1

A Trading-Ratio System for

Trading Water Pollution Discharge Permits

Ming-Feng Hung

Department of Economics, National Cheng-Chi University

Daigee Shaw

Institute of Economics, Academia Sinica

Nankang, Taipei, Taiwan

Running title: Water Pollution Trading-Ratio System Corresponding author:

Title: Research Fellow Name: Daigee Shaw Address: Institute of Economics, Academia Sinica, Nankang, Taipei, Taiwan e-mail: dshaw@sinica.edu.tw Tel: 886-2-27822791 ext. 303 Fax: 886-2-26533593, 27853946

JEL Codes: Q25, Q28

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Abstract

The fact that water flows to the lowest level uni-directionally is a very specific

and useful property of water. By utilizing this property, we design a trading-ratio

system (TRS) of tradable discharge permits for water pollution control. Such a

trading-ratio system has three main characteristics: (1) each zone’s effluent cap is set

by taking into account the water pollution loads transferred from the upstream zones;

(2) the trading ratios are set equal to the reciprocals of the exogenous transfer

coefficients among zones; and (3) permits are freely tradable among dischargers

according to the trading ratios. This paper shows that the TRS could take care of the

location effect of a discharge and could achieve the predetermined standards of

environmental quality at minimum aggregate abatement costs. Problems with hot

spots and free riding could be avoided, and the burdens on both dischargers and the

environmental authority would be comparatively more modest.

Key words: trading ratio, water pollution, discharge permit, location, transfer

coefficient, cost-effectiveness, zone, sequential bilateral trading

procedure, transaction cost, free rider.

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1. Introduction

The tradable discharge permit (TDP) has been introduced for about three decades

as a cost-effective economic incentive instrument to meet a set of predetermined

environmental quality standards. The design of a trading system depends rather

crucially on the nature of the pollutant being regulated and traded [16]. If it is a

uniformly mixed pollutant such as carbon dioxide, a simple TDP system on a

one-to-one basis will improve efficiency by equalizing marginal abatement costs

across dischargers. If the pollutant is non-uniformly mixed, such as sulfur dioxide and

bio-chemical oxygen demand, the extent and spatial pattern of the damages to the

environment depend not only upon the level of emissions, but also upon the locations

and the transfer characteristics of the emissions.

For such kinds of non-uniformly mixed pollutants, emission trading (or effluent

trading in the case of water pollution) has been proposed and discussed extensively in

the literature. Three important prototypes are the ambient-permit system (APS, [14]),1

the pollution-offset system (POS, [10]),2 and the exchange-rate emission trading

system with an exchange rate equal to the ratio of the marginal costs in the optimum

1 Montgomery explored an ambient permit system (APS) and an emission permit system (EPS). Because EPS has both theoretical problems in that it may not yield an efficient solution and practical problems in that it could be quite susceptible to market manipulation [7], we shall not consider EPS in the analysis that follows. 2 McGartland and Oates [13] developed a modified offset system (MOS) which considers both the predetermined standards and current environmental quality to prevent any deterioration in areas already cleaner than the standards. Because the nature of MOS is the same as that of POS, we shall not study it specifically in the following discussion.

4

(ER, [5, 9]). First, in the case of the APS, Montgomery [14] demonstrates that, by

issuing permits for each receptor point, the competitive equilibrium for an ambient

market exists and coincides with the cost-minimum attainment of a set of

predetermined environmental quality standards. The APS, however, suffers from the

problem of high transaction costs because every discharger must assemble a portfolio

of permits from each of the receptor points that is affected by its emissions. It also

suffers from a rather restrictive (and sometimes unattainable) condition in that the

initial allocation must make the pollution constraint binding at all receptor points to

ensure the market equilibrium coincides with the least-cost solution [10].

Second, under the POS, dischargers are free to trade as long as a beforehand

simulation of the environmental quality model shows that the proposed transaction

would not violate the predetermined environmental quality standard at any receptor

point. Free riding and its accompanying high transaction costs, and uncertainty in

trades resulting from simulations are serious problems with the POS, however [7, 12].

Third, under the ER, dischargers trade with each other according to the exogenous

exchange rates that are equal to the ratios of the marginal costs in the optimum. If the

initial allocation is not ‘too far’ from the optimal solution, and the abatement cost

functions are nice and smooth, one may come ‘quite’ close to the optimum. The

burden on the environmental authority is very high, however, since the authority must

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have full information regarding dischargers’ abatement cost functions. Besides, the

environmental quality might be violated after trading [8, chapter 9].

This paper proposes and explores an alternative scheme, the trading-ratio system

(TRS), to incorporate spatial elements into TDP trading for water pollution control

specifically. Although the general principles of the emission trading system hold

regardless of the type of pollution being regulated, differences between the properties

of air and water might make the design and choice of TDP trading systems different.

