Environmental regulation and international trade - Springer

Journal of Regulatory Economics; 8:61-72 (1995)
9 Kluwer Academic Publishers
Environmental Regulation and International Tradel
EFTICHIOS SOPHOCLES SARTZETAKIS
University of British Columbia
Faculty of Commerce and Business Administration, Vancouver, B.C., Canada V6T 1Z2
CHRISTOS CONSTANTATOS
Universit6 Laval
Ddpartement d' economique and GREEN, Sainte-Foy, Qudbec, Canada GIK 7P4
Abstract
In this paper, we investigate how a country's choice of environmental policy instrument affects the
international competitiveness of its firms. We show that in a Cournot-Nash equilibrium, the total market
share of firms regulated through tradeable emission permits increases relative to that of the firms
operating under command and control due to better allocation of total abatement among the firms in the
country. Our work suggests that free trade situations should not only result in similar environmental
standards but also in similar regulatory regimes. It may come as no surprise that the environmental
authorities in Canada are seriously considering following the United States in instituting a tradeable
emission permits mechanism.
1. Introduction
In recent years, increased awareness of environmental issues has made pollution control,
notably the control of emissions, an important topic in public policy discussions. A
commonly raised objection against emissions control is that this may impair the competitiveness
of the domestic industry in international markets. In particular, it has been argued
that firms operating in countries with low environmental standards will acquire substantial
Most of the work was completed during the time that E.S. Sartzetakis was a post-doctoral fellow at the
Department of Economics, Universit6 Laval. He gratefully acknowledges the hospitality of the
department during this period. Earlier.versions of the paper were presented at the fifth conference of the
European Association of Environmental and Resource Economists and at the 1993 Rancontre
Franco-Qu6b6coise du GREEN. We would like to thank Joseph Doucet, Thomas Ross, and Aart de
Zeeuw for extremely helpful suggestions. We would also like to thank two anonymous referees of this
journal for their comments. Financial support from the LRSA of the Facult6 des sciences de
l'administration, Universit6 Laval, the Groupe de rechearche en 6conomie de l'6nergie et des ressources
naturelles (GREEN), Universit6 Laval, and the Centre for International Business Studies (CIBS),
University of British Columbia, is gratefully acknowledged. The responsibility for errors and omissions
remains ours.

62 EFTICHIOS SOPHOCLES SARTZETAKIS AND CHRISTOS CONSTANTATOS
cost advantages over international competitors operating in more environmentally conscious
countries. Concern has even been expressed that some countries could become "pollution
havens" by attracting industries through low environmental standards; see for example,
Markusen et al. (1993). While earlier empirical research by Leonard (1988) and Tobey
(1989; 1990) suggested that differences in environmental standards did not have significant
impact on trade patterns, more recent work by Lucas et al. (1992) showed that this impact
may be important.
Substantial literature has been devoted to the impact of environmental policy on trade
patterns. 2 The link between trade and the environment is rooted in policy rigidities that
prevent authorities from achieving first best optimality. In the absence of any restrictions
on the use of environmental and trade policies, any impact the former might have on a
country's terms of trade could easily be offset by the appropriate choice of tariffs. International
agreements as well as the action of domestic lobbying groups may in fact limit the
applicability of trade and/or environmental policy instruments. Baumol and Oates (1988)
and Markusen (1975) consider limitations in the exercise of environmental policy and
examine modifications to the first-best tariffs necessary to account for environmental issues.
Krutilla (1991) and Markusen (1975) consider cases in which international trade agreements
limit the use of tariffs leaving environmental regulation as the only feasible policy towards
rent extraction from foreigners. In all cases, it is found that the second-best tariff or
environmental tax may be higher or smaller compared to its first-best level.
Kennedy (1994) also considers environmental policy as the only instrument in the
presence of transboundary pollution within an imperfectly competitive global environment.
Rather than looking at the optimal tax level, he determines the Nash equilibrium pollution
taxes and shows that strategic interaction between countries results to equilibrium taxes that
are lower than what is globally efficient. Finally, Copeland (1994) recognizes the possibility
of restrictions on the use of both environmental and trade policy instruments and investigates
conditions for gradual policy reforms to be welfare improving. His work emphasizes the
need for coordinated trade and pollution policies in order to avoid exacerbating distortions
and shows that small policy reforms may be more easily implemented under a quota rather
than a tax regime. He also finds that international factor mobility increases the benefits from
reforming pollution policy.
