Are Economic Sanctions Credible and Effective in Deterring Free-Riding of an
International Environmental Agreement?
by
Chui Ying Lui
BBA (Hons) Business Economics
City University of Hong Kong
An Extended Essay Submitted in Partial Fulfillment of the
Requirements for the Degree of
MASTER OF ARTS
in the Department of Economics
We accept this extended essay as conforming
to the required standard
____________________________________________________________________________
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© Chui Ying Lui, 2010
University of Victoria
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or other means, without the permission of the author.
Abstract
This paper analyses in a partial equilibrium model whether economic sanctions
can deter free riding of an International Environmental Agreement (IEA). The sanctions must be both credible, i.e. there is incentive to punish free-riders, and effective,
i.e. the punishment is strong enough to remove the incentive to free-ride. I analyze an IEA that requires signatories to impose a pollution tax on producers. The
analysis takes into account that countries have different roles in international trade
due to differences in their cost functions. I find that economic sanctions could be
credible, but alone cannot induce full participation of an IEA.
ii
Contents
1 Introduction
1
2 Literature review
2.1 A global pollution tax . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 IEAs and trade sanctions . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Other issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2
3
6
3 The
3.1
3.2
3.3
partial equilibrium model
Benchmark model without externalities . . . . . . . . . . . . . .
Externalities without an IEA . . . . . . . . . . . . . . . . . . . .
Externalities with an IEA . . . . . . . . . . . . . . . . . . . . . .
3.3.1 IEA of imposing a common tax . . . . . . . . . . . . . . .
3.3.2 Incentives for countries to deviate . . . . . . . . . . . . .
3.3.3 IEA of a common tax and trade restrictions . . . . . . . .
3.3.4 Incentives for countries to deviate with trade restrictions
3.3.5 IEA of a common tax and tariffs/a price floor . . . . . . .
3.3.6 Incentives for countries to deviate with T = t∗ . . . . . .
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4 The political economy of the Kyoto Protocol
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5 Conclusion
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6 Shortcomings and future research
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A Production Externalities
43
B Welfare of Country 2 and Country 3 when a prohibitive tariff is imposed
on Country 1
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C Condition for the prohibitive tariff to be a credible threat
45
D Mathematical appendix for the analysis of the incentives for Country 2
to deviate with a trade embargo
45
iii
1
Introduction
International Environmental Agreements (IEAs) are international agreements aimed at
correcting inefficiencies caused by environmental externalities. Because we don’t have
a world government, participation in these agreements must be voluntary. However,
Barrett (1992) [1] finds that, in the case when the number of eligible countries is large,
and the gains to cooperation are potentially large, which is the case for IEAs, a selfenforcing treaty cannot sustain a high participation rate. To illustrate this, suppose all
countries were to participate. If one country were then to withdraw from the agreement,
the marginal effect would be minimal. For the other countries to punish the free-rider,
they would have to lower their abatements together, but this would decrease the benefits
to all countries substantially, due to the large number of countries involved. Thus the
countries would not lower their abatement, so there is no punishment for the country that
withdrew.
The problem of free-riding is therefore prominent in IEAs. A credible and effective
punishment is necessary to deter free-riding. A punishment is credible when there is
incentive for signatories to punish free-riders, and it is effective when the punishment is
strong enough to remove the incentive to free-ride. Mechanisms proposed in the literature
are R&D protocols (Barrett, 2005 [5] ; Carraro et al., 1995 [11] ), and trade sanctions
(Barrett 1997 [3] ).
This paper investigates the possibility of using economic sanctions as a credible and
effective punishment to deter free-riding. Countries that sign the IEA are assumed to
impose a common environmental tax on emissions. Without such a tax, countries produce
and consume goods regardless of the emissions caused, and thus emit more than is efficient.
The external cost of emitting is neglected. The optimal tax rate is equal to the marginal
external cost of the efficient level of emissions. With the optimal tax imposed, social
welfare increases because at equilibrium, countries produce the quantity at which marginal
private cost with the tax is equal to marginal social cost. This quantity is also the efficient
quantity.
Countries that do not impose the tax face either a tariff (for exporting countries)
or a trade embargo (for importing countries) imposed by the countries that do. Given
that retaliation tariffs are not allowed under the General Agreement on Tariffs and Trade
(GATT) by the World Trade Organization (WTO), imposing tariffs could be a credible
punishment when the countries imposing the tariffs would benefit from them, compared
to letting free-riders go unpunished. There is a general agreement (see, for example,
Barrett 2005 [5] and Stiglitz 2006[21] ) that to protect the environment, the WTO should
allow countries to use tariffs as a punishment.1 It is, therefore, not a strong assumption.
There are also various real world examples of using trade embargoes for the production
of a global public good.2
The more effective the threat of sanctions is at increasing participation in the IEA,
the less the sanctions would need to be imposed, and the less welfare lost from imposing
sanctions. Ideally there is full participation and no sanctions. The sanctions are purely
1 Article XX of the GATT allows parties to take measures ”necessary to protect human, animal or
plant life or health” or ”relating to the conservation of exhaustible natural resources.”
2 Examples include United Nations sanctions against South Africa to combat apartheid (1962-1994),
United Nations sanctions against Iraq to stop the production of mass destructive weapons (1990-2003),
U.S. and Japan sanctions against India to stop development of nuclear weapons (1998-), etc.
1
a threat.
2
2.1
Literature review
A global pollution tax
I focus on using a global pollution tax to correct the inefficiencies due to externalities. The
tax would be levied on companies that emit pollutants in production, or that sell products
that emit pollutants when consumed. In the case of producers emitting pollutants in the
production of the good, such a tax would cause firms to adopt techniques that reduce the
amount of pollutant they emit, so long as the cost of doing so is less than the tax that
they would otherwise have to pay. In the case of consumers creating the externalities,
the tax on producers would increase the cost of production and therefore the price of the
good to consumers.
The higher cost of production incurred to reduce emissions would, of course, increase
the price charged to consumers. Consumers would respond by reducing their consumption
of those goods and services in favour of goods and services that create smaller amounts
of pollutants, and are therefore, relatively cheaper.
I focus on imposing a global pollution tax because it is advantageous as compared
to the most common alternative, the cap and trade system. Both cap and trade and
pollution tax are tools to give emissions a price target, which should be the optimal price
all countries should pay per unit of emission so that the world’s emission level is efficient.
This price is translated to a world abatement amount, as countries emit less due to the
higher cost. Under a tax, producers or consumers pay for the price of emissions directly.
Under cap and trade, the price of emissions is indirectly incorporated in the price of the
permits. Even though the governments give out ’free’ permits, firms still incur a higher
cost due to emissions, due to the requirement of permits. Taxes are not popular among
producers and consumers, so the cap and trade system is easier to implement politically
and thus more common, however, it is inferior to imposing a tax, which serves the same
purpose of giving emissions a price.
Stoft (2010)[22] criticizes the global cap and trade system by showing that in a global
public good game with a cap and trade system, players’ dominant strategies lead to
an inefficient outcome. He shows that cap and trade results in (1) a price target (for
emissions) that is too low and thus total abatement level is lower than efficient, and
(2) a polarization of commitment levels, i.e. low commitment countries adopt lower
abatement targets, and high commitment countries adopt targets above their abatement
levels without cap and trade. This is because in a standard public good game, countries
supply abatement up to the point at which its marginal cost equals its marginal benefit.
The optimal abatement price, call it Pi , is different for each country i. Cap and trade
makes it possible for countries that have chosen to abate up to a higher price level to
buy abatement at a lower cost from other countries. This abatement cost, call it P, is
the same among all countries. Countries that have Pi > P will find that their cost of
abatement has decreased, and will abate more than in the standard public good game,
and vice versa. Consequently, countries with high abatement tend to not ratify the IEA
as the game repeats.
Stiglitz (2006) [21] argues that the big advantage of a global pollution tax is that it
avoids most of the distributional debate. Under the Kyoto protocol, countries debate for
2
more rights to pollute. With a common tax, once the social per unit cost of emission is
determined, even though it may not be trivial, all countries pay the same price, and therefore there is no need for debate on how much each countries’ emissions target should be.
Also, a common tax does not limit developing countries to emit any less than developed
countries, and instead they all have to put in the same proportional effort level.
Note that a common tax may strike a distributional debate of whether a consumption
tax or a production tax should be imposed. I find that in a world with net exporting
countries and net importing countries, a tax on consumption generates more tax revenues
for importing countries while a tax on production generates more tax revenues for exporting countries. Countries would have to specify in the IEA whether a consumption
tax or a production tax or a mix of the two would be imposed. Otherwise, there may
be a problem of double taxing and inefficiency may occur. Nonetheless, the advantage of
the common tax over the cap-and-trade system is still valid, since the amount of overall
abatement is fixed once the tax rate is fixed, and countries do not have private advantages
to negotiate a lower tax rate, as the tax rate is a common global rate. With the cap and
trade system, even though a world emission cap is predetermined like in the case of a
pollution tax, countries tend to justify their own rights to pollute more. Consequently,
the overall abatement level decreases.
Another advantage of a common tax is that implementation costs are lower. First,
each country would keep the revenue it receives from the tax, rather than having to
give the money to another country, as in the case of the cap-and-trade scheme. Second,
a pollution tax causes each firm and household to respond to the same cost of adding
pollutants to the atmosphere. The uniform incentive allows total pollutants to be reduced
at a lower total cost than would be achieved by a variety of administrative requirements,
which are costly themselves.