Tietenberg [16] has distinguished pollutants into three different classes – uniformly

mixed assimilative pollutants, non-uniformly mixed assimilative pollutants, and

uniformly mixed accumulative pollutants; and has discussed their different

implementation details. As to the non-uniformly mixed assimilative pollutants, we

believe they should be further categorized into multi-directional pollutants such as air

pollutants and uni-directional pollutants such as water pollutants.

The fact that water always flows to the lowest level uni-directionally is a very

specific and useful property of water. This property allows the environmental

authority to take into account the water pollution loads transferred from the upstream

zones when prescribing effluent caps for different zones.3 By doing so, if a discharger

wishes to increase his effluent, he only needs to buy TDPs from another discharger 3 To maintain the environmental qualities, the environmental authority can divide a river basin into a number of zones and set a predetermined water quality standard to be met for each zone.

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located upstream or in the same zone to offset this increase, and does not need to buy

TDPs from dischargers located within the zones that are affected by his effluent as is

the case under the APS. Basically, the TRS has three main characteristics: (1) each

zone’s effluent cap is set by taking into account the water pollution loads transferred

from the upstream zones; (2) the trading ratios are set equal to the reciprocals of the

exogenous transfer coefficients among zones; and (3) TDPs are traded freely among

dischargers according to the trading ratios.

We show in this paper that the TRS is a cost-effective instrument that attains

predetermined environmental quality standards with minimum aggregate abatement

costs. It can avoid the well-known problems of high transaction costs resulting from

assembling a ‘portfolio’ of permits under the APS, high transaction costs of

approving trades by simulating trades beforehand and free riding under the POS, and

the possibility of violating the environmental quality standards under the ER.

In the following sections, we shall first define a formal setting of cost

minimization given environmental constraints. Next, in Section 3, a trading-ratio

system will be designed, and its efficiency gains and a mechanism of sequential,

bilateral trades will be studied. In Section 4, issues related to the TDPs’ allocation,

transaction costs and the free rider problem are discussed and compared among the

TRS, APS, POS, and ER to examine their feasibility for water pollution control. We

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summarize and draw conclusions in Section 5.

2. A Formal Statement of Cost-effectiveness: A Benchmark Case

The efficiency criterion requires that pollution control instruments should be set

so as to equate the marginal cost of control with the marginal damage caused by the

emissions. To be consistent with the efficiency criterion, however, the instruments

pose a heavy information burden and are so complex that their use has been rather

limited in practice. A general compromise is the goal of cost-effectiveness which is

that of achieving an environmental target with minimized abatement costs (e.g., [2,

17]).

Suppose there is a river basin. To maintain its water quality, the environmental

authority first divides the river basin into a number of zones and specifies water

quality (concentration) standards for each zone that must be met. The size of a zone

can be defined as an area in which the environmental effects of any unit of effluent are

the same. Then by using a water quality model, the zonal water quality standards can

be converted into the total load standards that cannot be violated within each zone.4

Let ni ,,1K= be dischargers and mj ,,1K= be zones. Zones are ordered by

4 Note that it is not necessary for the total load standard to be the same for each zone and all the time. The environmental authority could, for example, prescribe more stringent total load standards in densely populated areas and source water protection areas, or more lenient total load standards in zones or seasons that the assimilative capacity of the river is stronger.

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their locations. The most upstream zone is indicated by j=1 and the most downstream

zone, j=m. To cope with the location effects of non-uniformly mixed assimilative

pollutants, the mathematical formulation of the optimization problem that minimizes

the aggregate abatement costs of n dischargers to achieve the environmental standards

is given by (e.g., [6, 14, 16]):

∑=

−n

iiiieee

eecn 1

0

,,,)( min

21 L (1)

subject to the total load standards:5

jEehn

ijiij ∀≤∑

= ,

1

* (2)

[ ]0 ,0 ii ee ∈ (3)

where:

( )

. zonein effluent of load total the tomakes discharger

fromeffluent ofunit oneon that contributi theindicatest which coefficien transfer

, zonein effluent of standard load total

,dicharger of leveleffluent , discharger of leveleffluent primary

convex,strictly and increasing be toassumed , discharger of costsabatement

*

0

ji

h

jE

ieie

ic

ij

j

i

i

i

=

=

==

=⋅

A necessary condition for an interior solution with strictly positive effluent is:

. ,)(1

0' iheec ji

m

jj

optiii ∀=− ∑

=µ (4)

where:

5 For symbolic simplification in the following analysis, we assume no background pollution in each zone. Since background depositions are parameters, the assumption does not result in loss of generality.

9

( )

.otherwise) zero zones,

bindingfor zero toequalor an (larger th standard load totalon the price shadow

, discharger of levelseffluent effective-cost

, discharger ofcost abatement marginal '

*jj

opti

i

E

ie

ic

=

=

=⋅

µ

Equation (4) states that in a cost-effective effluent solution, any discharger’s

marginal abatement costs should be equal to the sum of the shadow prices of the total

load constraints ( jµ ) for all affected receptors weighted by their own transfer

coefficients (hij). The shadow price on a binding constraint shows the increase in the

aggregate abatement cost of reducing the total load by one unit. The shadow prices are

zero if zones have non-binding total load constraints, i.e., the total effluents are less

than the total load standards.