In this paper, we deal with the impact of environmental policy on trade patterns. Our
work differs from the aforementioned papers in that, instead of focusing on the level of
environmental standards, we concentrate on the impact of the type of regulatory regime on
a country's international competitiveness. This particular focus is motivated by the following
observations. First, the fact that some countries have already adopted "incentive based"
regulatory policy instruments--namely taxes and tradeable emissions permits--while others
are more hesitant to move in this direction and continue to apply command and control
regimes. Second, that environmental standards tend not to be significantly different among
developed countries; see Cropper and Oates (1992). The similarity of standards is merely
2 See, for instance, Markusen (1975a); Pething (1976); McGuire (1982); Merrifield (1988); Baumol and
Oates (1988); Krutilla (1991); Copeland and Taylor (1992); Copeland (1994); and Kennedy (1994).

ENVIRONMENTAL REGULATION AND INTERNATIONAL TRADE 63
due to similar preferences for environmental protection and/or international agreements.
Concerning the latter, one can argue that as rising environmental consciousness pushes
countries towards more stringent regulation, free-trade agreements will no longer be able to
neglect environmental issues; the need to prevent the use of lax environmental standards as
a substitute for trade policy will make international agreements a necessary complement to
any tariff-reducing agreement. Thus, a certain convergence of pollution standards among
countries may arise as a side effect of the current trend towards trade liberalization. 3 There
is, however, no apparent reason why international agreements should impose on participant
countries any specific regulatory regime.
Even in a context of differing environmental standards, the impact of differing regimes
on international competitiveness should not be neglected. As we show, for large differences
in abatement technology, a more efficient regulatory regime may yield an advantage
substantial enough to outweigh any trade disadvantage stemming from a more stringent
environmental regulation. Thus, the country with the more efficient regulatory regime can
either increase its international market share or afford a better environmental protection
without putting its firms in a competitive disadvantage.
Among the various regulatory instruments, Pigouvian taxes, tradeable emission permits
(TEP), and command and control (CAC) are the most commonly used. The equivalence of
emission taxes and permits, when there are no transaction costs or imperfections in the permit
market and the regulator has full information, is well established in the literature. While
Pigouvian taxes are used mainly in Europe, there is an increasing interest in North America
in the use of tradeable permits as an alternative to the widespread CAC regulation. In the
present paper, we employ emission permits as the representative of the incentive based
instruments. A number of studies have tried to evaluate the welfare merits of each system
by performing comparative statics in a closed economy; see, for example, Malueg (1990),
Copeland (1990), and Sartzetakis (1993). However, no work has yet examined the simultaneous
use of different types of regulation in an international trade context.
In this paper, we consider two countries imposing the same environmental standards
through different regulatory regimes and examine the potential effects of this asymmetry on
trade patterns. More specifically, we are interested in finding whether the adoption of any
specific regime might help a country's industry to increase its share in international markets.
The paper is organized as follows: section 2 describes the main model in the absence of
regulation; sections 3 and 4 derive the reaction functions of the firms under a CAC and a
TEP regulation, respectively; and section 5 analyses the free-trade equilibrium under the
simultaneous presence of both regulatory regimes. Section 6 contains the concluding
remarks. Most proofs have been abbreviated with more details provided in the corresponding
appendices.
This prediction should be moderated by the presence of issues related to transboundary pollutants,
differences in income distribution, and strategic considerations; see Markusen (1975b); Hoel (1991; and
1992); van der Ploeg and de Zeeuw (1992); Xepapadeas (1994); and Kennedy (1994).

64 EFTICHIOS SOPHOCLES SARTZETAKIS AND CHRISTOS CONSTANTATOS
2. The Model
We assume two countries, North, N, and South, S, producing a differentiated product which
is sold in an international market. Each variety of the product is produced exclusively in
= _b v ~ u
each country, and its inverse demand is pV a Q - Q , with b > ~ > 0 and v,u = N,S.
On the supply side, we assume that each country' s output is produced by two firms, acting
as Cournot oligopolists. 4 For analytical simplicity, marginal production cost, c, is assumed
constant and equal across firms. Firm i in country v, i = 1,2 and v = N,S, chooses qV to
maximize (pV _ c)qV, taking as given qy and QU, the total output in the other country. Firm
i,v's reaction function is qV= [(a- c)/2b] - [q]/2] - [SQU/2b].