Feldstein (2009) [14] expresses concerns of a cap-and-trade system causing serious
risks to international trade. Without international permit trading, each government sets
total allowable national emissions of CO2 per year and requires any firm that causes
CO2 emissions to have a permit per ton of CO2 emitted. These permits are then sold
by the governments. Because of the national differences in initial CO2 levels, there will
be differences in permit prices. And, because the price of the permits in a country is
reflected in the prices of its products, the cap-and-trade system affects its international
competitiveness. When the permit prices become large enough to have a significant effect
on CO2 emissions, there will be political pressure to introduce tariffs on imports that
offset the advantage of countries with low permit prices. Such offsetting tariffs would
have to differ among products and countries and they would ultimately threaten our
global system of free trade. He argues that a common carbon tax, even though politically
difficult to implement, is a better solution.
Note that while the above mentioned tariffs are destructive to social welfare, they
are not the same tariffs as the ones I propose in this paper as a punishment to deter
free-riding of IEAs.
2.2
IEAs and trade sanctions
Barrett (1994a) [2] shows that IEAs cannot sustain a large number of signatories without
any enforcement mechanism. This is because an IEA has to be self-enforcing, that is,
countries have to accede to it voluntarily, since there is no authority to enforce the agree-
3
ment. There are cases when self-enforcing IEAs can sustain a large number of countries,
but this requires that the difference in net benefits between the non-cooperative and fullcooperative outcome is very small. Because if countries would voluntarily accede to the
IEA, this implies that the externalities are more costly to them than abating, and they
are more likely to abate even without an IEA.
The main problem with imposing tariffs as punishments for free-riders is that it is
not a credible threat. In the absence of externalities, orthodox economic theory suggests
that the distortionary effects of tariffs would be welfare depressing for all parties and thus
free-riders do not believe that the punishment will actually be carried out. Brander and
Spencer (1984) [8] , without considering externalities, show that for a two country world
with bilateral tariffs, if transport costs are low, tariffs are inefficient as they decrease the
gain from trade. Tariffs are particularly undesirable if the domestic industries have higher
costs. However, they also show that a unilateral tariff is welfare enhancing to domestic
welfare, since gains in producer surplus and tariff revenue more than offset the loss in
consumer surplus. Assuming the WTO can prohibit retaliation of non-signatories, tariffs
could be a credible punishment, if the union of signatories is sufficiently large.
Barrett (1997) [3] considers using trade sanctions to deter free-riding. In his model,
countries first choose simultaneously whether or not to be signatories to an IEA, and then
signatories and non-signatories choose to play ”abate” or ”pollute” respectively. After
that, firms choose their segmented outputs. Firms are identical price setters and react
to the government’s decision accordingly. If the government chooses to be a signatory,
the firm will decrease the output level in reaction. The decrease in output for signatories
accounts for the leakage amount; that is, the shift of production from signatories to nonsignatories. This leakage reduces the benefit of being a signatory. He finds, with the
leakage effect, that the threat of imposing trade sanctions may be credible, and may be
sufficient to deter free-riding completely. But the sanctions must be accompanied by a
minimum participation clause if they are to be incentive compatible. In equilibrium, there
is full participation and trade is not restricted. That is, the threat of trade sanctions is
welfare enhancing.
His results sound promising, but are restricted due to his specific set up. In this paper,
there are a few refinements. First, firms (countries) are not identical, that is, they have
different cost functions, which is more realistic. Under this set up, I can investigate how
the cost functions affect the behaviour of the countries. Another difference is that firms
are price takers, and thus equilibrium prices and quantity are determined by the market.
Barrett (1999) [4] considers another game in which there is no leakage, i.e. shifting
of emissions from signatories to non-signatories. And, as a result, a trade ban is never
credible, even though it would be effective in deterring free-riding if signatories could
commit to imposing the trade ban. What distinguishes this model from Barrett (1997)[3]
is the presence of trade leakage. Given that a defection has occurred, since there is no
leakage, non-signatories can only be made worse off by restricting trade. But imposing
trade restrictions hurts the signatories (punishers) more than letting the free-rider go
unpunished. Therefore, the threat of trade restriction is not credible, because free-riders
are aware that the signatories will not carry out the threat. On the other hand, suppose
that if a country were to withdraw from an IEA, output in the pollution intensive industry
would increase substantially in this free-riding country, but only if there were free trade.
Then the remaining signatories would have an incentive to restrict trade, because by doing
so they stop the increased externalities caused by the leakage. Trade sanctions could be
4
credible, when the extra externalities caused by the leakage is more costly than restricting
trade. Of course, in these models, due to the countries being identical, the credibility of
the sanctions are not separately studied for exporting and importing countries. In my
analysis, I find that imposing trade sanctions on importing countries are not effective nor
are they credible, even with leakage.
Carraro and Siniscalco (1993) [13] demonstrate that, since a full agreement of all
players is unlikely, some players may act independently or unilaterally to maximize their
own welfare and self-interests, while other players create small and stable coalitions.
Carraro and Siniscalco (1998) [12] and Carraro (1999) [10] find that a stable coalition is
characterized by external and internal stability. Internal stability means that no country
in the coalition has an incentive to leave it. External stability means that no country
outside the coalition has an incentive to join it. Formation of stable coalitions improves
efficiency.
Kemfert (2004) [16] considers four different world regions, and investigates whether
a stable coalition can be formed on climate control. He follows the approach of Carraro
and Siniscalco (1995) [11] and Buchner et al. (2005) [9] where countries play a two-stage
game. Negotiating countries decide first non-cooperatively whether to join a coalition,
i.e. the coalition game. In the second stage, players not cooperating on climate control
are threatened either by the exclusion of technological innovations or by trade barriers.
He does not specify which kind of trade barriers.
His results show that trade barriers do not provide significant incentives to join a
coalition. Because of the international principal terms of trade effects of strong nations
like the USA, Europe and Japan, it seems that trade restrictions against non-cooperating
countries are a punishment against the countries that impose them. The only exception
is a partial coalition between Japan, Europe and Russia on climate control and trade
barriers against the USA. However, not all countries are better off in it than if there were
no agreement at all.
There are a few differences in the set up of Kemfert’s model and the model in my paper.
First, he uses a computerized general equilibrium model to construct the payoff matrices.
Even though heterogeneity of the countries is built-in, one cannot analytically investigate
the factors influencing a country’s payoff and thus abatement decisions. Second, in his
paper, climate control is assumed to be carbon permit trading, while in my paper a global
pollution tax is imposed. Third, in his paper, revenues from permit trading are used as
R&D investments. In my paper, technological spill-over effects are not considered. Lastly,
of the eleven regions in his general equilibrium model, he only considers four of them, the
other regions are assumed to not abate. In my paper, all countries are assumed to be in
a coalition by default.
Lessmann et al.(2009) [18] find that when the coalition imposes tariffs on imports from
free-riding regions, participation in the coalition rises. Global social welfare rises along
with participation despite small welfare losses due to the distortion caused by the tariff
instrument. Also, the threat of trade sanctions is credible only when the tariff rate is
smaller than a certain amount. This amount depends on the Armington elasticity, which
is the elasticity of substitution between products of different countries, and is based
on the assumption that products traded internationally are differentiated by country
of origin. He also finds a small leakage effect as mentioned in Barrett’s paper, that
is, non-members raise their emissions. In his paper, there are 9 identical firms. In
contrast, my paper examines firms with different cost functions. Also, in his paper,
5
trade is modelled by having all countries produce a generic output, but adopting national
product differentiation (Armington assumption). In contrast, in my analysis, there is
only one common product among all the countries, the other good is assumed to be
non-tradable.
All in all, my paper explores a relatively new area of research that incorporates global
negative externalities from pollutants into international trade theory. In my model, countries have different cost functions and different roles in international trade. As a result,
the different welfare impacts of punishing exporting non-signatories and importing nonsignatories can be deeply examined in a partial equilibrium model.
2.3
Other issues
Stiglitz (2006) [21] proposes to raise participation in a climate treaty by imposing trade
sanctions against non-signatories. He argues without a formal argument that this is
possible and even required in the legal framework of the GATT.
In another article, Stiglitz (2006) [20] suggests that other countries should prohibit
the imports of American goods produced using energy intensive technologies, or, at the
very least, impose a high tax on them, to offset the subsidy that those goods currently are
receiving, in order to reduce the emissions from the U.S. He suggests that Japan, Europe,
and the other signatories of Kyoto should immediately bring a WTO case charging unfair
subsidization.
My model supports Stiglitz’s view and shows that high tariffs on non-signing exporting
countries are a credible threat to punish free-riding countries.
Biermann and Brohm (2005) [6] focus on the question of whether tariffs are feasible
from a legal perspective. Ismer and Neuhoff (2007) [15] focus on the implementation
aspect. The implementation problems and legal aspects, though non-trivial, are not the
focus of this paper. This paper assumes that tariffs can be levied and analyzes, in a
partial equilibrium framework, whether the combination of a common tax and tariffs
could maintain an efficient outcome.