In principle, this cost-effective solution is the benchmark for any TDP trading

system to achieve. Montgomery [14] has shown that such an optimal vector of

effluents exists. It is also noteworthy that, because the transfer coefficients for

pollution from the downstream dischargers to the upstream zones are zero, the

environmental constraints (equation (2)) for water pollution are simpler than those for

air pollution.

3. Trading Discharge Permits with the Trading-Ratio System

In this section, we first design a trading-ratio system that is specific for water

pollution control in a river basin, and then prove that the TRS could reach the

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benchmark, cost-effective goal. Then, a sequential and bilateral trading procedure is

examined. Since in reality trades usually appear in a sequential and bilateral way, a

trading system should perform well in practice if it can attain cost-effectiveness

through a sequential and bilateral trading mechanism.

3.1 The Trading-Ratio System

The trading-ratio system is designed as follows:

1. The environmental authority takes the existing zonal total load standards ( *jE ) as

the environmental constraints for each zone.

The zonal total load standards are converted directly from the water quality

standards for every zone.

2. The environmental authority sets the zonal effluent caps ( *je ) one-by-one from the

upstream to the downstream zones such that the zonal effluent cap is equal to the

zonal total load standard minus the water pollution load transferred from the

upstream zones.

Accordingly, let *1

*1 Ee = for the first zone, and let the effluent cap of zone j be

set equal to ∑−

=

=1

1

*** -j

kkkjjj ehEe , where k denotes those upstream zones of zone j.6

6 Notice that determining zonal effluent caps one-by-one from the upstream to the downstream zones does not mean that the upstream zones will certainly be allocated higher effluent caps. How much a zone’s effluent cap will be in fact depends on the zone’s environmental quality standard. For example, if a zone is located at the upstream source water protection area, its water quality standard would be

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Moreover, one zone (zone j) might be a critical zone, that is, the total load standard of

this zone will be violated even if its immediate upstream zone obeys its total load

standard: **1)1( jjjj EEh >−− . In this case, the total load standard of the critical zone

becomes the binding constraint for its immediate upstream zone, i.e., the authority lets

0* =je and ∑−

=−− −=

2

1

*

)1(

**

1

j

kkkj

jj

jj ehh

Ee .

Note that, because of the specific property of water, i.e., flowing uni-directionally,

it is possible for the environmental authority to take the water pollution loads

transferred from the upstream zones into account at the time of determining the zonal

effluent caps. Setting the zonal effluent caps one-by-one from the upstream to the

downstream zones is specific to the TRS while allocating zonal caps. Later, we will

inspect the importance of considering the pollution loads transferred from the

upstream zones in advance using a graphic example (Figure 1).

3. The environmental authority allocates all the TDPs that are equal to the zonal

effluent cap to the dischargers located within the zone. Discharger i’s initial

allocation of TDPs is ie .

The authority should convert the zonal effluent cap into its equivalent amounts of

tradeable discharge permits and allocate all these permits to dischargers in the zone,

tighter and it therefore follows that there would be a lower zonal effluent cap.

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that is, ∑∈

=ji

ij ee * . The environmental authority does not need to have any

information whatsoever regarding abatement costs; it simply issues the prescribed

number of permits for each zone regardless of whether the total load standards were

originally binding or non-binding.7 Free trades will take care of matters from there

on.8

4. The environmental authority sets the trading ratios (r) equal to the reciprocals of

the transfer coefficients.9

Mathematically, ik

ki hr 1= , where kir is the trading ratio, which represents

how many units of TDPs a discharger i must sell to a discharger k to emit one more

unit of effluent. Because a river has assimilative capacity, transfer coefficients are

equal to or less than one for water pollutants flowing from the upstream to the

downstream zones; and zero, otherwise. Trading ratios are therefore greater than one

for upstream dischargers who sell TDPs to downstream ones, and equal to one for

trades within the same zone. No trades will occur in the case of an upstream

discharger who buys TDPs from a downstream discharger because there is no trading

7 For zones with lower aggregate primary effluent than the zonal effluent cap, either could we reset the cleaner present situation as the environmental constraint as McGartland and Oates [13] does in the modified offset system, or we could allocate all the cap to dischargers in the zone such that they own abundant permits to sell. For zones with no existing dischargers, the environmental authority could play a role to hold the initial TDPs allocation and join in following TDP trades. 8 With perfect information and no strategic behavior, the initial allocation of TDPs could be conducted either through grandfathering or an auction. 9 There are several practical programs that also use trading ratios to undertake the TDP trades. These trading ratios are, however, determined mainly on the basis of administrative considerations and are without theoretical basis.

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ratio for such kinds of trades.

