of new goods.
15
Proposition 4
(i) As far as we focus on the combination of the unit recycling rate and the consumption
quantities which can be achieved by a disposal fee, the disposal fee is superior to the
combination of the recycling subsidy and the sales tax on new goods.
(ii) The combination of the disposal fee and the sales tax is necessarily superior to the
combination of the recycling subsidy and the sales tax.
One point should be noted. In general, a disposal fee is compared with a combination
of a recycling subsidy and a consumption tax, because a disposal fee can play two roles:
to decrease the consumption quantity, and to increase the recycling quantity. However,
when consumption of used goods is taken into consideration, only a disposal fee may not
be able to achieve the social optimum because it cannot control the consumption quantity
of used goods in addition to other two variables noted above simultaneously.
4
Trade in Used Durables
We have so far considered a closed economy. However, in the real world, large amounts of
used goods are internationally traded both for secondhand use and as materials. In this
section, we consider two countries which trade used goods: the home and foreign countries.
Then, we examine the effects of home recycling policies on trade in used goods, foreign
recycling activities, and accordingly, foreign environmental damage. In the following,
superscript h and f represent the home and foreign countries, respectively.
We assume that there is one home monopolist that supplies new goods to both home
and foreign markets. The monopolist is able to differentiate the prices of new goods in
the both markets. On the other hand, the markets of used goods are integrated unless
trade is restricted. Although extracted resources after dismantlement are internationally
traded, they are transacted at the constant price, pr , in the world market. Thus, we focus
on the trade in used goods.
16
4.1
Trade Patterns
First, we examine the effect of exogenous variables other than recycling policies on the
trade pattern of used goods: in particular, we focus on the range of the valuations of
consumers (v̄ j j = h, f ) and the supply condition of recycling (Aj ).
11
Equation (11) reveals that the greater is v̄ j , the lower is the price of used goods in
country j when there is no trade in used goods. The reason is that consumers with
greater valuations tend to prefer new goods to used goods. Therefore, the greater is v̄ j ,
the greater is the demand for new goods.
Equation (6) reveals that the larger is Aj , the greater is the demand for used goods
for recycling. Therefore, without trade in used goods, the larger is Aj as compared with
Ak (k = h, f, j 6= k), the higher is the price of used goods in country j as compared with
that in country k. This result can also be directly obtained by observing (11).
Proposition 5
Given other exogenous variables equal, country j exports used durable goods (i) when
v̄ j > v̄ k , and/or (ii) when Aj < Ak , where j, k = h, f, j 6= k.
In the real world, in general, developed countries export used goods, while developing
countries import them. It is reasonable to consider that marginal valuations of consumers
in developed countries are higher than those in developing countries on average. Moreover,
the recycling costs in developing countries are usually lower than those in developed
countries, which implies that A of a developed country is generally smaller than that of
a developing country. Thus, Proposition 5 reflects the real situation. In the following,
without loss of generality, we assume that the home country exports and the foreign
country imports used goods.
11
The difference in the costs for quality certification (τ ) also causes trade in used goods. However, this
factor was analyzed by Clerides and Hadjiyiannis (2008) in details. Moreover, this point is less important
as compared with other variables when focusing on environmental issues related to wastes. Therefore,
we do not delve into the effect of a change in the quality certification.
17
4.2
The Effects of Recycling Policies
Now, let us examine the effect of recycling policies on the trade volume of used goods in
the case of no trade restriction. The market clearing condition for the used goods is given
by
Dnh + Dnf = Drh + Drf ,
(23)
where
Dnj = v̄ j −
pjn + tjn − ps − τ j
,
q̃
Drj = Aj + a · (πrj − ps ),
j = h, f.
See (1) and (6) for the details. Then, we obtain that
ps =
q̃(Ah + Af ) − q̃(v̄ h + v̄ f ) + aq̃(πrh + πrf ) + phn + pfn + thn + tfn − τ h − τ f
2(aq̃ + 1)
(24)
The profit of the monopolist is given by
Πn = Dnh · (phn − cn ) + Dnf · (pfn − cn ).
It is assumed that the marginal cost of producing new goods is the same for supplying
both markets. Thus, the FOC is given by
j
j
j
pjn − cn (pjn − cn ) + (pkn − cn )
∂Πn
j pn + tn − ps − τ
−
+
= 0,
= v̄ −
q̃
q̃
2q̃(aq̃ + 1)
∂pjn
j, k = h, f,
j 6= k.