Some (Barrett 1999[4] ,2005[5] , van Slooten 1994[24] , and Brack 1996[7] ) have studied
the Montreal Protocol on Substances that Deplete the Ozone Layer, an IEA which bans
trade between signatories and non-signatories. The treaty negotiators included staged
restrictions in the Protocol on imports and exports. Developing nations were encouraged
to become party to the Protocol within ten years. Despite a high participation rate,
Barrett (1994a,[2] 1999[4] ) finds that the Protocol is not as successful as it appears. He
finds that due to the high external cost imposed by CFCs, countries would have abated
even without trade sanctions. However, once an agreement is formed, trade sanctions are
necessary to stop leakage of CFC production to non-signatories. Without trade sanctions,
when the participation rate of the agreement is high enough, the leakage amount could
be substantial. The profits from the leakage amount could induce some countries which
would have abated to free-ride. The Montreal Protocol shows that policy makers consider
trade sanctions as a plausible punishment for free-riding.
6
3
The partial equilibrium model
For now I focus on a partial equilibrium model.3 Even though this simplified framework
neglects the feedback effect that may occur in other markets, it gives insights on a single
market in isolation of effects from other markets. Also, it allows for more realistic demand
and supply curves so that heterogeneity among countries can be examined. In a general
equilibrium model, one has to restrict the supply curve to a completely elastic one, or
cardinality of agents’ utility function would have to be assumed for welfare analysis.4
3.1
Benchmark model without externalities
As a benchmark, the model begins without tariffs or tax and no externalities. There are
N countries in the world and each country produces a tradable good x that is the same for
all countries, and a non-tradable good. For now I focus on the analysis of N = 3. Country
1 is assumed to be an exporting country; Country 2 is assumed to be an importing one;
and Country 3 is assumed to be self-sufficient. There is no transportation cost. Countries
benefit from the country with a comparative advantage in producing good x and are
importing it from the country with the lowest cost.
A given Country i has a cost function of:
Ci (x1 ) =
x2i
2αi
(1)
where xi is total output by Country i.
Marginal costs are represented by Ci′ (xi ) = αxii . αi is assumed to be positive for all i.
Marginal costs are increasing with quantity produced.
Pi is the price of good x in Country i. Firms are price takers, and they supply
according to the schedule of price equal to marginal costs:
Pi =
Si
αi
(2)
Si is the quantity produced in Country i.
Country 1 is the most cost effective country and Country 2 is the least cost effective
one such that α1 ∈ [1, ∞) and α2 ∈ [0.5, 1) and Country 3 has α1 > α3 > α2 .
Assume the demand curves of the countries are the following:
D i = a i − bi P i
(3)
In which ai , bi > 0 and Di is the quantity consumed in Country i.
Without trade, countries produce and consume at the quantities where their own
supply curves and demand curves intersect. Assuming that countries have the same
demand curves, Country 1’s autarky equilibrium price, P 1∗ , is the lowest, while Country
2’s autarky equilibrium price is the highest.
When countries trade, they all face the same price P . The world equilibrium price and
quantity are determined by the aggregate demand and aggregate supply of all 3 countries:
3 For a discussion of partial vs general equilibrium analysis, see Mas-Colell, Whinston and Green [19]
p.316-325.
4 See Tresch (2002)[23] , chapters 13 and 14 for a detailed discussion.
7
D = S = x∗
D and S are world supply and demand respectively. So:
a w − bw P = α w P
P3
P3
The subscripts w denote world quantities, and aw =
i=1 ai ; bw =
i=1 bi and
P3
αw = i=1 αi .
Solving for equilibrium world price and quantity, P ∗ and x∗ :
P∗ =
aw
αw aw
; x∗ =
bw + α w
bw + α w
(4)
Figure 1 shows the world market of good x.
World price
Figure 1: World Market of Good x Without Externalities
S
P∗
D
x∗
World quantity of good x
Country 3 remains self-sufficient. This is a result of the symmetry built into the
graphs with respect to the demand curves and supply curves of the countries. It is not
the general case. Country 2, the least cost effective country, imports from Country 1.
Import to Country 2 increases as α2 increases or α1 decreases. Figure 2 shows the exports
and imports of good x for Country 1 and 2:
8
Figure 2: Exports and Imports of Good x
Country 1
Country 2
Country 3
S2
Price
D1
S3
Price
Price
S1
Exports
P
∗
Imports
P
P∗
∗
D2
D3
Quantity in country 1
Quantity in country 2
Quantity in country 3
Under free trade, social welfare in each country is given by:
Wi = CSi + P Si
(5)
CSi is the consumer surplus gained from the consumption of good x in Country i.
P Si is the corresponding producer surplus.
Since Country 3 is self-sufficient, there is no change in welfare from trade.
Figure 3 shows the increase in welfare due to trade for Country 1 and 2.
For Country 1, there is a loss in CS due to the increase in price from P1∗ to P ∗ .
However, the P S gain from exporting at P ∗ is higher than the loss of CS, by the amount
as indicated by the triangle.
Similarly, Country 2 incurs a loss in P S due to the decrease in price from P2∗ to P ∗ .
But the CS gain from importing is higher than the loss, by the amount as indicated by
the triangle on the right:
9
Figure 3: Welfare Increase Due To Trade
Price
Gain in welfare from importing
Price
Gain in welfare from exporting
P∗2
P∗
P∗
P∗1
S1
D1
S2
Quantity in country 1
3.2
D2
Quantity in country 2
Externalities without an IEA
Now, assume that there are externalities. As countries consume good x their emissions
entail an external cost to all countries, denoted by T ECi , increasing social cost above
private cost. Externalities are generated both when the good is produced and when it
is consumed. Production externalities are dependent on the technology of a country.
Countries with cleaner technologies emit less per unit of the good produced, so emission
per unit of the good is different for different countries. The amount of emissions per unit
of the good caused by the consumption of the good do not depend on where the good
is produced or consumed, it is only dependent on what type of good it is. I focus on
consumption externalities in this analysis.5
Social welfare under free trade now becomes:
Wi = CSi + P Si − T ECi
(6)
In comparison with equation (5) the welfare function now includes the total external
cost function T ECi . It represents the damage caused by worldwide emissions when
consuming good x. Every country’s emissions are
and costly to all countries.
Pdamaging
N
T ECi are dependent on the world emission, e = i=1 ei , for all i:
T ECi =
5 For
σi 2
e
2
a discussion of how production externalities can be modelled, see appendix A.
10
(7)
Where σi describes how vulnerable Country i is to the world emission level. A country
having a low σ means that emission bears a lower cost to that country. Assume σi > 0
for all i.
Assume that regardless of where the good is consumed, it emits one unit of emission.
∗c
That is, emission from Country i due to consumption of good x is ei = x∗c
i , where xi is
the equilibrium quantity ofP
good x consumed
in Country i; i = 1, 2, ..., N .
PN
N
∗c
∗
Since ei = x∗c
and
e
=
e
,
so,
e
=
i
i=1 i
i=1 xi = x , and:
σi ∗2
x
2
The marginal external cost with respect to the world quantity consumed is:
T ECi =
(8)
M ECi = σi x∗
(9)
By summing up all TECs to each country, total external cost to the world is obtained:
T EC
=
=
=
PN σi ∗2
x
i=1
PN2
x∗2
i=1 σi
2
σ ∗2
x
2
(10)
And marginal external cost to the world is thus:
M EC = σx∗
(11)
With externalities under the free trade equilibrium, consumer surplus and producer
surplus are the same as in the benchmark case. However, due to the T EC, social welfare
is strictly lower.
Under free trade, the equilibrium quantity consumed, x∗ , is too high, as compared to
the efficient quantity, xe . In figure 4, the sum of the two triangles indicate the T EC from
consuming x∗ . It is the area between the social marginal cost (MSC) curve and the world
supply curve. If the world consumes xe , the decrease in T EC would be larger than the
decrease in CS and P S, and hence the world’s welfare would be increased by the small
triangle indicated in the figure.
11
Figure 4: Inefficiencies Due To Externalities
MSC
S
Pe
MEC
Price
P∗
TEC
D
MEC3
MEC1
MEC2
xe x∗
Quantity of good x
3.3
Externalities with an IEA
Assume that to correct the inefficiency from externalities under free trade, all countries
agree to sign an IEA of imposing a common tax on good x in all countries. I consider
three different IEAs. The first one is just an agreement of imposing the tax, without any
enforcement mechanism. The second one is an agreement of a tax and a trade restriction that punishes free-riders by forming a union market that excludes free-riders from
exporting/importing. Lastly, I examine an agreement of imposing a tariff on exporting
free-riders in the same amount as the tax, and imposing a price undertaking that restricts
the import price of importing free-riders.
Without the tax, the equilibrium quantity of good x consumed is x∗ at P ∗ . This is
higher than the efficient quantity xe , since the MEC is not taken into account. The actual
cost of producing good x to the society is the MSC curve, which is the world supply curve
(marginal private cost curve) with the MEC taken into account. The efficient quantity is
the quantity where the MSC curve intersects with the demand curve.
With the tax, good x is now supplied at a higher price everywhere. Since the demand
curve for the good remains unchanged, the equilibrium quantity of good x with the
agreement, represented by xa∗ , is smaller than the equilibrium quantity without the
agreement, as shown in figure 5. Total emission, represented by ea = xa∗ , decreases, as
the world produces and consumes less of good x. And the world’s social welfare increases
by the amount as indicated by the small triangle in figure 4.