5. Dischargers trade with each other freely on the basis of the trading ratios, and the

environmental authority must make sure that dischargers have sufficient TDPs to

cover their effluent at the end of each trading period.

According to the exogenous trading ratios, dischargers trade with each other

freely. At the end of a promulgated trading period, say one year or one season, every

discharger’s actual effluents must be less than or equal to the amount of the TDPs that

he owns. We could rewrite the trading mechanism into a trade equation as:

,∑∑≥≤

−+≤n

ikkiki

ikikii TrTee that is, the discharger’s actual effluent should be less than

or equal to the amount of TDPs that he owns, which is equal to the initial allocation,

plus the TDPs he bought and minus what he sold. In the equation, i and k are indexes

of dischargers; smaller numbers mean that the dischargers are located upstream. i

belongs to ],[ ii which is a set of dischargers in a same zone. )(kiikT is the amount of

TDPs that discharger i (k) buys from discharger k (i).

Taking Figure 1 as an example, let us assume there are four zones 1, 2, 3, and 4,

and that each zone has some dischargers within it. The aggregate primary effluents are

100, 60, 100, and 30 tons for zones 1 to 4, respectively. Suppose that the total load

standards are 80 tons for each of the first two zones, 140 tons for zone 3, and 100 tons

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for zone 4; the transfer coefficients for two adjacent zones are h13 =0.4, h23 =0.6, and

h34 =0.8.10

Under the TRS, first, the environmental authority takes the existing total load

standards as the environmental constraints, i.e., 80, 80, 140, and 100 tons for zones 1

to 4, respectively. Second, the authority sets the zonal effluent caps one-by-one from

the upstream to the downstream zones according to the allocation method described

above as 80, 80, 45, and 0 tons for zones 1 to 4, respectively. Note that when we

follow the one-by-one allocation method, the zonal effluent cap for zone 3 is

originally 60 tons. However, because zone 4 is a critical zone and its environmental

constraint is the actual binding constraint for zone 3, the effluent cap for zone 4

becomes zero, and the cap for zone 3 is reduced to 45 tons according to the formula

above.

Third, if we let one unit of TDPs equal a ton of polluting load, then discharger 3

could obtain an initial TDP allocation of 80 units, and discharger 6, zero units. For

zones 1 and 4, it makes no difference how the zonal effluent caps are allocated among

dischargers within each zone; allocations of permits based on proportionate effluent

reductions within zones might be appropriate, however.

10 h12=0 because the effluents from zone 1 will not have any effect on the water quality in zone 2 in this case.

15

Fourth, the trading ratios that are set equal to the reciprocals of the transfer

coefficients, are: ,1 54452112 ==== rrrr ,4.0

152514241 ==== rrrr ,

6.01 5343 == rr

,8.04.0

16261 ×== rr ,

8.06.01

63 ×=r .

8.01 and 6564 == rr Fifth, dischargers trade

with each other freely according to the exogenous trading ratios, and only need to be

sure that their final effluents are less than or equal to the amount of TDPs that they

own at the end of a trading period.

Finally, let us use this example to explain the importance of the method of setting

zonal effluent caps. Taking the pollution loads that are transferred from the upstream

into consideration at the time of determining the zonal effluent caps is a key that

simplifies trading in TDPs under the TRS. We know that under the APS, when

discharger 4 wants to increase a unit of effluent, he must trade simultaneously with

discharger 5 and discharger 6 (if there is room for trades) to offset the increase in his

effluent in each affected zone. However, under the TRS, discharger 4 only needs to

trade bilaterally with discharger 5 to offset the increase because the environmental

authority has considered in advance the effects of transferring pollutants from zone 3

to zone 4 at the time of setting zonal effluent caps. If the effluent cap of zone 3 is not

violated, the total load standard of zone 4 will not be violated.11

If dischargers act in such a way that all possible benefits from trading are 11 In addition to the opportunity of trading with discharger 5, discharger 4 can also choose to trade bilaterally with discharger 1, 2, or 3 to offset his effluent increase.

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exhausted, and no strategic considerations or transaction costs come into play, the

resulting effluent distribution will be as if a social planner were to minimize aggregate

abatement costs subject to the trading constraints [6, p. 408]. Therefore, the

optimization problem under the TRS is:

∑=

−n

iiiiTTe

eeckiiki 1

0

,,)( min (5)

s.t. , ,∑∑≥≤

∀≤+−n

ikikiki

ikiki ieTrTe (6)

,0, ≥kiik TT (7)

[ ]. ,0 0ii ee ∈ (8)

The necessary conditions for interior solutions with strictly positive effluent and

TDP trades are:

, ,)( *0' ieec iiii ∀=− λ (9)

,kikir λλ = ( ki ≤ ) (10)

where:

( )

.otherwise) zero ,situations bindingfor zero toequalor an (larger th TDPs ofamount gnet tradin and allocation TDP initial s'discharger a of sum on the price shadow