(25)
f∗
The two FOCs determines the equilibrium prices of new goods: ph∗
n and pn . Then, the
equilibrium international price of used goosd is determined (p∗∗
s ). On the effect of home
recycling policies, we obtain the following result.
Proposition 6
An increase in the home disposal fee (the home recycling subsidy, the home sales tax on
new goods) increases (decreases, decreases) the export quantity of used goods.
See Appendix for the details of equilibrium variables and the proof of Proposition 6. The
intuition is as follows. Propositions 1, 2, and 3 reveal that a home disposal fee decreases
the home price of used goods in a closed economy, while a home recycling subsidy and a
18
home sales tax increase it. Thus, in an open economy, the export quantity of used goods
from the home to the foreign country increases due to an increase in the home disposal
fee. On the other hand, the export quantity decreases due to an increase in the home
recycling subsidy or the home sales tax.
Proposition 6 has an important implication. In terms of world welfare, which is defined
as the sum of home and foreign welfare, both countries should adopt the combination of
the disposal fee and the sales tax on new goods. In the real world, however, environmental
and recycling policies are not implemented or do not function well as intended because of
corruption and imperfect monitoring in developing countries. In this respect, it may hold
that exporting countries of used goods, which are usually developed countries, should
adopt the combination of the recycling subsidy and the sales tax rather than the combination of the disposal fee and the sales tax. The former combination decreases the export
quantity. A decrease in environmental damage dominates a decrease in the economic
benefit in this case, although the economic benefit of the foreign country decreases,
4.3
Trade Restriction by the Exporting Country
The wisdom of this research field suggests that trade restriction works for improving
world welfare as a second-best policy when environmental policies malfunction. In this
subsection, we consider a case in which the home country restrict the export of used
goods by setting an export quota (X̄). Then, the market clearing condition ((7)) for each
country can be rewritten as follows:
phn + thn − phs − τ h
= A + a · (πrh − phs ) − X̄,
q̃
f
f
p + tn − pfs − τ f
v̄ f − n
= A + a · (πrf − pfs ) + X̄.
q̃
v̄ h −
These conditions reveal that the equilibrium prices and consumption quantities are determined separately for each county. Because A + X̄ is constant unless an export quota
changes, we can analyze the effect of recycling policies and the optimal combination in the
same way as the case of a closed economy: any given export quota, the combination of the
19
disposal fee and the sales tax on new goods is superior to the combination of the recycling
subsidy and the sales tax on new goods in terms of home welfare. When the export qota
and foreign recycling policies are fixed, a change in any home recycling policy does not
influence foreign welfare. Thus, the superiority of the combination of the disposal fee and
the sales tax also holds in terms of world welfare.
There exists an important problem relating to trade restriction on used goods and
wastes. In reality, many exporting and importing countries try to restrict the trade in
used goods because they often go directly into landfills without consumed as secondhand,
which causes serious environmental damage in importing countries. However, it is costly
for countries to monitor the trade, because used goods can be easily traded illegally. For
example, they can often exported as new goods. In other cases, they are exported as
recycled materials from which toxic substances has already been removed. In such cases,
trade restriction may not work effectively. Then, similar to the case under malfunctions
of environmental policies, the combination of the recycling subsidy and the sales tax on
new goods may be the best combination in terms of world welfare because it decreases
the export of used goods.
Proposition 7
When the government can set an export quota, and when it functions effectively, the combination of the disposal fee and the sales tax on new goods is superior to the combination
of the recycling subsidy and the sales tax on new goods in terms of home welfare even in
the presence of malfunctions of recycling policies in the importing country. On the other
hand, neither recycling policies in the importing country nor the export quota function
effectively, the superiority of the combinations may be reversed.
5
Pollution from Consumption
We have so far taken into consideration environmental damage related to disposal.12
However, there is one more important source which generates environmental damage:
12
As noted in Subsection 2.2, we have implicitly considered pollution emission from recycling activities.
20
consumption.13 In this section, we consider a situation in which consumption activities
also emit pollution.14 Environmental damage from the pollution emission in each country
is defined as15
Ec0 > 0,
Ew ((1 − α)Xrj∗ ) + Ec (Xnj∗ + Xsj∗ ),
Ec00 > 0,
j = h, f.
Consider a case of closed economy in which tw = Sr = tn holds. In this case, according
to the discussion in Subsection 3.1, the consumption quantity of used goods is smaller
when the combination of the recycling subsidy and the sales tax is adopted by the government than when the disposal fee is adopted. Consequently, we immediately obtain the
following result.