12
Figure 5: Equilibrium Quantity Is Efficient Due To Tax
Sa
S
World Price
MSC
Pa∗
P∗
t∗
Pn
D
xa∗x∗
3.3.1
World Quantity of good x
IEA of imposing a common tax
For now I follow most of the literature and focus on imposing a production tax as opposed
to a consumption tax. For a closed economy or a world economy as a whole, there is no
difference in equilibrium quantities as to which tax is imposed. However, for individual
countries which are exporting or importing countries, the amount of tax revenue collected
from the tax will be different, if a different type of tax is imposed.
By imposing a common optimal tax, t∗ , on suppliers, their supply curves shift upwards,
so that the equilibrium quantity with t∗ imposed is equal to the efficient quantity. t∗ is
the MEC at quantity xe , i.e. the difference between MSC at quantity xe and marginal
private cost at quantity xe .
With all countries signing the agreement, the cost functions for all countries are now:
Ci =
x2i
+ t∗ x i
2αi
(12)
The inverse supply curve for all countries are now:
P =
World supply with tax is S a =
price with the agreement are:
P3
i=1
Sia
+ t∗
αi
(13)
αi (P − t∗ ). The world equilibrium quantity and
13
P a∗ =
αw aw
bw t ∗
aw + αw t∗ a∗
;x =
−
bw + α w
bw + α w
bw + α w
(14)
Comparing these equilibrium quantities to the competitive equilibrium from equation
(4), it is clear that P a∗ > P ∗ and xa∗ < x∗ .
Figure 6 shows that due to the shift in supply, all countries are consuming fewer
amounts of good x. Note that for Country 3, it is only due to the specific parameters
chosen that Country 3 happens to be self-sufficient with the tax imposed. It is not the
general case. Depending on the countries’ demand curves and supply curves, Country 3
may become an exporting or importing country after the tax is imposed.
Figure 6: All Countries Signing the IEA
Country 1
Country 2
Country 3
Sa2
Sa3
Sa1
S3
S2
t∗
Price
Price
Price
S1
t∗
Pa∗
Pa∗
Pa∗
P∗
P∗
P∗
t∗
D1
Quantity in country 1
D2
D3
Quantity in country 2
xa∗
3
Quantity in country 3
Social welfare changes for a country due to the decrease in T ECi and decrease in
CSi and P Si , and because the government now collects tax revenues, T Ri , from the tax
imposed.
The increase in welfare from having the agreement due to the decrease in T ECi is:
∆T ECi
σi x∗ − σi xa∗
σi (x∗ − xa∗ )
=
=
(15)
The tax causes a price increase which causes a decrease in CS. The tax also decreases
supply at each price level which decreases P S. Governments gain tax revenue T Ri =
a∗
a∗
t∗ xa∗
i , where xi is the quantity of good x Country i produces at P .
14
Social welfare in this case is:
Wia = CSi + P Si − T ECi + T Ri
(16)
For countries with small T ECi , it is possible that they would be better off without
the IEA. The IEA decreases both CS and P S, but decreases the T EC more for the world
as a whole. Part of the lost CS and P S is recaptured by T R, but not all of it. For an
individual country, the decrease in CS and P S may not be compensated by the decrease
in T EC and the T R generated.
3.3.2
Incentives for countries to deviate
In what follows I assume that the IEA is formed and investigate whether there is an
incentive for each country to deviate, given that the other two countries are signatories.
The variables with superscript a* denote the equilibrium values when an IEA is formed
with all countries signing it; the variables with superscript * denote the equilibrium values
when no IEA is formed; and the variables with superscript in denote the equilibrium
values when Country i is not signing the IEA, while other countries are signing, i = 1, 2, 3.
If the deviating country, Country i, is an exporter after deviation, then, in equilibrium,
the aggregate import demand of other countries is equal to the export supply of the
deviating country:
Mu = X i
In which Mu is the aggregate of the import demand of all signatories and Xi is the
export supply of the deviating country. Substituting the supply and demand of the
countries in the above equation gives:
au − (bu + αu ) P in + αu t = (αi + bi ) P in − ai
If the deviating country is an importer after deviation, then, in equilibrium, the aggregate export supply of other countries is equal to the import demand of the deviating
country:
X u = Mi
Again, substituting supply and demand of the countries into above gives:
−au + (bu + αu ) P in − αu t∗ = − (αi + bi ) P ni + ai
In either case, the solving the equilibrium gives the price consumers pay when Country
i deviates:
P in =
a w + α u t∗
α w + bw
(17)
This implies the following:
1. The price consumers pay in the world is lower under deviation from Country i than
under the tax.
15
2. The price the union suppliers receive is lower under the deviation from Country i
than under the tax.
3. The price Country i suppliers receive under deviation is higher than under the tax.
4. More is consumed and produced under the deviation from country i than under the
tax.
5. The emissions are higher under the deviation from Country i than under the tax.
To prove (1), just compare P in with P a∗ :
P in − P a∗ = −
αi t
< 0.
α w + bw
For (2), sellers in the union receive P a∗ − t under tax but P in − t under the deviation
of Country 1. (2) follows from (1). For (3), Country i suppliers receive P a∗ − t under the
tax and P in under deviation.
P a∗ − t∗ =
a w − bw t
< P in
α w + bw
(4) follows immediately from (1), since consumers in the whole world pay a lower price
under deviation from country i, in equilibrium, world demand and supply is higher under
the deviation of country i than under the tax. This also implies (5) T ECiin > T ECi for
all i.
From these inequalities it is also clear that in Country i, CS and P S are higher under
deviation than under the tax. Social welfare under the tax can only be higher in Country
i if the benefits from T R and lower T EC under the tax outweigh the loss in CS and P S
compared to the deviation.
Incentives for Country 1 to deviate
Now I investigate more deeply whether Country 1, the lowest cost country, has an incentive
to deviate given the other two countries sign the IEA.
If Country 1 deviates, all countries except Country 1 now have a cost function as
represented in equation (12).
The inverse supply curves for all countries except Country 1 are represented in equation (13).
The welfare equation for Country 1, W1 , is now the same as in equation (6). It does
not gain tax revenue because it does not impose a tax on its producers. World supply in
this case is S 1n .
To solve for world equilibrium price and quantity when Country 1 deviates, P 1n and
1n
x , set supply equals to demand:
S 1n = D = x1n
In which S 1n = S1 + S2a + S3a = α1 P + (α2 + α3 )(P − t). Demand remains unchanged.
Solving this gives:
P 1n =
αw aw
bw t ∗
α 1 t∗
aw + αw t − α1 t 1n
;x =
−
+
bw + α w
bw + α w
bw + α w
bw + α w
16
(18)
Comparing these equilibrium quantities to the competitive equilibrium from equation
(4) and (14), we can see that P a∗ > P 1n > P ∗ and xa∗ < x1n < x∗ .
Figure 7: World Market With Country 1 Not Signing the IEA
Sa
World price
S1n
S
Pa∗
P1n
P∗
D
t∗
x
′
xa∗x1n x∗
World quantity of good x
Figure 7 shows the equilibrium world prices with different participation rates of the
IEA. If all countries sign the agreement, world price is P a∗ . The equilibrium world price
without an agreement and no country taking any action to reduce emissions is P ∗ . World
price with all but Country 1 signing the agreement is P 1n .
Since Country 1 did not impose the tax, it is the only country that is supplying when
′
world price is below t∗ . It is the sole supplier up to quantity x . When world price is above
t∗ , other countries also supply. Since all other countries’ supply of good x shift upwards
but Country 1’s, Country 1 now has a price advantage due to the tax, in addition to its
low production cost. As shown in figure 8, export increases from Exporta to Exportna .
The trapezium indicates the net gain in welfare from signing the agreement while the
triangle indicates the net gain from not signing the agreement. If the area of the triangle
is smaller than the trapezium, Country 1 has no incentive to deviate, since this implies
that Country 1’s increase in T R more than compensates the loss in P S, and, in addition
to that, T EC1 decreases from σ1 x1n to σ1 xa∗ .
17
Figure 8: Incentives for Country 1 To Deviate from an IEA Without Tariffs
S1
Price
Sa1
Pa∗
P1n
D1
Exporta
t∗
Exportna
xa∗c
x1nc
1
1
xa∗
1
x1n
1
Quantity in country 1
If the area of the triangle is bigger than the trapezium, the increase in T EC1 due to
the increase in consumption needs to be considered. The above graph does not capture
the T EC1 which also enters the social welfare function of Country 1. Since there is an
increase in quantity consumed, both T EC and T EC1 increase, as indicated in figure 9
by the big and small trapeziums, respectively.
18
Figure 9: Increase in T EC When Country 1 Deviates
D
World price
MEC
Sa
S1n
Pa∗
P1n
P∗
MEC1
xa∗x1n
World quantity of good x
Even though the increase in quantity consumed increases T EC, Country 1 is only
concerned about the increase in T EC1 . Assuming that an IEA is needed to induce
countries to decrease consumption, it is reasonable to assume that in the case when the
area of the triangle is bigger than the trapezium, ∆T EC1 is minimal, so that it does not
induce Country 1 to sign the agreement. If this is not the case, punishments would not
be necessary, since this indicates that the IEA is self-enforcing for Country 1, as T EC1
was so high that Country 1 would have no incentive to deviate from the agreement, even
without any punishment.