, discharger of leveleffluent trade-post

, discharger of costsabatement marginal *

'

==

=⋅

i

i

i

ie

ic

λ

Equation (9) shows that every discharger should abate pollution until his

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marginal abatement cost is equal to the shadow price of the discharger’s trade

constraint. In a binding situation, the shadow price is the increased cost of reducing a

discharger’s TDPs by one unit. If it is non-binding, i.e., if the discharger’s excess

TDPs are not bought out, the shadow price is zero. In this case, the discharger would

not abate and would emit up to his primary effluent level. Equation (10) shows that,

for TDP trades, dischargers trade with each other until the ratio of their marginal

abatement costs equals the trading ratio (equation (10) can be rewritten as

)()( *0'*0'kkkiiiki eeceecr −=− by using equation (9)). Within each zone, dischargers’

marginal abatement costs are the same ( 1=kir ).

If the post-trade effluent level ( *ie ) is equal to the cost-effective effluent level

( optie ), then by comparing equation (4) with equation (9), we can obtain

ji

m

jjiiii

optiii heeceec ∑

===−=−

1

*0'0' )()( µλ in equilibrium. That is, any discharger’s

marginal abatement costs should be equal to the increased costs of reducing a

discharger’s TDPs by one unit ( iλ ) and equal to the sum of the shadow prices of the

total load constraints ( jµ ) for all affected receptors weighted by their own transfer

coefficients (hij). In the next section, we will prove that ,*i

opti ee = namely, the

cost-effective effluent levels may be attained through the trading ratio system.

For the sake of symbolic simplification and without loss of generality, we assume

that there is only one representative discharger in each zone in the following sections.

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3.2 Cost-effectiveness

Proposition 1: Assuming perfect information regarding cost functions, cost-minimizing

dischargers, and no transaction costs or strategic behavior, the trading-ratio system

can achieve the goal of cost-effectiveness.

Proof:

For any specific discharger j, the trade constraint (equation (6)) in the

optimization problem under the TRS can be rewritten as:

,1

1∑∑>

−

=

≤+−n

jkjkjkj

j

kjkj eTrTe

Assume ,0, ≥ij AA then

∑∑∑−

=>

−

=

==++−1

1

*1

1-

j

iiijjjj

n

jkkjkj

j

kjkj ehEeATrTe

Rearranging, the equation becomes:

*1

1

1

1jj

n

jkkjkj

j

kjk

j

iiijj EATrTehe =++−+ ∑∑∑

>

−

=

−

=

Expanding ie , we have:

*1

1

1

1

1

1

1

1

1

1

1

1)( jj

n

jkkjkj

j

kjk

j

i

n

ik

j

iiijki

ik

ijj

i

j

i

i

kikijiijj EATrTAhT

hh

Thehe =++−++−+ ∑∑∑∑ ∑∑ ∑∑>

−

=

−

= >

−

=

−

=

−

=

−

=

Equivalently,

,*

11 1j

j

iiij

j

i

j

i

n

jkki

ik

ijiij EAhT

hh

eh =++ ∑∑ ∑∑== = >

19

Because 0≥kiT (equation (7)), and ,0≥iA

. ,*

1jEeh j

j

iiij ∀≤∑

=

(11)

This equation is exactly the same as equation (2), the constraint of the

cost-effective model.12 Since both the objective function and the constraints under the

TRS (equations (5)-(8)) are exactly the same as the objective function and constraints

of the cost-effective model (equations (1)-(3)), the optimal solution *ie under the

TRS is the same as optie , the cost-effective solution. This means that the

environmental authority could achieve the cost-effective goal by employing the

trading-ratio system.13

3.3 A Sequential Bilateral Trading Procedure

A trading system that promises cost-effectiveness by a sequential bilateral

trading procedure is more practical. In reality, as Atkinson and Tietenberg [1]

discussed, trades are made sequentially, and usually bilaterally, at changing

non-equilibrium prices.

Proposition 2: Assuming perfect information regarding cost functions, cost-minimizing

12 The only visual difference is that the upper limitation of summation is n in equation (2), and j in equation (11). This is not an actual difference, however. Equation (2) can be decomposed as

,1

*

1∑ ∑= +=

≤+j

ij

n

jiiijiij Eeheh where the second part is zero because hij is equal to zero for i>j, i.e., the

downstream effluent does not have an effect on the upstream zones. 13 The proof for the case with a critical zone could proceed in a similar way. We should note, of course, that the actual binding environmental constraint under the cost-effective model setting is also the critical zone’s total load standard.

20

dischargers, and no transaction costs or strategic behavior, the trading-ratio system

can achieve the goal of cost-effectiveness through a sequential bilateral trading

procedure.

