Intermediate Liability Rule with No Apology:
An Economic Prescription for Social Costs of Electricity
Akim M. Rahman, Ph.D. *
*Contact author: Office of Strategic Research, Ohio Department of Development, 77 S. High Street, 27 th Floor, Columbus, OH 43215,
USA, Phone 614-466-4151, Email: [email protected] or The Ohio State University, 1735 Neil Avenue, Room no. 10,
Columbus, OH 43210, Phone 614-292-3786, Email: [email protected]
Clive A. Edwards, D.Sc.
Environmental Science Graduate Program, The Ohio State University, 1735 Neil Avenue, Columbus, OH 43210, US, Phone: 614292-3786, Email: [email protected]
Abstract
Traditional law and economic theory suggest that electric companies can be made to pay the
costs of the pollution through assignment and enforcement of full liability and then pass these
incurred costs on to the end-users by charging higher rates per kWh of electricity used.
Questioning this conventional theory in this study, with implicit weighting of welfare gains
and losses to society, consisting of a three-groups, consumers, producers and victims of the
emission, supply-demand models are developed, and the net welfare effects of the policy are
analyzed. Calculating welfare effects to each group, the liability share parallel to zero net
welfare effects is used to single out end-user's optimal liabilities. With a plausible parameter
value used, this analysis shows that the intermediate liability(s) are preferable on both
economic efficiency and equity grounds. However, the model is very sensitive to changes in
the parameter values.
Keywords: Climate policy, coal combustion, electricity generation and emission liability.
The objective of this paper is to debate the controversy surrounding intermediate
liability rule in assigning taxes on externality evolved from production processes where
producer and consumer both have joint interest in profit maximization but they may have
dichotomy in their approaches. Like few other commercial sectors, utilities, especially,
electric utilities where a company generates electricity through coal combustion either to
compete in market and to generate targeted revenue (deregulated-market) or to reduce the
costs of electricity generation where market prices along with investors' rate of return are set
by regulators (regulated-market). By contrast, modern technology, especially, time-saving
opportunities or appliances likely encourage consumers to change the pattern of their
approaches, because expending energy use allows them to increase their overall productivity
and personal comfort. These changes cause additional demands on energy supplies and; it
could cause the downfall of our environment where externalities are not internalized in
market. At the economic status quo, we plan to show that intermediate liability(s) over a full
or a zero liability is preferable in terms of economic efficiency, equity, and ethical grounds.
Moreover, by taking the approach, we plan to review two reasons why the full liability rules -- Polluter Pays Principles (PPP) will not produce an allocation of resources that maximize
social welfare. (a) Full liability creates an enhanced incentive for the electricity generation
through coal combustion and thereby changing the costs and benefits associated with
electricity generation. (b) The breakdown of assignment of liability affects the distribution of
costs and benefits among affected parties.
Firstly, we derive relationships between the assignment of liability for pollution
abatement costs and the level of CO2 emitted from power plants, using a supply-demand
model where people’s willingness to pay (principles of new welfare economics) are financial
measures of welfare gains and losses. Secondly, we calculate end-users' optimal liabilities
using principles of compensation and equivalent variation and use this liability share to
maximize the social welfare function. Consequently, we define liability assignments that
maximize (taking derivatives of the model) economic welfare where all parties, end-user(s)
and generating company(s) both favor profit maximization in order to reach their goals but
they may dichotomize in their activities.
1. Some Background
Recent environmental concerns in many countries are likely to contribute to reduction
domestic CO2 emissions to levels matching the ongoing environmental campaign internationally
2
under the Kyoto Protocol that has entered in its first step based on the resolutions of recent
Conference of Parties on Climate Change (COP7) in Marrakech. In spite of the recent outcome of
the COP7, policy practitioners in many countries are obligated currently to react to perceived
domestic environmental damages. This may result from externality issues in relation to policies,
which favor domestic political maneuvers. Like few other sectors, energy utilities such as coalbased electric companies (producers) are often identified as a major source. The debate over these
issues is likely to center on determining the appropriate allocations of liability. Such liabilities
must be aimed to internalize the costs incurred, so that it becomes most appealing to parties and
ensure preserving equity aspects.
To address these issues, institutions often attempt to identify fully liable parties,
instead of questioning the roles of various parties' involved in causing the problem. This is
often called the Polluter Pays Principle (PPP). Under the PPP the generating companies
could be made to pay all environmental costs through the assignment and enforcement of full
liability and then the companies would pass these costs incurred on to end-users by charging
a higher rate per kWh of electricity usage. Alternatively, the companies may charge the endusers as emission compliance costs per kWh of electricity usage.
Laws and regulations are not the only means of accounting for liability for this
problem. Economists have long advocated different options to define liability rules in
externalities. A. C. Piguo (1932) made a seminal suggestion of the adoption of a system of