Solving the system of
A
reaction functions, we obtain each firm's output level, qV = (a - c)/(3b + 25). The aggregate
level of output in each country is
^ 2 -
Qv = ~ . (1)
Production of the differentiated good is assumed to result in emissions of a common
pollutant. It is further assumed that the discharge of the pollutant is proportional to the firm's
^ A
level of output, E v = rq v, which implies that each country's level of emissions is E v = rQ v.
We assume that the governments in the two countries decide to reduce pollution by imposing
similar ceilings in emissions. Reducing emissions is costly in that it requires either a
reduction in output and/or the undertaking of some costly abatement. Total abatement,
A v
= o~i
v
qi,
v
is a function of a firm's level of output as well as of its chosen level of abatement
per unit of output ~v. Total abatement cost is assumed to be quadratic in abatement,
C v v v , v v,2
= dt~i qi + eil.t~i qi) , i = 1,2, v = N,S, where d, e i > 0 represent technological parameters.5
Abatement technologies differ among firms within the same country, but they are identical
across countries, e N = e S = ei, i = 1,2. 6 Also, e 1 > e2, such that firms characterized by e i may
be thought of as having less modern abatement technology. The similarity in the abatement
cost profiles of the two countries rules out any changes in market shares originating in
technological advantages of one of the counlxies, thus, allowing us to concentrate on changes
strictly attributable to the difference in the regulatory regimes.
While an equally stringent regulation is assumed in both countries, 7 the regulatory regime
through which environmental protection is sought is different: country N imposes a CAC
4 The model generalizes for n number of firms as long as at least two distinct abatement technologies
remain in use. The model also generalizes in the case of free entry, as long as there is restricted entry in
the use of the more efficient technology.
5 The assumption of quadratic abatement costs yields downward sloping demand curves for emission
permits, in the case that a tradeable emission permits regulation is chosen.
6 The main result of the paper holds even if we allow dl > d2. However, expositional complexity increases
substantially with differences in d term.
7 We assume that the regulation is not as stringent as to induce the exit of some firms under any regulatory
regime, i.e., qlv > 0, i = 1,2, v = N,S.

ENVIRONMENTAL REGULATION AND INTERNATIONAL TRADE 65
regulation, while in country S a TEP system is implemented. The assumptions of similar
standards and similar technology profiles isolate the effects of the regulatory mechanisms
and avoid results that are due to other factors.
3. North (Command and Control)
In the present paper, we specify the CAC regulation as requiring all polluters to reduce their
emissions by the same amount, E~/- ~/, with L-/r 2~/, i= 1,2, the aggregate emissions
ceiling in country N. In order to avoid unnecessary repetitions, hereafter, ij = 1,2 and i r
Each firm in country N chooses output and abatement per unit of output by maximizing
profits subject to the emissions constraint, ~v/= E~/- A N. Firm i's Lagrange maximization
problem is
.NN r NNV N
max L N = (a - bQ N- 5Q S) qN_ cqN_ clo~ i qi - e i~O~i qi ) + It'i~--~ - rqi + ~ J"
N
Setting ~LN/~o~ N = 0, we obtain 8 Li = d + 2eiaNq N, which implies that each firm reduces
output to the point at which the marginal loss in profit from foregone output is equal to the
marginal cost of abatement. 9 Firm i's output as a function of the Lagrange multipliers and
country S's output is
qN = a - c - r(29~ i - )~j) 5 a S.
3b - -377 (3)
Aggregating over i, we obtain North's total output as a function of South's total output,
QN = 2(a - c) - r(~, 1 + ~'2) 25 a S.
30 - 3-6 (4)
As shown in Appendix 1, if e 1 > e 2 then ~1 > )~2, which by simple inspection of equation
N N 9 v v --
(3) implies ql < q2. This, together with the regulatory constraint Ai = rqi - EN/2, implies
A N < A N. Thus, within country N, the firm with the higher marginal abatement cost engages
in a relatively lower level of abatement, and its market share is reduced relative to the other
firm.
4. South (Tradeable Emissions Permits)
Country S implements a TEP regulation by which polluting sources are required to obtain
emission permits for the quantity of pollutant they wish to emit. Each permit specifies an
amount of allowable emissions, assumed to be one unit, and is freely transferable. The
8 See Appendix 1 for details on the maximization of (2).
9 We assume that the value of d relative to demand parameters is not so high as to induce farms to engage in
no abatement under any regulatory regime.