Proof:

Two dischargers with different marginal abatement costs trade with each other to

reduce their joint abatement costs. The condition for a cost-minimum solution for

each bilateral trade between discharger i and discharger k is as follows (without loss

of generality, we assume that ki < ):

),()( min 00

, kkkiiieeeeceec

ki

−+−

s.t. ).ˆ()ˆ( kkkiii eeree −−=−

where e is the effluent allowed by the TDPs that the discharger owns at the time of

trading. The constraint states that the trading equation between two dischargers under

the TRS, i.e., the decrease in effluent of discharger i )ˆ( ii ee − is equal to the increase

in the effluent of discharger k )ˆ( kk ee − multiplied by the trading ratio kir .

The first-order condition is , )()( 0'0'kkkiiiki eeceecr −=− the same equation as the

first-order condition of the cost minimization problem under the proposal of a social

planner (equations (9) and (10)). Since this equation must hold for each trade between

any pair of dischargers (i, k) at any time, the effluent solution of the sequential,

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bilateral trading process can therefore converge to the cost-effective solution.

3.4 Equilibrium Prices of Permits

Faced with the need to choose a nonnegative level of effluent and quantity of

permits traded, a discharger must minimize his cost that is composed of abatement

costs and expenditures on TDPs. The ith discharger’s choice can be characterized as:

),()(min1

1

0

,, ∑∑>

−

=

−+−n

ikkikii

i

kikiiiiTTe

TrPTPeeCkiiki

(12)

where Pi is the price of TDPs that prevails in the ith zone. Since the revenue from

selling permits is equal to the expenditure incurred in buying permits for an equivalent

environmental effect, kikkikii TPTrP =)( . By substituting kikTP for )( kikii TrP in

equation (12) and assuming the discharger’s TDP trading constraint is binding, i.e.,

∑∑>

−

=

=+−n

ikikiki

i

kiki eTrTe

1

1 such that ∑∑

>

−

=

+−=n

ikkikiii

i

kik TreeT

1

1, equation (12) may be

written as:

,)()(min 0

, ∑∑>>

−+−+−n

ikkik

n

ikkikiiiiiiiTe

TPTreePeeCkii

(13)

The conditions for minimizing this cost are:

iPeec iiii ∀=− ,)( 0' (14)

).( , kiPPr kiki <= (15)

By comparing equations (14) and (15) with equations (9) and (10), with iP

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equal to the shadow price iλ (the increased costs of reducing a discharger’s TDPs by

one unit), the effluent vector which satisfies equations (14) and (15) is the solution of

equations (9) and (10). In equilibrium, the discharger will abate himself until his

marginal abatement cost equals the price of the TDPs; and the buying price of the

TDPs is equal to their selling price times the trading ratio.

To sum up, because of the specific property of water that it flows to its lowest

level uni-directionally, the environmental authority can set the zonal effluent caps

one-by-one from the upstream to the downstream zones that take the transferred water

pollution loads from the upstream zones into account. Given the allocation method

and exogenous trading ratios, TDPs can be traded freely and bilaterally among

dischargers, and the TRS can achieve the goal of cost-effectiveness. In equilibrium,

every discharger abates pollution until his marginal abatement costs is equal to the

price of the TDPs within the zone in which he is located; and the buying price of the

TDPs is equal to their selling price times the trading ratio.

4. Further Thoughts and Comparisons

In addition to cost-effectiveness and the procedure of sequential, bilateral trading,

other issues such as the initial TDP allocation, transaction costs, free riding, and the

number of zones, etc. are important in deciding the performance of alternative TDP

23

trading systems.

4.1 Number of Receptor Points and Zones

The pollution control laws for water or air pollution in most countries generally

require that the environmental quality standards be met at all locations. Most trading

systems are designed, however, in terms of a given and fixed set of receptor points at

which the attainment of predetermined levels of environmental quality is required.

When the number of receptor points is small, environmental quality in some locations

(other than the receptor points) may become worse after trading, i.e., hot spots, and

those in certain other locations may become better after trading.

To prevent the occurrence of localized hot spots for pollutants with more

localized effects, a relatively fine mesh of receptor points will be needed [2, 10]. A

large number of receptors implies higher transaction costs for the APS and POS,

however. Since each receptor is associated with an individual permit market for the

APS, more receptors gives rise to more difficult trading and administrative problems.

With respect to the POS, as the number of receptor points increases, more

environmental constraints should be considered when simulating beforehand.

Uncertainties relating to the exchange rates and doubts over whether a successful

trade faced by dischargers can be made arise, causing transaction costs to be

24

subsequently raised.

Under the TRS, by dividing a river basin into a larger number of zones defined

as an area in which the environmental effects of the effluent of a particular pollutant

are the same, we can require that the environmental quality standards be met at all

locations. While doing so, the TRS does not become more complicated, however.

There are two reasons for this feature. First, the trading ratios are pre-determined by

the transfer coefficients between any pair of locations where the traders locate. No

matter how many zones exist, the number of trading ratios a discharger faces is equal

to the number of dischargers minus one, and the sequential, bilateral trading

procedure still works. The transaction costs are therefore essentially unchanged as the

number of zones increases to a relatively large number.