unit taxes or subsidies to curb pollution where taxes on a particular activity are equal to the
marginal social damages caused which in term is equal to the marginal divergences between
private and social costs. This proposition has attracted considerable attention among policy
practitioners in relation to many externality issues (Lands and Posner 1980; Sullivan 1986). It
remained unchallenged until 1965 when Ronald Coase (1965) published his key article where
he argued that regardless of the liability principle in practice, all gains from the business
would be exhausted in efficiency perspectives. The Coasian theory of externality has been
preserved in the economic literature although a group of academic economists (Davis and
Whinston 1965; Calabresi 1968) this group first attacked Coasian's zero transaction cost
assumption and extended their analyses to the case where both parties were consumers. The
second group (Dolbear 1967; Mishan 1971; Randall 1972) accepted Coase's static-perfect
competition assumptions for the sake of argument but rejected Coase's rules of liability
neutrality. Mishan and Randall used two different active party cases (producers and
consumers) instead of two homogeneously active parties (producers or consumers) that were
3
used by Dolbear under the same the assumptions. They have theoretically supported the full
liability rules. The primary author of this article has investigated their suggestions in a case
where both consumers and producers have joint interest in profit maximization but they may have
dichotomy in their approaches. With plausible parameter values, using supply-demand models, he
singled out intermediate liability(s) over a full or a zero liability rule on both economic efficiency
and equity grounds (Rahman 2000).
2. Liability Rules
In this section, we provide a technical assessment of probable liability rules cognate to
aforementioned problem.
Full liability rule
It puts responsibility on the party who uses electricity in his or her daily activities. The
magnitudes of this liability depend on the volume of electricity usage in kWh. In this case,
the electricity generating company does not bear externality costs but passes it on to the enduser by raising the price of electricity per kWh or collecting the incurred costs of emission
compliance per kWh of electricity usage. Under this rule, the company is liable to meet the
emission standards or domestic emission targets and faces the consequences if it fails.
Zero liability rule
This liability rule puts responsibility on to the electricity generating company. The magnitude
of this liability depends on the volume of electricity in kWh generated through coal
combustion. In the case of a regulated industry, the company tries to pass on these costs as
production costs to the end-users. In this case, companies are solely responsible for meeting
the overall emission targets.
Intermediate liability rule
It puts responsibility on the end-user as well as on the generating company and an infinite
number of shared burdening scenarios can be contemplated. Here the company can collect
the compliance costs from end-users based on its responsibility, which can be calculated from
its total electricity usage in every electricity-billing period.
3. Cursory Investigation of Liabilities
In this section, we discuss supply-demand models, which were developed by the
author of this article to investigate efficiency and equity trade-off of several different liability
rules for externality issues (Rahman 2000). In practice, the generating companies are free to
4
choose a range of various fuels to generate electricity such as electricity from coal
combustion, electricity from nuclear power plant, electricity from oil, etc. or use of a
combination of fuels. For our study, we have chosen American Electric Power-Ohio (AEPOhio), a solely coal based electricity generating company in the State of Ohio, USA, which
transmits electricity to other electricity markets using transmission grids after meeting local
electricity demands.
Traditional law and economic theory suggest that public policy
determines the price of electricity per kWh in a regulated retail market and the price of
electricity per kWh in a competitive retail market depends indirectly on the prevailing
environmental enforcement policy. In general, environmental enforcement will increase the
anticipated cost of electricity generation, thereby decreasing the over all volume of electricity
generation under coal combustion, and increasing the amount of electricity generation from
nuclear power plants. In aiming to maximize extra profits, in practice, a company may wish
to use the environment as a waste disposal medium (illegal operation) and, by so doing, it
may decrease its generation cost. In other words, electricity generation in the market where
environmental enforcement is fully enforced i.e. where a company pays compliance costs, if
it fails to match the level of emissions required (legal operation) is a substitute to illegal
electricity generation where company pays fines or penalties if it is convicted for pollution.
Underpinning the above assumptions, Cp, (Figure 1), represents a private cost curve
of electricity generation where the rate of return is included when the market is regulated, C s
is the marginal social cost of electricity generation and E(D) is the demand for electricity.
Point X (Figure 1) is the market equilibrium only if the company covers the marginal private
costs (MPC) of electricity generation and passes it on to the end-users in terms of electricity
price per MWh. The equilibrium price and volume of electricity generation under coal fired
are P2 and D2, respectively. But if the full marginal externality costs are covered by the enduser together with the marginal private costs, then a market equilibrium occurs at point K
(where MPC = MSC) with an equilibrium price P1 and a volume of electricity generation