Proposition 8
Consider a closed economy. When environmental damages are generated not only from
disposal but also from consumption activities, the combination of the recycling subsidy
and the sales tax on new goods may superior to the disposal fee or the combination of
the disposal fee and the sales tax on new goods in terms of welfare.
In the case without pollution from consumption, the disposal fee can be superior to the
combination of the recycling subsidy and the sales tax because the former can realize
the larger consumption quantities of used goods than the latter can do. However, when
pollution is emitted from consumption, an increase in the total consumption quantity
may reduce welfare. Moreover, from the analysis of Subsection 4.3, Proposition 8 also
holds in the case with an export quota, because changes in home recycling policies do not
influence the foreign equilibrium variables.
13
It is natural to consider that pollution emission from production of new goods is also important.
However, because the production of new goods is equal to the quantity of recycling, the case of pollution
emission from production can be analyzed in a similar way as the case of environmental damage from
waste disposal.
14
Strictly, one more additional policy tool is needed to tackle with this additional externality in terms of
theory. However, in this paper, we focus on the comparison between disposal fees and recycling subsidies.
15
Because we do not consider quality improvement through periods, we assume that one unit of new
goods and one unit of used goods emit the same amount of pollution. However, even if the former unit
emits a smaller amount of pollution than the latter unit, the results do not change.
21
Then, does this result hold in the case of free trade in used goods? From (1) and (2),
the total consumption is given by:
Xnj∗ + Xsj∗ = v̄ j −
(1 − δp∗∗
s )+τ
,
qs
j = h, f.
It is obvious that an increase in the international price of used goods decreases the foreign
total consumption. A home disposal fee decreases the international price, while a home
recycling subsidy increases it. Consequently, it becomes clear that Proposition 8 holds
even in the case of free trade in used goods.
6
Conclusion
Assuming that durable goods can be used for two periods, we examined the effects of
recycling policies on prices and consumption quantities of both new and used goods, the
quantity of recycling, the amount of waste disposed of into landfills. We also considered
what kind of combination of recycling policies is the most effective. Moreover, we examined a situation in which used goods are internationally traded and a situation in which
not only waste disposal but also consumption activities generate environmental damages.
First, the effect of a disposal fee is different from that of a recycling subsidy in particular
on the consumption quantity of used goods: the former increases the quantity, while the
latter decreases it. This result arises because the disposal fee discourages the recycling
activities, by which the demand for used goods by recyclers decreases. Contrarily, the
recycling subsidy encourages the recycling activities.
Second, when focusing on the combination of the unit recycling rate and the consumption quantities which can be achieved by a disposal fee, the disposal fee is superior to
the combination of the recycling subsidy and the sales tax on new goods. Moreover, the
combination of the disposal fee and the sales tax on new goods is necessarily superior to
the combination of the recycling subsidy and the sales tax on new goods. The reason is
that the consumption quantity of used goods in the former case is greater than that in
the latter case given the unit recycling rate and the consumption quantity of new goods.
22
Third, when used goods are traded internationally, and when neither recycling policies
in importing countries nor an export quota function effectively, the combination of a
recycling subsidy and a sales tax may be superior to the combination of a disposal fee and
a sales tax. The reason is that the former combination discourages the recycling activities
in importing countries, while the latter encourages them.
Fourth, the superiority of the combination of a recycling subsidy and a sales tax can
also be obtained when environmental damages are generated not only from waste disposal
but also consumption activities.
It is important for the government to determine what kinds of recycling policies it
adopts. According to the literature, which policy is superior depends on what kinds
of distortion exist. We provided additional important standards for determining the
desirable policy combinations for achieving greater welfare.
Possible extensions are as follows. First, we did not take into consideration illegal
activities explicitly. Illegal activities are important factors in terms of both theory and
policy implementation. The theoretical results sometimes change drastically when illegal
activities are introduced into the model. Second, policies on used goods may be needed.
In reality, the older are goods, the more pollution they emit during consumption and/or
recycling. In such a case, policies that discourage the use of secondhand goods may
improve welfare.