One real world example for such a case is the Montreal Protocol. Barrett (1994a)[2]
argues that countries have no incentive to deviate from the IEA even without punishment.
Hence the inclusion of an enforcement mechanism is not very important. If this is true,
the ”successful” inclusion of trade sanctions as an enforcement mechanism in the protocol
may be due to the self-enforcing nature of the IEA, not because trade sanctions work as
an enforcement mechanism. They are, in fact, irrelevant.
In all the following analysis, the change in T ECi due to a deviation of Country i
is assumed to be minimal so that a country has an incentive to deviate from the IEA
whenever its social welfare excluding T ECi increases.
Refer back to figure 8. The area of the triangle (the gain in P S from not signing the
agreement), denoted by A, is:
A=
a∗
∗
a∗
(x1n
− P 1n ))
1 − x1 )(t − (P
2
19
(19)
The area of the trapezium (the loss in T R from not signing the agreement), denoted
by B, is:
B=
a∗
(P a∗ − P 1n )[Exporta + (Exportna − (x1n
1 − x1 ))]
2
(20)
(P a∗ − P 1n
) is the decrease in world price from not signing the agreement, and it is
∗
1t
. Given that the values of t∗ , αw and bw are fixed, it is positively related
equal to bwα+α
w
to the ratio of ααw1 . Intuitively, in a model with symmetric demand but different cost
functions, the country with the highest cost will have the lowest exports, or could still be
importing, even after the deviation, and its deviation will lead to the smallest difference
in consumer prices.
Increase in export from not signing is:
x1nc
1
a∗
1nc
(Exportna − Exporta ) = (x1n
− xa∗c
1 − x1 ) − (x1
1 )
1n
xa∗c
1
(21)
a∗
In which
and
are Country 1’s domestic demand at P and P respectively.
In the case of the real world, even though the degree varies case by case, in general
a single country has a relatively small market ratio such that a big increase in exports
of that country due to not signing the agreement causes a small increase in world price.
Since the difference between P 1n and P a∗ is small, the difference in the home quantity
demanded in that country at those prices is also small. So increase in export from not
a∗
signing is approximately (x1n
1 − x1 ), from equation (21).
a∗
a∗
Since gain of P S from not signing increases as (x1n
−P 1n )
1 −x1 ) increases, and as (P
decreases (from equation (19)), in the case of the real world, the gain is relatively large.
The loss in T R that is not being recaptured by increased P S from not signing, decreases
a∗
a∗
as (x1n
− P 1n ) decreases (from equation (20)). That is,
1 − x1 ) increases, and as (P
there are incentives for exporting countries to deviate from signing the agreement.
Or, if one thinks about it by industry, exporting industry would be advocating not
signing the IEA, but hoping other countries will sign, as this boosts their P S.
In my graphical example, there are only three countries, and so Country 1 has a fair
market share of the world market. It is not obvious that Country 1 gains from not signing
the agreement.
A consumption tax vs a production tax
Note that although in a closed economy or the world economy, there is no difference in
whether a production tax or a consumption tax is levied, there is a difference for individual
countries. In the case of an exporting country, if a consumption tax is levied instead, the
export amount does not generate T R, it is only the domestic consumption on which T R
is collected. Therefore, T R can be recaptured by increased CS and P S from not signing
the agreement.
Figure 10 shows that regardless of Country 1’s market ratio, it has incentives to deviate
when a consumption tax is imposed instead of a production tax. When a consumption
tax is imposed, the supplier charges P as while the consumers pay P a∗ . Government gains
∗
T R = xa∗c
1 t . If Country 1 decides not to sign the agreement, the supplier charges and
the consumers pay the same price P 1n . The triangle and the trapezium indicate the CS
gain and the P S gain from deviating respectively.
20
Figure 10: A Consumption Tax Instead of A Production Tax for Country 1
Price
S1
Pa∗
P1n
P
D1
t∗
as
xa∗c
x1nc
1
1
xa∗
1
x1n
1
Quantity in country 1
Incentives for Country 2 to deviate
As shown in figure 11, the world price of good x with Country 2 deviating is P 2n , it is
lower than P a∗ , since Country 2 now supplies more at each price level. Since the supply
curve of Country 2 is steeper than Country 1, P 2n is higher than P 1n . Due to the tax
′′
imposed in other countries, Country 2 is the sole supplier of good x up to quantity x ,
′
which is smaller than x again due to Country 2’s higher marginal cost.
21
Figure 11: World Market With Country 2 Not Signing the IEA
World price
Sa
S2n
S
Pa∗
P2n
P∗
D
t∗
x
′′
xa∗x2n x∗
World quantity of good x
Analytically, the world equilibrium quantity and price when Country 2 deviates are:
P 2n =
aw + αw t − α2 t 2n
αw aw
bw t ∗
α 2 t∗
;x =
−
+
,
bw + α w
bw + α w
bw + α w
bw + α w
(22)
,respectively. Since α2 < α1 , P ∗ < P 2n < P 1n < P a∗ and x∗ > x1n > x2n > xa∗ .
Without tariff, Country 2 has an incentive to deviate from signing the IEA, as show
in figure 12. If Country 2 signs the IEA, consumers gain CS from quantity xa∗c
2 , and
a∗ ∗
supplier gains P S from quantity xa∗
.
Government
gains
T
R
=
x
t
.
If
Country
2 does
2
2
2
and
the
supplier
gains
P
S
from
not sign the IEA, consumers gain CS from quantity x2nc
2
.
The
trapezium
and
triangle
indicate
the
CS
and
P
S
gain
from
deviating
quantity x2n
2
respectively.
This situation is the worst in terms of having a country sign. Both consumers (although in a less extent) and the producer gain if Country 2 does not sign. And, in
addition to that, T EC2 will increase by a smaller amount than in the case of the other
countries, i.e. (x2n − xa∗ ) is smaller than (x1n − xa∗ ) and (x3n − xa∗ ), due to Country 2
being the highest cost country. That being said, due to the smaller increase in T EC, the
inefficiency caused by Country 2 not signing is the smallest.
22
Figure 12: Incentives for Country 2 To Deviate from an IEA Without Tariff
Sa2
Price
S2
Pa∗
P2n
t∗
D2
xa∗
2
2nc
xa∗c
2 x2
Quantity in country 2
Incentives for Country 3 to deviate
As shown in figure 13, the world price of good x with Country 3 deviating is P 3n , it is
higher than P 1n but lower than P 2n , since α1 <3 < α2 . Due to the tax imposed in other
′′′
′′
′′′
′
countries, Country 3 is the sole supplier of good x up to quantity x . x < x < x .
23
Figure 13: World Market With Country 3 Not Signing the IEA
Sa
World price
S3n
S
Pa∗
P3n
P∗
D
t∗
x
′′′
xa∗x3n x∗
World quantity of good x
Analytically, the world equilibrium quantity and price when Country 3 deviates are:
P 3n =
aw + αw t − α3 t 3n
αw aw
bw t ∗
α 3 t∗
;x =
−
+
,
bw + α w
bw + α w
bw + α w
bw + α w
(23)
respectively. Since α2 < α3 < α1 , P ∗ < P 2n < P 3n < P 1n < P a∗ and x∗ > x1n >
x > x2n > xa∗ .
Without tariff, Country 3 also has an incentive to deviate from signing the IEA, as
show in figure 14. If Country 3 signs the IEA, consumers and the supplier gain CS and
a∗ ∗
P S from quantity xa∗
3 . The government gains T R3 = x3 t . If Country 3 does not sign
the IEA, it becomes an exporting country exporting Exportn a amount of good x as shown
in the figure. Consumers gain CS from quantity x3nc
and the supplier gains P S from
2
quantity x3n
.
The
small
and
big
triangles
indicate
the
CS
and P S gain from deviating
2
respectively.
3n
24
Figure 14: Incentives for Country 3 To Deviate from an IEA Without Tariff
Sa3
D3
Price
S3
Pa∗
P3n
Exportna
t
∗
3nc
xa∗
3 x3
x3n
3 Quantity
in country 3
The IEA is a typical prisoner’s dilemma game: even though the world would benefit
from the IEA as a whole, each country, given that the other countries abate, does not have
an incentive to abate. All countries would deviate if the incentives were not corrected by
a punishment mechanism.
From the above analysis, we can see that importing countries have a higher incentive
to deviate from the IEA than exporting countries, due to the gain in T R for exporting
countries.
3.3.3
IEA of a common tax and trade restrictions
To motivate countries to sign the agreement, trade restrictions, which prohibit the freerider to trade with the rest of the world and force them to be autarky economies, are
introduced as a punishment for free-riding.
If an exporting country deviates from the agreement, a prohibitive tariff will be imposed on it and prohibit it from exporting to the world market.
A trade embargo will be imposed on importing countries if they deviate. With a trade
embargo, they are prohibited from importing from the world market.
With trade restrictions added to the IEA, I now ask whether each country has an incentive to deviate, given the other two countries sign the IEA, and impose the restriction
on the free-rider. That is, I examine whether trade restrictions are effective in deterring free-riding. I also examine whether signatories are better off imposing the trade
restrictions on the free-rider i.e. whether the trade restrictions are credible.