under coal combustion D1. An intermediate situation can also arise in the market (Figure1). It
is possible that the end-users will pay all of the marginal private costs of electricity but only a
fraction of marginal externality costs. This possibility can be represented by the C n schedule
(Figure1). The market equilibrium occurs now at point G, with any equilibrium price of P,
and an equilibrium volume of electricity generation using coal-fired D. It is assumed in the
remaining discussion that point X represents the initial equilibrium and point G describes the
5
equilibrium point of electricity generation in legal operations responding to environmental
enforcement policies.
Considering equity trades off aspect in liability assignments, three groups are
represented (Figure1). They are (i) electricity users, (ii) the electricity generating company
and (iii) individuals (excluded or included the above two) impacted adversely by the
marginal externality costs resulted from electricity generation under coal combustion i.e.
victims of emissions. The effects on each of these groups will be examined in detail in the
following discussion.
Consider first the impacts on the end-user that has a requirement for electricity.
Increasing the market price from P2 to P means that the end-user suffers a loss in consumer
surpluses equal to the area P2PG X. In contrast, the generating company now provide D units
of electricity from coal-fired and charge a price of P. This results in a revenue transfer from
consumers to producers that is equal to the area P2PGL. However, these generating
companies experience a reduction of electricity generation using coal combustion provided in
market-one equal to the distance D2D. This, in turn, implies a loss to the producers' surplus
equal to area - BPG + AP2X. The third impact is concerned with externality costs. If the total
electricity generation using coal fired is equal to D2 the associated levels of externality costs
is equal to the area CNXA. But if the level of electricity generation under coal combustion is
D, then the associated level of externality cost is CFYA. A net impact on the external costs of
reducing the volume of electricity generation using coal-fired from D2 to D is equal to the
area FYXN.
Despite any environmental enforcement policy in practice, the generating companies' needs
to dispose CO2 into air depend on two factors: the policy costs of its acts, and policy costs (Cs
- Cn,) in the market where some companies do not choose to pass the waste into air. The
consequences of changes in demand of electricity generation using coal-fired in a case where
the company chooses to use the air as waste disposal medium are shown in Figure 2. PI, the
policy costs of electricity generation per MWh are assumed constant in the prevailing market.
Increasing the costs of electricity generation in to a generating company in market-one means
that the demands for electricity generation in market-two increases from I' to I". When the
demands for electricity generation using coal-fired in market-two is I (C'n, PI), the total
benefits for the consumers are equal to the area OI'MP' I, while the total costs in market-two
are equal to the area OI'MPI. This implies a net benefit equal to PIMP'I. But if the demand is I
(C"n, PI), then the total benefit is OI"NP"I and total cost is OI"NPI. This implies a net benefit
6
equal to PINP"I. Thus, increasing the demand in market-two from I' to I", implies that the
generating company may receive a net benefit equal to the area (P INP"I - PIMP'I) that
ultimately passes on to the end-users.
Activities in market-two also imply that there is a possibility of environmental damage
associated with marginal externality costs. Discussion and measurement of such costs are
based on another model (Figure 3). The marginal externality costs of electricity generation
using coal-fired in market-two consist of two components. The first is the quantity of
electricity generation under coal fired allowing the permitted levels of emission. There are
two sizes: I' (Figure 3) associated with P2 and I" associated with P (Figure 1).
The second component is the cost of the resources that would be required to make the
external effects of CO2 emission harmless to any third parties that are affected by markettwo. These costs are assumed to be a single value per unit; i.e. per unit cost is assumed to
be  Cs, where  quantifies the electricity costs in market-two as a fraction of electricity
costs in market-one; note  can be greater than one. The  < 1 situation indicates that
impact on market-two is cost-effective and this option scheme then becomes appealing to the
generating company; otherwise it becomes a disincentive. The exact relationships
between  Cs and PI are not known on a priori basis. Moreover, whether the bargaining
outcome under market-one or market-two leads to decreased gaseous emissions or to
improved social welfare depends crucially on the model parameters. Since the price rises
from P2 to P in market-one, the welfare losses, associated with total electricity generation
under coal combustion, is shown by the area I'I"AB in Figure 3. This area is a relatively
accurate measure of minimum welfare losses, provided the third parties in market-one, value
a cleaner environment more than the cost of cleanup.
To quantify parties' behavior aforementioned in a geometrical explanation, we begin to
construct a mathematical model defining the symbolic terms that are used in the model.
R1: Net welfare effects to electricity end-users.
R2: Net welfare effects to companies who produce electricity under coal combustion.
R3: Net welfare effects to victims of emission.
To analyze welfare effects, we calculate each group's net effect separately. Following Figures 1
and 2, the net welfare effects for end-users can be stated as follows:
R1 = - P2PGX + P'IMNP"I
(1)
Note that P2PGX has a negative sign representing a loss in consumers' surplus.
From Figure 1
7
P2PGX = P2PGL + GLX
(2)
GLX = G DD2X - L DD2X
(3)
P2PGL = E(D) * D - P2D
(4)
GLX = [