Second, it is not necessary to establish water quality monitoring stations that

might be very expensive in every zone. The monitors could be established only at

locations with critical environmental qualities. The environmental authority needs

only to check the amounts of TDPs and effluents. If dischargers’ actual effluents are

less than or equal to the amount of TDPs that they own, the environmental quality

within each zone would not be violated.

4.2 The Binding Problem in the Initial TDP Allocation

25

For such trading systems as the APS and ER, whether or not the initial allocation

of permits is binding at all receptor points affects whether or not the market

equilibrium coincides with the cost-effective solution (e.g., [8, 10, 14]). When the

environmental constraints are not binding initially, the market equilibrium will not be

the cost-effective solution under either the APS or ER; the environmental quality may

even deteriorate after trading under the ER. Moreover, it becomes very difficult to

have an initial allocation binding for all receptors simultaneously as the number of

receptor points becomes large.

Under the TRS, the attainment of the cost-effective solution is also not

independent of the initial allocation of TDPs among zones. However, the

uni-directional nature of water pollution can easily make the initial allocations binding

for every zone. Because there are no complicated inter-zone relationships, the

authority could always set zonal effluent caps that are binding sequentially from the

upstream zones to the downstream zones according to the transfer coefficients and

total load standard of every zone. For zones with aggregate primary effluent levels

that are lower than the cap, we could either reset the cleaner present situation as the

environmental constraint as in the case of the modified offset system [13], or else we

could allocate the whole of the cap to dischargers within these zones so that they own

an abundance of permits that they can sell. New dischargers or existing dischargers

26

with higher abatement costs in other zones will buy such dischargers out. Through

inter-zonal trades, cost-effectiveness can be attained.14

Under the TRS, the administrative burden associated with making the initial

allocation of TDPs is lighter. It requires the authority to have only information

regarding the transfer coefficients and to prescribe environmental quality standards

for zones, as what the command-and-control approach does. Moreover, the burden

borne by the dischargers is also light. While applying the APS, a discharger must

assemble a “portfolio” of permits from each of the receptors that is affected by his

effluents. Here under the TRS, because the zonal effluent caps have already taken the

transferred pollution loads from the upstream zones into consideration, a discharger

needs only hold TDPs that are equal to his effluent in the zone in which he is

located.15

4.3 Transaction Costs

In practice, the magnitude of the transaction costs is a very important

consideration regarding the choice of alternative trading systems. Several authors

14 If there were still an excess supply of permits, the price of permits would be zero. 15 Because of the complicated multi-directional influences, the allocation method in the case of air pollution could not take into consideration the inter-zonal impacts in advance. For example, after subtracting the background pollution from the target emission loads in each receptor, the remaining emission loads are converted into TDPs and distributed among dischargers. In the case of water pollution, however, the uni-directional property of water allows us go further to deduct the transferred pollution loads from the upstream zones to set the zonal effluent caps. The caps are then converted into TDPs and allocated. Dischargers therefore do not need to take care of the inter-zonal impacts of their effluents.

27

have pointed out that the transaction costs associated with the APS are very high (e.g.,

[7, 10, 12]), especially with a large number of receptors. Moreover, thin markets may

give rise to non-price-taking behavior and result in even higher transaction costs [7].

With respect to the POS, although it keeps the number of receptors of concern to a

minimum (only binding receptors), polluters do not know the trading ratios until their

trades are simulated [12]. The POS might therefore face higher transaction costs than

the APS because a dispersion model must be run before each trade is approved [8].

Besides, if a trade needs to be approved first, the associated transaction cost would be

higher and the willingness to trade would be depressed because the approval process

creates uncertainty for dischargers [18].

In the case of the ER, the exchange rate that is equal to the ratio of the marginal

abatement costs in the optimum explicitly specifies how much of an increase in

emissions is to be compensated by a reduction elsewhere. While the exogenous

exchange rates reduce the transaction costs significantly, solving the

cost-minimization problem to determine the optimal exchange rate requires not only

information regarding the dispersion characteristics of emissions within the air or the

river basin, but also information regarding dischargers’ abatement costs. The burden

placed upon the environmental authority is therefore heavy, and it is highly likely that

dischargers will cheat in terms of the control cost information that they provide.

28

Incorrect cost information may bias the trading results and result in high enforcement

and monitoring costs.

In the case of the TRS, the trading ratios are calculated from the exogenous

transfer coefficients. By precluding the need to simulate beforehand or solve the

cost-minimization problem, the TRS reduces substantially the administrative costs

and trading uncertainty faced by dischargers. Furthermore, the permits are not

associated with a particular receptor market as in the case under the APS. Allowing

one discharger to purchase permits directly from another promises substantial savings

in transaction costs to dischargers. In addition, because dischargers can freely trade

inter-zonally according to the trading ratios, market thinness is not a serious problem

while applying the TRS.