25
3.3.4
Incentives for countries to deviate with trade restrictions
Incentives for Country 1 to deviate with prohibitive tariff
If Country 1 does not sign the agreement, a prohibitive tariff will be imposed such that
Country 1 cannot export the excess supply. The supplier charges and consumers pay
the same autarky price P1∗ . And Country 1 produces and consumes x∗1 . Country 1
incurs a loss in both tax revenue and producer surplus from not signing the agreement,
as indicated by the quadrilateral in figure 15. CS increases with prohibitive tariff due
to the lower autarky price of Country 1. However this gain is not offset by the loss on
T R and P S.There is a loss in T R due to no tax being imposed as compared to the nondeviating case. There is a loss in P S due to the decrease in production, as it is prohibited
from trade. Again, ∆T EC1 is not captured by the graph. However, it is reasonable
to assume that the increase in T EC1 when Country 1 signs the agreement is not large
enough to induce Country 1 to voluntarily reduce the production of good x. Therefore,
with prohibitive tariffs, Country 1 has no incentive to deviate from the agreement.
Figure 15: Welfare of Country 1 With Prohibitive Tariff
S1
Price
Sa1
Pa∗
D1
Exporta
P∗1
x1a∗cx∗1 xa∗
1
Quantity in country 1
Incentives for Country 3 to deviate with prohibitive tariff
Since Country 3 becomes an exporting country when it deviates, the prohibitive tariff
causes Country 3 to not gain as much as in the case without the tariff. However, Country
3 still gains both CS and P S from deviating, as indicated by the triangles in figure 16.
If Country 3 signs the IEA, consumers and supplier gain CS and P S from quantity xa∗
3 .
26
∗
Government gains T R3 = xa∗
3 t . If Country 3 does not sign the IEA, it becomes an
autarky country and produces and consumes the same amount x∗3 . Even with a credible
threat of prohibitive tariff, Country 3 has an incentive to deviate from the IEA.
Price
Figure 16: Welfare of Country 3 With Prohibitive Tariff
Sa3
D3
S3
Pa∗
P∗3
∗
xa∗
3 x3
Quantity in country 3
Is the prohibitive tariff a credible threat?
Here I ask the question of whether countries 2 and 3 will want to impose the prohibitive
tariff, if Country 1 deviates. I assume that if there is a joint benefit, the winner will
compensate the loser, and both will impose the tariff, even if one of them is hurt from
the tariff. I focus on the case of Country 1 deviating.
As discussed, if the threat of imposing a prohibitive tariff on Country 1’s export when
it deviates is credible, Country 1 will not deviate. However, since imposing the prohibitive
tariff stops Country 1, the lowest cost country, from exporting to the union, the world
price rises from P 1n to P u . The CS of the union decreases, as shown in figure 17. P 1n is
the world price when there is no prohibitive tariff imposed on Country 1. Su is the union
supply curve, which is the aggregate Country 2 and 3’s supply curves. Du is the union
demand curve, which is the aggregate of Country 2 and 3’s demand.
27
Figure 17: Market Excluding Country 1 Due To A Prohibitive Tariff
Sau
Price
Su
P∗u
P1n
Du
x1n
u
x∗u
x1nc
u
Quantity of good x
The CS of the union falls by the amount indicated by the top triangle. But the union
gains T R and P S when imposing the tariff as indicated by the rectangle and the triangle
respectively.
The prohibitive tariff is a credible threat if and only if the welfare of the union when
imposing the tariff is higher than the welfare when the union isn’t imposing tariff:
CSu +P Su −T EC2 (x∗u +x∗1 )−T EC3 (x∗u +x∗1 ) ≥ CSnu +P Snu −T EC2 (x1n )−T EC3 (x1n )
(24)
In which CSu and P Su are the consumer surplus and producer surplus of the union
when a prohibitive tariff is imposed, and CSnu and P Snu are the respective surplusses
when no tariff is imposed. Since x1n > x∗u + x∗1 , the prohibitive tariff on Country 1 is a
credible threat when the sum of the area of the rectangle and area of the bottom triangle
is no less than the area of the top triangle. Note that the height of the top triangle is
Pu∗ − P 1n and the height of the bottom triangle is (Pu∗ − t∗ ) − (P 1n − t∗ ), and so both
∗
∗
1n
triangles have the same heights. So, if (x1nc
u −xu ) < (xu −xu ), then the threat is credible.
Depending on the T EC functions and the supply and demand of the countries, the
prohibitive tariff could be a credible threat. Appendix C shows the condition required
for it to be credible.
Individually, Country 3, becoming an exporter after imposing the tariff, is strictly
better off. It is ambiguous on whether Country 2 is better off imposing the tariff. Country
3 may have to compensate Country 2 for the threat to be credible. For a more detailed
28
analysis of the welfare of Country 2 and 3, please refer to appendix B.
The case of Country 3 deviating is similar. Due to the tariff, Country 3 cannot export
the excess supply to Country 1 and 2 when it deviates. The union price is higher than
the price with no union. The CS of the union decreases, to a lesser extent, since Country
3 isn’t exporting as much as Country 1. T R and P S increase, also to a less extent for the
same reason. Country 1 absorbs the export amount and is better off, Country 2’s welfare
is ambiguous.
Incentives for Country 2 to deviate with trade embargo
To also be able to punish importers, we have to impose a trade embargo on the importing
country. Figure 18 shows the welfare of Country 2 in this case. If Country 2 deviates,
other countries stop exporting to Country 2, and it is under autarky. The supplier charges
the consumers the autarky price P2∗ and Country 2 produces and consumes x∗2 . If Country
2 signs the IEA, Country 2 imports Importa . CS increases by the amount of the area
∗
of the top triangle. P S is not fully recaptured by T R2 = xa∗
2 t , and decreases by the
amount of the other triangle.
The CS loss from deviating due to not being allowed to import changes ambiguously
when b2 and α2 increase, respectively. The gain in P S from deviating is increasing on α2 ,
given t∗ is fixed. This means that, as the production costs of Country 2 decrease relative
to the world, the increase in P S from deviating increases. For a proof is this, refer to
appendix D.
Figure 18: Welfare of Country 2 With Trade Embargo
Sa2
Price
S2
P∗2
Pa∗
Importa
D2
∗
xa∗
xa∗s
2
2 x2
xa∗c
2
Quantity in country 2
29
The trade embargo can induce Country 2 to sign the IEA only when the gain in CS
when signing is higher than the sum of P S loss and increase in T EC2 due to importing
from the rest of the world when signing, i.e. (T EC(xa∗ ) − T EC(x∗u + x∗2 )). The trade
embargo does not guarantee Country 2 will ratify the IEA, even when the threat of it is
credible.
Is the trade embargo a credible threat?
Again, I ask whether the trade embargo could be a credible threat under the same rationale that as long as there is a joint benefit, Country 1 and 3 will cooperate and impose
the trade embargo. Figure 19 shows the welfare of the union in this case.
If the union imposes the embargo, P = Pu∗ and the union consumes x∗u . If the union
does not impose the embargo, the union exports to Country 2 and gains T R as indicated
by the bold area. The triangle below it indicates the P S gain of the union in this case.
Without considering the change in T EC, the union is strictly worse off imposing the
embargo.
The area of the gain from not imposing the embargo is dependent on how much
Country 2 will import from the union, if there is no embargo. This amount is dependent on
(1) how much the world price increases when the embargo is not imposed, i.e. (P 2n − Pu∗ )
and (2) how much production is shifted to Country 2 due to the price advantage Country
2 gains by deviating. If the price difference is small, then exports to Country 2 decrease,
and both T R and P S gain from not imposing embargo decrease. For a country that is
small relative to the world, P 2n is close to Pu∗ , due to a small country being less influential
on the world price. Also, due to free-riding, Country 2 now has a price advantage over
the other countries, and therefore imports less compared to the non-deviating case, when
no embargo is imposed. This is the leakage amount as mentioned in Barrett(1997) [3] .
If the decrease in T EC from imposing the embargo is higher than the gain from not
imposing, then the trade embargo is a credible threat.
30
Price
Figure 19: Market Excluding Country 2 Due To Trade Embargo
Sau
P2n
P∗u
Su
Du
x∗u
x2nc
x2n
u
u
Quantity of good x
To conclude, prohibitive tariffs are effective in deterring exporting countries from freeriding, but trade embargoes cannot guarantee that importing countries will be induced to
sign the IEA. Economic sanctions are not effective in deterring free-riding of self-sufficient
countries.
3.3.5
IEA of a common tax and tariffs/a price floor
Extreme measures such as a prohibitive tariff or a trade embargo will be difficult to
implement politically. Here I investigate whether a weak version of the punishments
could be effective and credible.
An intuitive choice for the amount of tariff imposed on the free-rider is an amount
that is the same as the optimal tax. When an exporting country deviates, other countries
impose a tariff with T = t∗ on its import.
On the other hand, when an importing country deviates, a symmetric punishment
will be for other countries to impose an export tariff with T = t∗ . However, it will be
challenging to explain to the exporters of the signatories that an export tax will have
to be imposed, on top of the pollutant tax already imposed on them. Even though the
effect will be similar, setting a price floor that restricts importing countries to pay at
least P a∗ will be more sensible, since the exporters gain the revenue from this measure
automatically.
In what follows, I examine whether there is an incentive to deviate for each country
individually, given that other countries sign the IEA, and impose either a tariff of T = t∗
31
on the exporting free-rider, or a price floor of P a∗ on the importing free-rider. I also
investigate whether the tariff is a credible threat, if the punishment is effective.