D2
E (d )dD - P2(D2 - D)]
D
(5)
Substituting equations (4) and (5) into equation (1) yields:
P2PGX = [E (D) * D - P2 D] + [

D2
D
E ( D)dD - P2(D2 - D)]
(6)
From Figure 2
P'IMNP"I = PI N P"I - PI M P'I
(7)
Where
PI N P"I =

PI

PI MP'I =
P 'I
P "I
PI
I (C" n, PI )dPI
(8)
I (C ' n, PI )dPI
(9)
Substituting expressions (9) and (8) into expression (7) yields:
P'I MNP"I =

P 'I
PI
I (C" n, PI )dPI -

P "I
PI
I (C ' n, PI )dPI
(10)
We add expression (6) and (10) in order to obtain R1
R1 = [E (D) * D - P2D] + [

P 'I
PI

D2
D
I (C" n, PI )dPI -
E ( D)dD - P2(D2 - D)] +

P "I
PI
I (C ' n, PI )dPI
(11)
To calculate R2, the initial equilibrium in market-one, prior to any policy action is P2 and D2
(Figure 1). The area P2XA, therefore, shows the initial producer's surplus.
Next, we calculate shared liability instead of full liability imposed on end-users. In other words,
we presume that generating company shares a portion of liability, which is equal to (C n - Cp) in
Figure 1. A new equilibrium in market-one is reached at point G. Thus, after the policy action the
market price is P and equilibrium total electricity generation under coal fired is D. The producers'
surplus in this case is the area PGB (Figure 1). The net welfare effects for the electricity
generating company can be defined as the net changes in the producer's surplus that occurs when
a generating company shares social costs of electricity generation through coal combustion. Thus
we can state changes in producers’ surpluses resulting from an increase in the share from zero to
(Cp - Cn) can be stated as:
R2 = - BPG + AP2X.
(12)
8
From Figure 1
R2 = -BPG + AP2X
(13)
BPG = OPGD - OBGD
(14)
AP2X = AP2LY + LYX
(15)
AP2 LY = OP2LD - OAYD
(16)
LYX = LDD2 X - DYXD2
(17)
Substituting expression (14) to (17) into expression (13) yields:
R2 = - OPGD + OBGD + OP2 LD - OAYD + LYX
(18)
Let us define the schedules for Cp and Cn in Figure 1 as Cp(D) and Cn(D) respectively. Using
these functions, we can convert the geometric areas of expression (18) and obtain R2.
R2 = - Cn(D)D +

D
0
Cn( D)dD + P2 D + P2(D2- D) -

D2
D
Cp( D)dD
(19)
Following from Figures 1 and 3, the net welfare effects for victims of CO 2 emission from
generating company under coal combustion can be stated as follows:
R3 = FNXY - I' I"AB
(20)
From Figure 1
FNXY =

D2
D
[Cs( D)  Cp( D)]dD ;
(21)
From Figure 2 and 3
I'I"AB = ΦCs [I(C"n, PI)] - I(C'n, PI)
(22)
Where ΦCs represents the externality cost per unit of electricity generation under coal
combustion in market-two. [I(C"nPI) - I(C'n, PI)] represents the change in demand of electricity
generation under coal combustion in market-two for a fixed unit price of electricity (PI).
Subtracting expression (22) from (21) we obtain R3.
R3 =

D2
D
[Cs( D)  Cp( D)]dD + ΦCs[I(C"n, PI) - I(C'n, PI)]
(23)
Since the determination of CO2 emission policy (Liability Rule Program) involves implicit
weighting to three-group, our social welfare function can be written as follows;
W = ω1R1 + ω2R2 + ω3R3
(24)
Where ω1, ω2, ω3 are weights for end-users, generators and victims of CO2 emission due to coal
combustion respectively.
Since the ultimate goal of this calculation is to determine the optimal liability share for
end-users, we define optimal liability share ( λ) as the portion Cs(D) - Cp(D) which, if paid by the
9
liable party (s), will maximize the value of expression (24). This determination has two steps.
Firstly, an expression for the optimal quantity of electricity generation under coal combustion D
is established. Second, the optimal D is substituted into the expression
[E(D) - Cp(D)]  [Cs(D) - Cp(D)]
to determine the optimal liability share for the end-users. The calculation of the optimal
electricity generation through coal combustion begins with the substitution of expression (11),
(19) and (23) into expression (24). This substitution yields:
W = - ω1[{E(D) * D - P2D} + {
+ ω1 [

P 'I
PI
+ P"(D2- D) -

D2
D
D2
D
E ( D)dD - P2(D2 - D)}]
I (C" n, PI )dPI -
+ ω2[- Cn(D)D +
+ ω3 [



D2
D
D
0

P 'I
PI
I (C ' n, PI )dPI ]
Cn( D)dD + P"De -

D
0
Cp( D)dD
Cp( D)dD ]
{Cs( D)  Cp( D)}dD - ΦCs {I(C"n, PI) - I(C'n, PI)}] (25)
Expression (25) is the optimal social welfare function for the problem outlined in
introduction section. We postulate that the total electricity generation D under coal combustion is
determined so as to maximize expression (24). Taking first derivative of expression (25), the
optimal total electricity generation under coal combustion yields:
P "I
1 [ PI
I
C " n
(C"n,PI)
C " n
D
+  3 {-[Cs(D) - Cp(D)] - 
- I(C'n(D),PI)] -  Cs(D)[

P 'I
PI
I
C ' n
(C'n,PI)
dPI
C ' n
D
dCs( D)
[I[C"n(D),PI)
dD
I
C " n
(C"n(D),PI)
C " n
D
I
C ' n
(C ' n( D), PI
D
D = ---------------------------- C ' n
dE ( D)
dCn( D)
1
2
dD
dD

Adding the calculated values of R1, R2 and R3 yields:
W = - ω1[{E(D) * D - P2D} + {

D2
D
E ( D)dD - P2(D2 - D)}]
10
(26)
+ ω1 [

D
0

P 'I
PI

I (C" n, PI )dPI -
Cp( D)dD + P"(D2- D) -
P 'I
I (C ' n, PI )dPI ] + ω2[- Cn(D)D +
PI