66 EFTICHIOS SOPHOCLES SARTZETAKIS AND CHRISTOS CONSTANTATOS
assumption of identical environmental standards between countries requires that the number
of permits issued by the regulator in country S is equal to the maximum allowable units of
emission in country N, i.e., ~v = ~.s. The regulator distributes the permits free of charge to
the firms, with firm i receiving E~/= Es/2 permits. After the initial distribution of permits,
firms can freely trade permits.
With the introduction of tradeable permits, another market is added to the model. This
market can either be perfectly or imperfectly competitive. We assume here that the pollutant
in question is emitted by many industries producing goods with zero cross-price elasticity
of demand and that the distribution of high and low abatement cost firms is similar across
industries. Thus, while firms are Cournot players in the product market, they are price takers
in the emission permits market. Firm i's net demand for permits is NE~/= E//- ES/2, where
E~/= E~/- A s is firm i's demand for permits; in equilibrium, ]E2=1NE~i=O.
Firm i's profit maximization problem is
max n S = (a - bQS-SQN) qSi-s- cqi - a~ ss qi - ei (~SqS~ - P ~ (r - c~ S) qS _~__2_1
s s
i
qi ,~i (5)
where P~ is the price of permits. Setting ~/S/~o~S = 0 implies 10 pE = d + 2eio~Sq S, so that
each firm sells or buys permits until its marginal cost of an extra permit is equal to its marginal
cost of abatement. Firm i's output as a function of the permit price and North' s output is
qS= a - c - rP e 8
3b - 3-~ QN. (6)
Aggregating output over i, we obtain total output in South as a function of North's output,
Qs 2(a-c-rP E) 28
= 3b - 3-6 QN. (7)
From (A. 14), it is clear that el > e2 implies A s < A s. Therefore, the lower abatement cost
firm engages in a relatively higher level of abatement and sells its excess permits to the high
abatement cost firm. Since at the equilibrium the marginal abatement cost of both firms
equals pC, the introduction of environmental regulation leaves relative market shares of the
firms in country S unchanged, so that ~/QS=qS/QS.
5. Trade Equilibrium with Regulation
Solving simultaneously equations (4) and (7), we obtain QN, Qs as functions of the
equilibrium values of L1, ~2, and pE,
10 See Appendix 2 for details on the maximization of (5).

ENVIRONMENTAL REGULATION AND INTERNATIONAL TRADE 67
QN = 2(3b - 28) (a - c) - 3rb(~, 1 + ~'2) + 4rSPE
(3b - 2~5) (3b + i5)
(8)
and
Qs = 2(3b - 25) (a - c) + 2r5(~, 1 + L2) - 6rbP ~
(3b - 25) (3b + i5) (9)
From the above expressions, we can see that QN+QS-2Q=r(45-6b)[Pe
+ (~,1 + ~,2)/2] < 0, since b > 5. Thus, total output decreases after the introduction of
environmental regulation. This should not come as a surprise, as the regulation imposes an
additional cost upon the firms. What is crucial in our analysis is to determine how the burden
of output reduction is distributed among countries. To that end, we need first to establish a
relation between the equilibrium price of permits and the values of the Lagrange multipliers.
Under the assumption that both countries set the same emissions ceiling, ~r = ~7 S, we have
rQ N - A N = rQ S - A S, where A v = Z2=1 A v, v = N,S. Substituting into this condition the
values of QN, Qs, A N and A S from (8), (9), (A.5), and (A.14), respectively, we derive the
following relationship between the competitive permit price and the Lagrange multipliers:
pE = (3b - 25) (3b + 2fi) (el~, 2 -I- e2~,l) + 2ele2r2(3b + 45) (~1 + ~'2) (10)
4ele2r2(3b + 45) + (3b - 25) (3b + 28) (e 1 + e2)
Setting the RHS of (10) smaller than the average of L's and cross-multiplying, we obtain
(3b - 25) (3b + 25) (el - e2) (L2 - ~,1) < 0. Since b > 5, a necessary and sufficient condition
for pe < (L1 + ~,2)/2 is that (el - e2) (~,2 - ~,1) < 0. The LHS of this expression can never be
positive, since el > e2 implies ~,I > ~,2; it cannot be zero either, unless both firms in the N
country possess the same abatement technology. Thus, in the free-trade regulated equilibrium,
if el ~e e2 then the price of emission permits in country S is lower than the average of
the Lagrange multipliers in country N, i.e., e 1 #: e 2 pE < (~1 + ~2)/2.