3.3.6
Incentives for countries to deviate with T = t∗
Incentives for Country 1 to deviate with T = t∗
If Country 1 decides not to sign the agreement, its cost function will remain the same as
in the benchmark model (See equation (1)). However, all other countries will impose a
tariff T = t∗ on the quantity of goods imported from Country 1.
The IEA creates two opposing effects brought about by (1) the common tax t∗ imposed
on all countries except Country 1 and (2) the tariff T = t∗ imposed on the goods exported
from Country 1.
The common tax imposed on all other countries causes their supply curves to shift up.
However, Country 1’s supply curve is not affected by the tax. Therefore, export increases
due to the price advantage Country 1 has, in the absence of a tariff.
The tariff imposed on Country 1 from all other countries reverses this effect. Due to
the tariff, the export supply for Country 1 shifts upwards but the import demand curves
for all other countries stay the same. Therefore, export decreases due to the tariff.
Assume P is the price consumers pay, P − t is the price producers receive. Recall the
supply curve and the demand curve of Country 1 are as follows:
D1
S1
=
=
a 1 − b1 P
α1 P
The supply curve when Country 1 imposes the tax is:
P
=
S1
+t
α1
The excess supply of Country 1 when it does not impose the tax is:
S1 − D 1
X1
=
=
(α1 + b1 ) P − a1
(α1 + b1 ) P − a1
In which X1 denotes exports of Country 1 without tax.
The excess supply of Country 1 when it imposes the tax is:
S1′ − D1
X1′
= (α1 + b1 ) P − α1 t − a1
= (α1 + b1 ) P − α1 t − a1
′
In which X1 denotes exports of Country 1 with tax.
The excess supply of Country 1 with tariff (T denotes tariff) is:
X1′′
=
X1′′
=
(α1 + b1 ) (P − T ) − a1
(α1 + b1 ) P − (α1 + b1 ) T − a1
32
In which X1′′ denotes exports of Country 1 with tariff.
The import demand of the union of Country 2 and Country 3, with the tax imposed
on producers is found by subtracting union supply from demand of the union (P is the
price consumers pay, P − t∗ is the price producers receive):
Du
Su
=
=
a u − bu P
(α2 + α3 ) (P − t)
The import demand of the union is:
D u − Su
Mu
=
=
au − bu P − (α2 + α3 ) (P − t)
au − (bu + α2 + α3 ) P + (α2 + α3 ) t
In which Mu denotes the imports of the union of countries 2 and 3.
Equilibrium when Country 1 deviates, and a tariff is imposed on it
When Country 1 deviates, Country 2 and Country 3 impose a tariff T = t∗ on its export.
The equilibrium price and quantity in this case are calculated by setting import demand
of the union equal to the export supply:
Mu = X1′′
Substituting the supply and demand of the countries to obtain:
au − (bu + α2 + α3 ) Pu + (α2 + α3 ) t = (α1 + b1 ) Pu − (α1 + b1 ) T − a1
Solving for the equilibrium gives the price consumers pay:
PuT =
au + a1 + (α2 + α3 ) t + (α1 + b1 ) T
α 1 + b1 + bu + α 2 + α 3
Note that if T = t∗ ,
PuT =
aw + (αw + b1 ) t∗
α w + bw
(25)
This implies the following:
1. The price consumers pay in the union is higher under the tariff than under the tax,
i.e. CS of the union decreases with the tariff.
2. The price the union suppliers receive is higher under the tariff than under the tax,
i.e. P S of the union increases with the tariff.
3. The price the supplier of Country 1 receives under the tariff is higher than under
the tax, i.e. P S of Country 1 increases with the tariff.
4. The price consumers pay in Country 1 is higher under the tax than under the tariff,
i.e. CS of Country 1 increases with the tariff.
33
5. More is sold and consumed and therefore emitted under the tariff than under the
tax, i.e. T EC increases with the tariff.
To prove (1), just compare the world competitive equilibrium price, P a∗ from equation
(14) with PuT .
Since P a∗ < PuT and sellers receive P a∗ − t∗ under tax but PuT under the tariff, (2)
follows.
Country 1 suppliers receive P a∗ − t∗ under the tax and PuT − t∗ under the tariff if
T = t∗ . Since P a∗ < PuT , (3) follows.
For (4), Country 1 does not impose the tariff, so consumers pay P1T = PuT − t∗ under
the tariff, but P a∗ under the tax. And P1T < P a∗ :
P1T
=
=
=
PuT − t∗
aw + (αw + b1 ) t∗ − αw t − bw t
α w + bw
aw − (b2 + b3 ) t∗
< P a∗
α w + bw
(5) follows immediately from (2) and (3), since suppliers in both countries receive a
higher price under the tariff than under the tax, world supply is higher under the tariff
than under the tax. This also implies T ECiT > T ECi for all i.
From these inequalities it is also clear that in Country 1 CS and P S are higher under
the tariff than under the tax. Social welfare under the tax can only be higher in Country
1 if the benefits from T R and lower T EC1 under the tax outweigh the loss in CS and
P S compared to the tariff.
To answer the question of whether the punishment is effective, i.e. if Country 1 is
better off signing the agreement than deviating, if the punishment is T = t∗ , refer to figure
20. The triangle indicates the net P S increase from deviating that is not recaptured by
T R when Country 1 does not deviate. The trapezium indicates the net T R increase
from imposing the tax not recaptured by P S gain when Country 1 deviates. Since T EC
decreases if Country 1 signs the IEA, if the area of the trapezium (denoted by A) is bigger
than the area of the triangle (denoted by B), Country 1 has no incentive to deviate, and
the tariff is effective.
34
Figure 20: Welfare of Country 1 With T = t∗
D1
Price
Sa1
Pa∗
S1
t∗
PT
1
Pa∗s
c
xa∗c
xT
1
1
T
xa∗
1 x1
Quantity
in country 1
The superscript denotes when a tariff T is imposed on Country 1. The two areas are
given by:
A =
a∗c
Tc
xa∗
+ xa∗
1 − x1
1 − x1
P a∗ − P1T =
2
xT1 − xa∗
1
2
Note that
B
=
xa∗c
+ xT1 c
1
xa∗
1 −
2
!
xT − xa∗
1
PuT − t∗ − (P a∗ − t∗ ) = 1
PuT − P a∗
2
P a∗ − P1T
(αw + bu )t∗
b1
t∗ ; P a∗ − P1T =
.
α w + bw
α w + bw
Clearly with T = t∗ , Country 1 may be induced to sign the IEA and thus this is an
effective punishment to deter free-riding.
The analysis for Country 3 will be similar, since Country 3 will be an exporting country
if it is the only country that deviates. In this case Country 3’s role of a self-sufficient
country is not there. It is just an exporting country with higher costs. So, there is no
need for a separate analysis for Country 3.
PuT − P a∗ =
Is the tariff a credible threat?
Next we check if Country 2 and Country 3 want to impose T = t∗ . That is, we compare
whether these countries have a higher joint social welfare if they chose to punish the
35
deviating country, Country 1, rather than letting it free-ride unpunished.
The equilibrium if Country 1 is unpunished is found by equating Country 1’s export
supply without tariff and the union’s import demand:
X1
Mu
=
=
(α1 + b1 ) P − a1
au − (bu + αu ) P + (αu + αu ) t∗
The world equilibrium price consumers pay is:
(α1 + b1 ) P − a1
=
P nT
=
au − (bu + αu ) P + (αu + αu ) t∗
a w + α u t∗
α w + bw
Note that this price is lower compared to the price resulting from the tariff.
PuT − P nT =
aw + (αw + b1 ) t∗
a w + α u t∗
α 1 + b1 ∗
−
=
t
α w + bw
α w + bw
α w + bw
Since the union imposes the tax on suppliers whether it punishes the free-rider or not,
the price the suppliers receive is the equilibrium price minus t∗ in either case. The price
the suppliers of the union receive is higher when there is a punishment than when there
is not.
α 1 + b1 ∗
PuT − t∗ − P nT − t∗ =
t
α w + bw
Given these changes in prices, we can conclude the following:
1. The CS of the union is higher if Country 1 goes unpunished.
2. The P S of the union is lower if Country 1 goes unpunished.
3. Tax revenue of the union is lower if Country 1 goes unpunished.
4. No tariff revenue will be collected if Country 1 goes unpunished. So, tariff revenue
is lower if Country 1 goes unpunished.
5. T EC is higher if Country 1 goes unpunished.
The change in social welfare of the union imposing a tariff vs no punishment, ignoring
T ECu is shown in figure 21. If the union impose the tariff, it will gain tax revenue and P S
as represented by the trapezium (A), and tariff revenue as represented by the rectangle
(B). The area of the top triangle (A) is the loss in CS under the tariff.
36
Figure 21: Welfare of Union With T = t∗
Sau
Price
Su
PTu
PnT
xnT
u
xTu
Du
T c nT c
xu xu
Quantity of
good x
The areas are given by the following equations:
A =
B
=
C
=
t∗ + P nT − PuT − t∗
xTu − xnT
u
2
T c
P nT − PuT − t∗
xu − xTu
c
PuT − P nT xnT
− xTu c
u
2
Thus change in social welfare ignoring T EC is
c
PuT − P nT xnT
T c
− xTu c
t∗ + P nT − PuT − t∗
u
nT
T
∗
T
T
nT
xu − xu −
x u − x u + P − Pu − t
A+B−C =
2
2
Certainly there are cases in which the tariff will be credible.