D2
D

D
0
Cn( D)dD + P"De -
D2
Cp( D)dD ] + ω3 [  {Cs( D)  Cp( D)}dD - ΦCs {I(C"n, PI) D
I(C'n, PI)}]
(27)
Taking first derivative
W
dE ( D )
= - ω1[{
* D + E(D) - P2} + {- E(D) + P2}]
dD
De
+ ω1 [

P 'I
PI
+ ω 2[ -
I
C " n
(C"n, PI)
dPI C" n
De

P 'I
PI
I
C ' n
('n, UI)
dPI ]
C ' n
De
dCnD
* D - Cn(D) +Cn(D) + P2 - Cp(D) - P" + Cp(D)]
dD
+ ω3[-{Cs(D)-Cp(D)} - 
 Cs(D){
dCs( D)
{I[C"n(D), PI] - I(C'n(D2), PI)}
dD
I
C " n I
C ' n
(C"n(D),U'I)
(C'n(D),PI)
}]
D
C " n
D C ' n
(28)
Simplifying expression (28) yields:
P ' I I
W
dE ( D )
C " n
= - ω1 [
* D] + ω1 [ 
(C"n, PI)
dPI
PI C "
D
dD
De
P "I
I
C ' n
dCn( D )
(C'n, PI)
dPI] - ω2[
* D] + ω3 [ - {Cs(D) - Cp(D)}
C ' n
D
dD
-

-Ф
dCs( D)
I
C " n
{I(C"n(D), PI) - I(C'n(D), PI)} - ФCs(D){
(C"n(D)
dD
C " n
D
-
I
C '
(C'n(D), U'I)
}]
C '
D
PI
(29)
Solving expression (29) provides optimal electricity generation (D) under coal combustion.
To make the model simple, we work with linear versions of the demand and cost functions.
E(D) = E - δD
(30)
Cp = A + αD
(31)
Cs = C + γD
(32)
Subtracting expression (30) from (31) and rearranging the terms, yields:
E(D) - Cp = (E - A) - (δ + α)D
(33)
Subtracting expression (11) from (10) yields:
11
Cs - Cp = C + γD - A - αD = C - A
When α = γ
(34)
The optimal liability share (λ) that maximizes social welfare is determined by noting that the
following condition holds:
From Figure 1
λ=
E ( D)  Cp( D)
Cs( D)  Cp( D)
(from Figure 1)
(35)
Substituting expressions (33) and (34) into expressions (35) and remaining terms, yields:
P "I
1 [ PI
I
C " n
(C"n,PI)
dPI C " n
D
+  3 {-[Cs(D) - Cp(D)] - 
-I(C"n(D),PI) -  Cs(D)[

P 'I
PI
I
C ' n
(C'n,PI)
dPI]
C ' n
D
dCs( D)
[I(C"n(D),PI)
dD
I
C " n
(C"n(D),UI)
C " n
D
I
C ' n
(C ' n( D), PI
EA
 