This result reflects the advantage of a TEP regulation in distributing abatement effort more
efficiently between firms. Indeed, since pe > ~,2 (see Appendix 2 for the proof), it follows
from (A.5) and (A.14) that As = (pC _ d)/2e2 > (~,2 - d)/2e2 =A N. Thus, in South the low
abatement cost firm undertakes a greater amount of abatement activity than its counterpart
in country N. By encouraging higher abatement by the low cost firm, a TEP regulation results
in a more efficient allocation of abatement effort. This advantage vanishes when technologies
are similar and its importance is directly related to the technological heterogeneity within
the country that implements a CAC regulation.
Turning to the question of changes in market shares after the introduction of regulation,
recall first that all firms produce similar outputs in the pre-regulation equilibrium. Taking
the difference between (8) and (9) and rearranging terms, we can show that the difference
Qs_ QN is proportional to the expression r(25+ 3b) (~1 +L2- 2PE) > 0, since
el r e2 Pe < (~,1 + ~2)/2.
Thus, in the presence of diverse abatement technologies

68 EFTICHIOS SOPHOCLES SARTZETAKIS AND CHRISTOS CONSTANTATOS
within each country, the aggregate market share of the firms regulated through a TEP system
increases relative to its pre-regulation level while that of the firms operating under a CAC
system is reduced. Therefore, for the environmental regulation not to have any effect on the
trade pattern between two regions, not only similar standards, but also similar regulatory
mechanism must be adopted.
The advantage of country S's industry in this model is due to the fact that while a TEP
system results in the efficient allocation of abatement effort between firms with differing
technologies, a CAC regulation fails to do so. This advantage increases with the diversity
in abatement technologies and can become so significant as to outweigh the impact of
regulation and result in an increase in country S's output in absolute terms. Comparison of
(1) and (9) reveals that for this to be true the second term in (9) must be positive, i.e.,
2~r(~,i + ~j) - 6brP e > 0, which holds when pe < (2~5/3b) (~,i + ~,j)/2. The latter is more
likely when ~5 is close to b, so the two countries' products are close substitutes and the
equilibrium price of permits is very low compared to the average of the Lagrange multipliers.
6. Conclusions
We investigate how a country's choice of environmental policy instrument affects the
international competitiveness of firms in that country. We show that in a Cournot-Nash
equilibrium, the total market share of firms regulated through a TEP system increases relative
to that of the firms operating under a CAC system. This is due to the fact that a TEP system
better allocates total abatement among the firms in the country. The advantage of a TEP
system becomes more pronounced as the diversity of abatement technologies within the
country that implements a CAC regulation is increased. For large differences between the
two firms' abatement costs, the enactment of environmental regulation may increase the
output of the country that implements a TEP regulation relative to the pre-regulation
situation. Our work suggests, therefore, that free trade situations should not only result in
similar environmental standards but also in similar regulatory regimes. The fact that
environmental authorities in Canada are seriously considering following the United States
in instituting environmental regulations through tradeable emission permits systems is
consistent with the above result.
The advantage of TEP regulations must be qualified for the competitive emission permit
market assumption. Hanh (1984) has shown that in autarky, when the industry is competitive,
a non-competitive permit market result in efficiency losses, but remains more efficient
than a CAC system. Further, Sartzetakis (1993) fias shown that a CAC regulation may be
welfare superior to a non-competitive permits market when the industry is also non-competitive.
These results indicate that the advantage of a TEP system may be substantially
reduced in the presence of imperfections in the permits market.
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70 EFTICHIOS SOPHOCLES SARTZETAKIS AND CHRISTOS CONSTANTATOS
Appendix
In this appendix, we provide some additional steps of the solution to the firms profit
maximization problem both in country N and S.