Appendix
Proof of Propositions 1 and 2
From (15), we obtain that
dp∗n
dp∗s
dp∗
−δ
· Xn∗ − (1 − δ) s · Xs∗
dσ
dσ
dσ
o
∗ n
1 − δ dps
∗
∗
∗
−
·
· θ̂ qs − (ps + τ − δps ) ,
qs
dσ
dCS ∗
= −
dσ
where σ = tw or Sr . dp∗i /dtw < 0 (i = n, s) holds. From (20), dp∗s /dσ = (2aq̃ + 1)/(aq̃ +
23
1) · dp∗n /dσ (σ = tw , Sr ) holds. Moreover, because θ̂∗ is the marginal consumer who is
indifferent between buying a used good and buying nothing, the third term is equal to
zero. Thus, unless δ > (aq̃ + 1)/(2aq̃ + 1), dCS ∗ /dtw > 0 holds. On the other hand,
dp∗i /dSr > 0 (i = n, s). Thus, in a similar way, we obtain that dCS/dSr < 0 if δ ≤ 0.5.
Proof of Proposition 3
From (15), we obtain that
dCS ∗
= −
dtn
dp∗n
dp∗s
dp∗
+1−δ
· Xn∗ − (1 − δ) s · Xs∗
dtn
dtn
dtn
o
∗ n
1 − δ dps
−
·
· θ̂∗ qs − (p∗s + τ − δp∗s ) .
qs
dtn
Because dp∗n /dtn + 1 > 0 and 0 < dp∗s /dtn < 1 hold, dCS ∗ /dtn < 0 holds.
Moreover, from (16) and (17), it is obtained that
∗
dps
p∗n − cn
dΠ∗r
dp∗
dΠ∗n
·
=
− 1 < 0,
= −Xn∗ s < 0.
dtn
q̃
dtn
dtn
dtn
International Equilibrium Prices and Proof of Proposition 6
From (24) and (25), the following equilibrium prices are obtained.
(4a2 q̃ 2 + 2aq̃ − 1)v̄ h − v̄ f + 2(aq̃ + 1) · Ah + Af + a(πrh + πrf ) − 2a(thn − tauh − cn )
h∗
,
pn =
8a(aq̃ + 1)
h
f
2 2
f
h
f
h
f
f
+
π
)
−
2a(t
−
tau
−
c
)
(4a
q̃
+
2aq̃
−
1)v̄
−
v̄
+
2(aq̃
+
1)
·
A
+
A
+
a(π
n
n
r
r
pfn∗ =
,
8a(aq̃ + 1)
h
f
h
f
h
f
(2aq̃
+
1)
2(A
+
A
)
−
(v̄
+
v̄
)
+
2a(π
+
π
)
+ 2a(thn + tfn − τ h − τ f ) + 4acn
r
r
p∗∗
=
.
s
8a(aq̃ + 1)
(26)
Then, the quantity of consumption of new goods are given by
Xnh∗ =
1
· 4q̃(aq̃ + 1)v̄ h − 2q̃v̄ f + 2q̃(Ah + Af + a(πrh + πrf ))
8q̃(aq̃ + 1)
−2(2aq̃ + 1)(thn − τ h ) + 2(tfn − τ f ) − 4aq̃cn
Xnf ∗ =
1
· 4q̃(aq̃ + 1)v̄ f − 2q̃v̄ h + 2q̃(Ah + Af + a(πrh + πrf ))
8q̃(aq̃ + 1)
−2(2aq̃ + 1)(tfn − τ f ) + 2(thn − τ h ) − 4aq̃cn
24
(27)
As examined in Sections 2 and 3, an increase in the home disposal fee decreases πrh and,
accodingly, the demand for used goods by recyclers. Observing (26), a decrease in pihr
leads to a decrease in the international price of used goods. On the other hand,
d(πrh − ps )
4aq̃ + 1
= −(1 − α) · 1 −
<0
dtw
4(aq̃ + 1)
holds. Thus, the amount of recycling increases in the foreign country, while it decreases
in the home country. Equation (27) reveals that a decrease in πrh decreases the supply
of new goods in the foreign country. An increase in the recycling and a decrease in the
supply of new goods implies an increase in the foreign import of used goods.
An increase in the home recycling subsidy increases πrh and, accordingly, the demand
for used goods by recyclers. Observing (26), an increase in pihr leads to an increase in the
international price of used goods. On the other hand,
d(πrh − ps )
4aq̃ + 1
=α· 1−
>0
dSr
4(aq̃ + 1)
holds. Thus, the amount of recycling decreases in the foreign country, while it increases
in the home country. Equation (27) reveals that an increase in πrh increases the supply
of new goods in the foreign country. A decrease in the recycling and an increase in the
supply of new goods imply a decrease in the foreign import of used goods.
In a similar way, the effect of sales tax on new goods is proved.
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