D
λ=[
]-[
] * ------------------ C ' n
dE ( D)
dCn( D)
CA
CA
1
2
dD
dD

(36)
The second-order condition for maximization is:
ω1
dE ( D )
dCn( D )
- ω2
< 0
dD
dD
(37)
Model Parameterization
It is clear from expression (16) that the optimal liability share depends on the values
of a number of parameters. Parameters' values can be determined by a search of literature on
emission issues in electric companies, public policy related to externality problems,
especially, the Clean Air Act Amendment (CAAA). Here a policy of using an SO 2 permit
market is utilized to facilitate use of a CO2 permit market in our models. Electricity rates per
kWh, volumes of electricity produced by coal combustion and other related information can
be obtained from relevant reports compiled and or published by related agencies at both state
and federal levels. Costs of damages due to CO2 emission as well as prices of CO2 permits
can be obtained from articles in the popular press and the environmental scientific literatures.
The dollar amount of penalties or fines for violation can be determined by a search of CAAA
cognate to SO2 emission regulations.
12
Sensitivity Analysis
Whether directly or indirectly related to the issue discussed, it is certain that a range
of plausible parameter values are available in the relevant literature. Thus, it is necessary to
make a thorough sensitivity analysis to determine a plausible range of values for λ. This
analysis is summarized in the following section, for non-marginal changes in λ. The effects
of increasing or decreasing key parameters on marginal changes in λ can be determined by
inspecting equation (16). The results of this inspection are summarized in Table I.
Most of the effects on λ of larger values for the parameters in Table I are straightforward.
The exceptions are
The larger
I
, PI and ω3 .
Cn
I
, the larger the amount of electricity generation demanded under coal
Cn
combustion. The larger I results a larger the consumer's surplus from electricity generation
through coal combustion (the term multiplied by  1 in the numerator of equation 16) and the
larger external cost of electricity generation through coal combustion (the term multiplied by
 3 in the numerator of equation 16). The larger values for a consumer's surplus in markettwo increase λ; larger values for external costs in market-two reduce λ. Therefore, the net
effect on λ is ambiguous, a priori. Larger values for PI have just the opposite effects to larger
values for I / Cn ; they reduce the consumer's surplus from electricity generation under
coal combustion and reduce the external costs from market-two. Smaller values for the
consumer's surplus in market-two reduce λ; smaller values for external costs in market-two
increases λ. The net effect on λ is once again ambiguous.
If ω3 increases, it increases the external costs in both markets. Neither of these results
is desirable. However, the avoidance of the higher external costs in market-one requires an
increase in λ, and the avoidance of higher external costs in market-two requires a lower λ.
Whether the optimal λ should rise or fall can not be determined, a priori.
4. The Market for Electric Utility in Ohio, USA
In this section, we summarize the information that we have derived from different
sources mentioned with the subheading Model Parameterization in Section 3. Since the
State of Ohio is the fourth largest coal-burning state in the United States and is the largest
coal burning state in the Midwest region, we chose Ohio in our model to explore the potential
contributions of all power plants to CO2 emission scenarios. In the forth of 1999 quarter,
13
Ohio electricity generation was 36.92 million MWh of which 87.49 percent of overall
generation was generated through coal combustion system.
American Electric Power Company (AEP) has a number of power plants in many
states in the United States and in few other countries. American Electric Power in Ohio
(AEP-Ohio) is one of five investor-owned parent electric companies in Ohio. In Table II, the
ratios of AEP -Ohio electricity generation through coal combustion from 1994 to 1999 were
between 93 percent and 100 percent. Since the AEP-Ohio is the largest generating company
in Ohio and is the most coal-based production system in Ohio (AEP 2000; PUCO 1992), we
choose AEP-Ohio as paradigm of a coal-based generating unit to incorporate the available
information in our models. Like few other companies, the AEP-Ohio provides services to
residential, commercial, municipal, and other customers where they charge different rates for
different group of customers. In 1999, AEP-Ohio generated MWh of 54,908,135 of
electricity in which 99 percent of the electricity was generated under coal combustion (AEP,
1999). Electricity usage charges in Ohio per MWh in 1999 to residential, commercial and
industrial were $ 88.43, $85.23 and $ 43.85 respectively (PUCO 2000). By contrast, the First
Energy Company (FE) generated electricity mainly through the combination of nuclear
power plants, steam and oil production in 1999 and its estimated usage charge per MWh was
$118.89 and the estimated fixed cost was $83.69 (FE 1999).
Electricity generating companies in the United States are subject to regulations
concerning the effects of their operations on air and water quality, hazardous and solid waste
disposal, and other environmental matters, by related Federal, State and local agencies. To
deal with climate change issues, the US government introduced an Energy Policy Act in
1992. Energy Policy Act-1992, Section 1605(b) requires that U.S. electric utilities and other
manufacturers record the results of voluntary measures taken by the companies to reduce,
avoid, or sequester GHG emissions in essence to mitigate potential environmental impacts.
Therefore, in 1998, they had adopted 1,507 projects that achieved GHG emission reductions
equivalent to 212 million metric tons of CO2 (EIA 1998). In 1997, the Clinton Administration
announced that it favored offering "credit for early reductions" as a means to limit future U.S.
GHG emissions (EIA 1998). On July 27, 2000, a group of U.S. Senators led by Senator Sam
Brownback introduced a bill entitled: Carbon Sequestration Investment Credit. The short title
is Investment Tax Credit. Under this bill, the eligible projects could receive funding at a rate
of $ 2.50 per verified ton of carbon stored or sequestered up to 50 percent of the total project
cost. The minimum time length of these projects must be 30 years and the Implementing
14
Panel can only approve $ 200 million tax credits each year. Despite an international outcry
along with domestic likely concerns for sound environmental policies, in March 2000, the
Republican Administration, US President George W. Bush balked at supporting the Kyoto
Protocol. The COP7 took place in 2001 in Marrakech where the United States stayed on the
sidelines. Despite the US President's position into Kyoto Protocol Agreement, the Protocol
has entered in its first step based on the resolution of the COP7.
Under current environmental regulations, each company can use its own strategies to
comply with the regulations. Since these regulations do not control the levels of CO2