Appendix 1: North (command and control)
Country N implements a command and control regulation. Firm i chooses qi and ~i,
i = 1,2, by solving the following constrained profit maximization problem:
max N LN = (a - bQN- SQS) qNi - d~ qi - ei(~i qi ) + ~'i
qi '~
The first-order conditions are:
a- 2bqN-bqN-~QS-c-do~ N- 2ei(~i )2q N- ~i(r- ~N) = 0, (A.1)
qbiTi(- d- 2ei~Niq N + ~'i) = 0,
(A.2)
NN
~i qi = ---2-" (A.3)
Using (A. 1) and (A.2), we obtain firm i's output reaction function as function of the Lagrange
multiplier and country S's output,
N a-c-r)~i 1 N
qi = 2b - ~ qJ - ~2~ Qs. (A.4)
Solving equations (A.4) for ij = 1,2 yields firms' output as shown in equation (3) in the main
text.
Firm i's level of abatement is,
AN N N ~'i - d
i = I~i qi = ---2-~i ' (A.5)
which follows immediately from (A.2). Substitution of qN and A N from (3) and (A.5)
respectively into (A.3) yields firm i' s Lagrange multiplier as a function of country S' s output,
2eir(b + 2ejr 2) (a - c - 8Q S) - 6bei(b + 2ejr 2) ~
+ b[3b + 2(2ej + el) r 2] d
~i = 3b 2 + 4b(e i + ej) r 2 + 4eiejr 4 (A.6)
The difference between the two firms' marginal costs of abatement in equilibrium is
~1 - ~2 =
2b(el - e2) [r(a - c - rd- 8QS) - 3bl~l - 2b(el - e2) r2d
3b 2 + 4b(e 1 + e2) r 2 + ~e~e2 r4
(A.7)
Rearranging terms, equation (A.7) can be written as follows,

ENVIRONMENTAL REGULATION AND INTERNATIONAL TRADE 71
3b2(el - e2) [ r2(a - c - rd-
- EN]
9~1 - )~a = 3b 2 + 4b(e 1 + e2 ) r e + 4ele2r4 (A.8)
Excluding corner solutions, c~ N > 0, qN > 0, implies that )~i > d, from (A.5). This inequality,
along with equation (4), implies,
Equations (A.8) and (A.9) yield
2(a-c-rd) 28QS
3b - -3B > QN. (1.9)
3b2(e1 - e2) (rQ N- E N)
9~1 - L2 > 3b 2 + 4b(e 1 + e2 ) r 2 + 4ele2 4" (A.10)
Aggregating the constraints of the two firms in country N, equation (A.3), we obtain:
rQN _ A N = ~-dg.
Since we exclude corner solutions for both output and abatement per unit of output, the
aggregate emissions constraint implies rQ N > ~4v. The last inequality along with equation
(1.10) implies L1 > )~2, since el > e2. It follows that (el - e2) ()~2 - )~1) < 0.
Appendix 2: South (competitive tradeable emissions permits market)
Country S implements a tradeable emission permit system. We assume that both firms
are price takers;in~e Permit market. Firm i's optimal choice of qi and ~i, i = 1,2, is derived
by solving the following profit maximization problem:
max Jrc S = (a - bQ S - 8Q N) qS
- cqi
s
- dtxi
s
qi
s
- ei(~
s
qi
$2
) - Pe[(r - ~i
s
)
qS _ ~_~2_].
S S
qi ' O~i
The first-order conditions are:
a- 2bqS-bqy-SQN-c-do~ S- 2ei(o~S)2qS-pe(r-o~S)=o, (A.11)
qSi(- d - 2eicxSq S + pE) = 0,
(A.12)
fr~om which we obtain firm i' s output reaction function
qS=a-2;PPE 1 _ ~ qS_ ~/~ QN.
(A.13)
Solving the two reaction functions in (A.13) for ij = 1,2, we obtain (6).
Equation (A. 12) yields the equilibrium abatement of firms in country S as function of the
competitive permit price, P~,
A S ~s s pe _ d
i = iqi=--~i . (A.14)

72 EFTICHIOS SOPHOCLES SARTZETAKIS AND CHRISTOS CONSTANTATOS
Finally, in order to prove that pe > ~,2, we replace pE by the RHS of (10). Simplifying
and rearranging terms, we obtain that a necessary and sufficient condition for pe > L2 is
(3b - 2~5) (3b + 25) e2(~, 1 - ~'2) + 2ele2 r2(3b + 4~5) (~1 - ~'2) > 0,
which is true since ~,1 > ~,2 and b > 5.