4.4 Free Rider Problem

One difficulty with the POS is the free rider problem. McGartland [12] points out

that because dischargers can always obtain additional emission rights from the

environmental authority if they do not violate ambient standards, dischargers would

like to be free riders. Since the TDPs being traded are state-dependent, i.e., their

definition depends on the actions of other dischargers [7], high transaction costs may

therefore arise and free riding will impede the cost-effectiveness of the POS.

29

Under the TRS, since all TDPs are allocated and any additional increase in

effluent should come with more permit purchases like the APS, the free rider problem

is avoided. Some might think that the selling of permits by upstream dischargers to

downstream ones would make the upstream and midstream zones cleaner and give

dischargers located there the opportunity to be free riders so that they can increase

their effluent without violating the environmental standards where they are located.

This is not permissible, however, since downstream zones are still binding after

trading, and any increase in effluent in the upstream or midstream zones will lead to a

violation of the environmental quality standards in the downstream zones.

5. Conclusions

In the literature, several trading systems such as the APS, POS, and ER have

been designed for cost-effective pollution control. These incentive instruments,

however, might not be appropriate for water pollution control.

With water having the specific property of flowing in one direction, water

pollution allows us to design a trading-ratio system that is specific for its control. As

discussed above, the TRS has the property that it can achieve the goal of

cost-effectiveness, i.e. attain the predetermined standards of environmental quality in

all locations with minimum aggregate abatement costs. Such cost-effectiveness could

30

also be reached by a sequential bilateral trading procedure, a more realistic trading

sequence in reality.

TDP systems provide dischargers with an opportunity to reduce their abatement

costs. However, if the designed system is too complicated and not sufficiently

clear-cut ex ante, the dischargers’ willingness to trade will be frustrated. Under the

TRS, based on exogenous and predetermined trading ratios, dischargers may trade

with each other freely. The existence of exogenous trading ratios also means that

trades need not be verified beforehand as under the POS. Besides, by taking the

pollution loads transferred from the upstream zones into consideration at the time of

setting the zonal effluent caps, dischargers need not assemble a portfolio of permits as

under the APS. Trades are therefore easier for dischargers to engage in under such

circumstances relative to trades under other trading systems. The administrative costs

borne by the authority are also lower under the TRS. Officials only need information

regarding the transfer coefficients and no information whatsoever regarding

abatement costs. To sum up, the transaction costs are relatively modest.

In addition, since environmental quality standards could be attained in all

locations and some places might become cleaner because of trades, environmentalists,

the general public, and officials all benefit from the TRS. For example, in the case of

a where a downstream discharger buys TDPs from an upstream discharger, the

31

reduction in the seller’s effluent makes both the upstream and midstream zones

cleaner.

Although the TRS is specifically related to water pollution control, it could be

applied to air pollution control in certain cases where the direction of the pollution is

more clear and fixed. Simulations based on the TRS may be conducted to empirically

examine its cost-effectiveness too.16 Moreover, the TRS can easily be extended to

point/nonpoint sources and multiple-period, multiple-pollutant TDP trades linked by

appropriate trading ratios. These topics deserve further research in the future.

16 Some articles simulating tradable discharge permit systems in the case of water pollution control use either one-to-one trading ratios or simplified versions of APS and POS as the trading systems to be simulated (e.g., [3, 4, 11, 15]).

32

References

1. S. Atkinson and T. Tietenberg, Market Failure in Incentive-Based Regulation: The

Case of Emissions Trading, Journal of Environmental Economics and

Management 21, 17-31 (1991).

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Cambridge University Press (1988).

3. E. D. Brill Jr., J. W. Eheart, S. R. Kshirsagar, and B. J. Lence, Water Quality

Impacts of Biochemical Oxygen Demand under Transferable Discharge Permit

Programs, Water Resources Research 20 (4), 445-55 (1984).

4. J. W. Eheart, E. D. Brill Jr., B. J. Lence, J. D. Kilgore, and J. G. Uber, Cost

Efficiency of Time-Varying Discharge Permit Programs for Water Quality

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for the Colorado River of Texas below Austin, Water Resources Research 28 (5),

1311-18 (1992).

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Management 12, 207-228 (1985).

34

14. W. D. Montgomery, Markets in Licenses and Efficient Pollution Control Programs,

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15. W. Tao, B. Zhou, W. F. Barron, and W. Yang, Tradable Discharge Permit System

for Water Pollution, Environmental and Resource Economics 15, 27-38 (2000).

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Washington DC: Resources for the Future (1985).

17. T. Tietenberg, Tradeable Permits for Pollution Control When Emission Location

Matters: What Have We Learned? Environmental and Resource Economics 5,

95-113 (1995).

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United Nations Conference on Trade and Development (1999).

35

◆ 1 0.4

0.8

Figure 1 Schema of a River System

Zone 1

Zone 3

Zone 2 Zone 4

◆ 2

◆ 4

◆ 5

◆ 6 ◆ 3

0.6

Legend — River Zones ◆ Dischargers