emission, the generating units can easily compete in the market by minimizing the cost of
electricity generation through practices that often emit huge amount of CO 2 into the
atmosphere. The transmission grid systems becomes an impetus to these activities and;
therefore it imposes additional emission burden on any State like Ohio where AEP-Ohio
transmits surplus electricity to other state(s) after meeting their local electricity demands. The
recent deregulation policy can be an incentive to their practices related to CO 2 emission if
there are no specified and strict regulations related to the issues.
5. Application of the Model
We begin with a benchmark case that was established from observed data and
assumed parameters for the supply-demand and external cost functions. Using a procedure
for determining changes in economic welfare, we calculated the optimal  , then assumed
different values for these parameters and calculated a series of additional values for  . We
found that  varied widely over the assumed range of values.
The Benchmark Case
The model underlying the benchmark case was the same as that depicted in Figures 1 to
3. Here we have assigned values to the parameters of the linear functions. The parameters'
values are incorporated below. The model can be specified as a system of 6 equations:
(1) E(D) = E - δD
(2) Cp = A + αD
(3) Cs = C + αD
(4) I = K - g(dD) - βPI
(5) PI = P"I
(6) ФCs = Ф Cs
15
E (D) is the demand for total electricity generation under coal combustion. Here each unit of
electricity demand estimates how much the end-user is willing to pay for an additional unit of
electricity usage. Cp = MPC and Cs = MSC are marginal private costs and marginal social
costs respectively for electricity generation under coal combustion in market-one. Here the
marginal social cost is equivalent to the sum of the marginal private costs as well as external
costs in market-one. I is the demand for electricity generation in market-two. UI is the price
of electricity per kWh and ФCs is the per unit value of the external cost in market-two.
Solution of the model also requires the assignment of welfare weighting to the gains or losses
experienced by the end-users, the generating company and the pollutees. In terms of the
models developed in Section 3 of this article, we have assigned values for ω1, ω2 and ω3.
The parameters in Table III are consistent with the initial prices and quantity in
market-one and with assumed values for the elasticity of demand and supply for electricity
generation through coal combustion. The initial prices and quantity in market-one was $72.50
per MWh and 54,908,135 MWh respectively (AEP 2000). To assess the economic welfare
losses by end-users, due to a particular increase in the price of electricity, we have used
residential price elasticity, ranging from -0.4 to -0.5 (PUCO 1992). Long-run price responses
to the commercial and industrial customers' range were -0.9 to -1.2. (PUCO 1992). With this
data, an average price response of -0.75 for end-users was chosen to incorporate in our
benchmark case study. Since the externality costs associated with CO 2 emissions are
excluded from the generating costs per MWh of electricity generation, we have assumed that
the response of electricity generation under coal combustion is 2.0 (responsive). The crossprice elasticity (EI) for electricity generation through coal in market-two is assigned to 1.0.
This means that if the cost of electricity generation under coal-fired system in market-one
rises by 10 percent then the demand for electricity generation under coal-fired systems in
market-two rises by 10 percent. Since the electricity transmission grid facilitates a generating
company transmitting its excess electricity to other states after meeting local demands, the
assumptions cognate to elasticity are palatable. Here the external costs causing harm to the
third party is assigned initially to $200 per metric ton of CO2. Since Americans, in general,
prefer a safe and comfortable life style at any costs; therefore, the assigned external costs
should be self-defensible at least for the near future. The value for ф is assumed to be 0.20,
which indicates that the one fifth of the total electricity generation through coal combustion
takes place in market-two in our imaginary world. This value is derived from CAAA cognate
to SO2 emission compliance policy likely CO2 emission policy in our hypothesized statutes.
16
Incorporating aforementioned values, and CO2 emission tax $2.50 per ton (Lee 2000) in
supply-demand models, market-one is in equilibrium at P = $ 74.21 per MWh and demand
for electricity generation under coal fired is D = 54,120,712.00 MWh. Market-two is in
equilibrium, initially I = 10,824,142.40 MWh and PI = $ 40 per MWh.
The first step in the determination of the optimal  is to compute the hypothetical
equilibrium when full liability (  = 1) is imposed on electricity generating companies that
they pass on to customer in full in terms electricity prices. This is the level of total electricity
generation under a coal-fired system in market-one where E (D) = Cs. Given the above
parameters, this equilibrium occurred at 2,044,017.92 MWh. The simultaneous equilibrium
in market-two occurred at I = 593,378.40 MWh.
With these starting points, the technique for determining the optimum  was to
specify smaller or larger values for  and then to calculate their net effects on economic
welfare. To examine the direction of optimal  , smaller and larger values of  were tested as
long as W was positive. An optimal  was found when W reached zero. As  is reduced, full
liability shifted to a lower liability, over the range between 1 and 0, the quantity of electricity
generation under coal-fired systems in market-one increased and the quantity of electricity
generation under coal fired in market-two decreased. Thus, economic welfare increases due
to increased for consumer and producer surpluses and there was a reduction in the
deadweight losses in market-one. On the other hand, it reduced external costs in market-two
(ECI). Following the same argument, however, economic welfare would fall, due to increased
external costs in market-one (ECL), and to loss of consumer's surplus in market-two (CSI).
With  Cs = $200, PI = $40 and other given parameters values, as reported as case 1 in Table
IV, the optimal  = 0.92. At  = -1, the generating company would face all the liability, so
the net gain in CSL plus PSL would be maximized, and consumers would continue to reap
gains. It would be necessary, however, to subsidize electricity producers because the price
per MWh of electricity in market-one would be less than the marginal private cost (Cp). In
this case, in the absence of subsidies, investing capital in other businesses becomes an
incentive to the generating company. On the other hand, the subsidies required for producers
are a loss to the taxpayers that exceeds the gain to the consumer. Neither scenario satisfies
the Pareto optimality condition.
Again, at  = 1, the generating company faces the liability and passes it on to
customer in full so that the net gain in PS L is maximized, and the company continues to reap
17
financial gains. It becomes appealing to the company to produce excess electricity through
coal combustion and to transfer the excess supply to customers in other states where
competitive markets are facilitated with transmission grids. Consequently, this may create an
extra gaseous emission burden for the end-users in the state where the company's plants are
located. In any case, the optimal  can be negative i.e. only the generating company faces the
liability; if the reduction in ECI is large enough and policy-makers prefer to prevent illegal
operations related to emission issues. If there are no net gains from lowering  , then it is
necessary to check if  should be raised above 1. With  >1, the demand for electricity
becomes sensitive. End-users, especially, the commercial and industrial customers may
switch to other competitive price energy sources such as natural gas. Electricity generating
companies may reap the economic gains.
Application of these procedures in the benchmark case produced an optimal  of 1.23
as was reported as case 5 in Table IV. In this case, the assumed value of  Cs is very large.
To implement  = 1.23, it would be necessary to pay a huge subsidy or provide a tax break in
some fashion to the end-users and this may creates budget deficits. On the other hand, in the
absence of subsidies, the policy maneuver may stand against policy-makers.
Other Cases
In practice, the benchmark case would be constructed upon econometric estimates of
the parameters of the demand, supply and external cost functions and the optimal estimated
 would be close to the true  . Since our supply-demand models are developed based on
hypothesized statutes, there are good reasons at this stage to question some of the values
assigned to these parameters in the benchmark case. Thus, we calculated the optimal  for a
few more cases, characterized by different sets of parameter values. Since the optimal  in
the benchmark case depends on heavily upon  Cs, it is necessary to look at  Cs carefully.
There might be different ways to look at the  Cs. We chose a measure that deals with
people's willingness to pay either to accept gaseous emissions or to get rid of them. In this
scenario, willingness to pay for eliminating emissions is equal to the apparent risks of
damage (natural environment) multiplied by the hypothetical value that people place on this
damage. It is entirely possible that the risks associated with CO2 emissions are quite small.
To allow for this possibility, we constructed two cases, where  Cs = $200 and  Cs =
$100. As expected the optimal  rose in these cases.  = 0.92 when  Cs = $ 200 and  =
0.95 when  Cs = $100. The new optimal  = 0.95 is reported as case 2 in Table IV.
18
The next parameter that we can examine is PI. If the CO2 emissions were regulated
and if the necessary data were available, then, PI could be estimated as follows
PI = p (prosecution) x p(conviction if prosecuted) x present value of any expected fine, if
convicted. Here p represents probability. Since CO2 emissions are not currently regulated, we
assumed PI values for two different cases. In case 3, that is reported in Table IV of this
section, we combined PI = $80 with a value of  Cs = $200. This produced, corresponding
data are in Table IV, a value for  of 0.88, compared with  = 0.92 when PI = $40 and  Cs
= $200. In other words, raising PI from $40 to $ 80 (100 percent increase) that means a strict
emission regulation has a little impact on  . First of all, implementation of strict regulations
requires higher monitoring costs. Secondly, as electricity is an essential commodity, it may
cause undesirable political maneuvers.
So far, we have put same weight on all parties involved regardless of who gained or
lost from the outcomes of the policy. However, the history of social policy suggests,
however, that policy-makers may want to attach a higher weight to the gains and losses of
lower-income individuals than to gains and losses of higher-income individuals. Examining
this phenomenon closer, we developed case 4, where  Cs = $200 and  3 = 2, the liability
dropped by 0.12024.
6. Conclusions
The results of this investigation suggest a critique of the mainstream view, in both
economic theory and public policy, that: party (s) should be liable for the externality or
should share the economic externality burdens that they create as results of their own
acts. In the power plant case, the pivotal theme is that the generating companies produce
electricity as a commodity in a cost-effective manner in order to achieve their business
goals and ensure reliable and safety utility services. On the other hand, consumers use
electricity to ensure their basic needs and obtain a safe and comfortable life style cost
effectively. Here both parties are rational and they attempt to maximize their budgets.
Relying on this prototype, it warrants a set of rules that place both parties as responsible
for internalizing CO2 emission costs.
Since there is no current law that directly controls CO2 emissions, we incorporate SO2
emission regulation in our model, we find that full liability of external costs is in place where
both consumers and producers are involved, especially in the case of electric utilities. The
19
generating company meets the emission standards in different fashions under the CAAA and
passes on the incurred costs to the end-users, in terms of compliance cost or emission fees.
Under the umbrella of CAAA, each state can be authorized to implement its strategies to
meet the federal requirements. The State of Ohio is no different in this way from other states.
Under the Ohio Revised Code, Section 4905.31(B)(2) and (B)(3), the State of Ohio allows
electricity companies to charge emission rider fees to all retail customers and it will continue
to increase until the emission fees levied pursuant to 3745.111, Revised Code, is recovered.
The company produces excess electricity through coal combustion and transfers it to
competitive markets only after meeting local demands. Consequently, this transferable full
liability law creates extra gaseous emission burdens on the local end-users. The feature of
this law reflects the view that the application of full liability, in a two-party case where both
consumers and producers are involved, does not follow efficiency principles in resource
allocation, or fairness in the distribution of external costs. However, it results in a greater
degree of abatement of CO2 emissions than intermediate liability rules. According to this
model, the potential inefficiency of our assumed CO2 regulation and Pigouvian taxes is
implied in all cases, where optimal liability is less than 1, but approaches to it when the
weights assigned to gains or losses of victims,  3 = 1. In other words, in designing
regulated emission policy, intermediate liability rule is recommended rigorously and unapologetically where economic efficiency and equity aspects are in question.
Note: This paper reflects author's view and it has no linkage with or endorsement from the Ohio Department of Development
Acknowledgement: I am in debt to Prof. C.A. Edwards, The Ohio State University, for his encouragement and continuous supports.
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