Incentive for Country 2 to deviate with a price floor of P a∗
Country 2, an importing country, will not be affected by a tariff of T = t∗ . To punish
Country 2, a price floor of P a∗ is set so that Country 2 does not gain CS from importing
for a lower price by deviating. Figure 22 shows that this is not an effective punishment,
i.e. this punishment cannot induce Country 2 to sign the IEA.
37
The area of the triangle is the gain in P S from deviating. Since consumers pay P a∗
whether Country 2 signs the IEA or not, CS is unchanged. P S increases if Country 2
deviates, since the producer doesn’t have to pay the tax.
Figure 22: Welfare of Country 2 With A Price Floor of P a∗
Sa2
Price
S2
Pa∗
t∗
D2
a∗s
xa∗
2 x2
xa∗c
2
Quantity in country 2
∗2
The area of the triangle is given by α22t , which is increasing in α2 and not dependent
on b2 . So, if the production costs in Country 2 are lower, the gain will be higher.
This result is consistent with the earlier result of imposing a trade embargo on Country
2. Given that even a trade embargo is unlikely to be effective on Country 2, a weaker
version of the punishment is of course not effective. The price floor leads to a shift of
production from the union to Country 2 and so increases Country 2’s social welfare at the
expense of the union. In order to avoid such a case, one might have to adopt a mixture
of consumption and production taxes, or switch to consumption tax, because the main
cause for the positive impact on Country 2 with the price floor is that tax revenues are
relatively low for an IEA of a production tax.
4
The political economy of the Kyoto Protocol
The Kyoto Protocol is one of the most prominent IEAs. It has the goal of achieving
”stabilization of greenhouse gas concentrations in the atmosphere at a level that would
prevent dangerous anthropogenic interference with the climate system.”6 Under the Pro6 See
Article 2 of the convention of The United Nations Framework Convention on Climate Change.
38
tocol, 37 industrialized countries (called ”Annex I countries”) commit themselves to a
reduction of four greenhouse gases (GHG) (carbon dioxide, methane, nitrous oxide, sulphur hexafluoride) and two groups of gases (hydrofluorocarbons and perfluorocarbons)
produced by them, and all member countries give general commitments. The Protocol
allows for several ”flexible mechanisms”, such as emissions trading and joint implementation to allow Annex I countries to meet their GHG emission limitations by purchasing
GHG emission reductions credits from elsewhere, through financial exchanges, projects
that reduce emissions in non-Annex I countries, from other Annex I countries, or from
Annex I countries with excess allowances.
The Protocol has a high participation rate with 187 countries having ratified it so
far. The U.S. is not among the countries which have ratified. Assuming the countries
which ratified the Protocol have intention to comply, the high participation rate implies
TECs are quite high for many countries, since the Protocol is self-enforcing without a
mechanism that punishes free-riders.
However, due to the weak enforcement mechanism,7 few countries are expected to
achieve the commitment target. Incorporating tariffs in the Protocol therefore could be
beneficial, since this gives exporting countries real incentive not to deviate, and decreases
the incentive for self-sufficient countries to deviate. In the case of a trade embargo,
incentive for importing countries to deviate also decreases.
The U.S., being the second biggest emitter in the world,8 is also one of the biggest
importers. It is therefore crucial and yet difficult to induce the U.S. to ratify the IEA.
Even though the Kyoto Protocol uses the cap-and-trade system instead of a global
pollution tax, the main effect is the same: the costs of producers increase due to the permit
prices they have to pay, and some or all of the cost is transferred to the consumers. My
analysis can thus be applied to the Kyoto Protocol for the most part.
One important point to note when applying my analysis to the political economy is
that countries are seldom social welfare maximizers. In fact, various trade instruments
commonly used by governments, which include voluntary export restraint9 and export
subsidies10 , are unambiguously welfare decreasing.11 In particular, for export subsidies,
the only players who gain are the producers of the industry. This shows that industries
are influential in shaping international trade policies.
There are various reasons as to why trade policies do not reflect consumers’ opinions.
First, the marginal benefit for an individual to influence trade policies is minimal, as
compared to an industry’s benefits from a trade policy. Therefore, incentives for industries
to lobby the government are high while the incentives for consumers to oppose them are
low. Second, consumers are less educated about what trade policies are in place, and
tend to be unaware of the negative impacts on them.
Applying my analysis to the Kyoto Protocol, even with the threat of a trade embargo,
7 If the enforcement branch determines that an Annex I country is not in compliance with its emissions
limitation, then that country is required to make up the difference plus an additional 30%. In addition,
that country will be suspended from making transfers under an emissions trading program.
8 In 2005, the U.S. emitted 16% of the global total GHGs. The biggest emitter is China, contributing
17% of the total emission. Source: MNP (2007). ”Greenhouse gas emissions of countries in 2005 and
ranking of their per capita emissions. Table 2.a. Top-20 countries of greenhouse emissions in 2006 from
fossil fuels and cement production”. Netherlands Environment Agency website.
9 For example, the 1981 Automobile VER by Japan requested by the U.S.
10 For example, the U.S. and EU have export subsidies on agricultural products.
11 See Krugman and Obstfeld (2008) [17] .
39
the U.S. still would not have had an incentive to sign the IEA. As one can see from figure
18, if a trade embargo were imposed, even though there would be a loss in CS, there would
be a gain in P S. Domestic industries which were hurt by imports would be pleased with
the embargo. Of course the exporters would be hurt, but they were a minority and could
be compensated, as there was a total gain in P S for the whole country. Applying this to
the economy of the U.S. shows that it would not have had any incentive to sign the IEA
even with economic sanctions.
Table 1 shows a summary of different trade sanctions and their effects comparing to
a benchmark case. For the free-riders, the benchmark is the welfare when they sign the
agreement; for the punishers, the benchmark is the welfare of the union when no sanction
is imposed and the free-rider goes unpunished.
Recall that it is assumed that the decrease in T EC is minimal that it alone does
not induce a country to change its actions. Also, the decrease in T EC is higher when
the deviating country is an exporter. That is, the decrease in T EC is higher when the
prohibitive tariff is imposed on Country 1. The big down arrow indicates a bigger decrease
in T EC.
If we assume international trade policies are highly influenced by producers, then,
even though the union imposing a prohibitive tariff and Country 2’s welfare change ambiguously (refer to forth and fifth columns of the second to last row of the table), we can
conclude that, for the union, the threat of imposing the tariff is likely credible, since P S
of the union increases. And, for Country 2, an embargo is likely not effective on making
it sign the IEA, since P S increases if an embargo is imposed on it.
Table 1: The Effects of Trade Sanctions Comparing to Signing the IEA
Prohibitive Tariff
Trade Embargo
Free-rider
Punisher
Free-rider Punisher
Effects on
Country 1 Country 3
Union
Country 2
Union
CS
↑
↑
↓
↓
↑
PS
↓
↑
↑
↑
↓
TR
↓
No change
↑
↓
↓
TEC
↓
↑
⇓ (C1)/ ↓ (C3)
↓
↓
Overall
Worse off
Better off
Ambigous
Ambigous Worse off
√
√
Effective/Credible?
X
Likely
Likely X
Likely X
However, if the U.S. ratifies, China will follow. With economic sanctions, an IEA
could have full participation. I find that if all other countries impose a prohibitive tariff
on an exporting non-signatory, the exporting country will have an incentive to sign the
IEA. But is it credible in the case of the U.S. and China?
From figure 1 in appendix B, Country 2 (the U.S.) gains P S and loses CS, and
Country 3 is strictly better off. Since the U.S. is one of the countries that are mostly
driven by industries in trade policies making, it will have incentives to stop importing
from China, even without compensation from Country 3. Country 3, without needing to
compensate Country 2, stays better off imposing the tariff. Therefore, the threat of the
prohibitive tariff is credible in this case. This implies that China has an incentive to sign
the IEA with the U.S. signing.
Of course, I do not expect this outcome to be the equilibrium. As explained, the U.S.
40
would deviate even with the threat of economic sanctions, and China, responding to that,
would also deviate, which is the outcome in reality: countries are not expected to achieve
their abatement targets in the Kyoto Protocol.
5
Conclusion
I find that, in a partial equilibrium model, countries have incentives to deviate from an
IEA without economic sanctions. Economic sanctions are effective in inducing exporting
countries to sign an IEA that requires signatories to impose a pollution tax. It is not
effective in non-exporting countries, even when the threats are credible. This is because,
for self-sufficient countries, they are, by definition, not reliant on trade and thus trade
sanctions do not have an effect on them; for importing countries, they gain P S from not
importing from other countries when a trade embargo is imposed, which is exacerbated
by the production shifts to them due to free-riding.
The threat of imposing a prohibitive tariff is likely credible, since the loss in CS from
imposing the tariff could be compensated by gain in T R and P S and decrease in T EC.
Trade embargoes are only credible when the deviating country is relatively small such
that the loss from imposing the embargo is lower than the T EC, or when T EC is high
enough to make the countries carrying out the threat better off by doing so. The threat of
imposing a tariff of t∗ maybe credible, especially when countries do not place importance
on CS.
Economic sanctions are helpful but not sufficient to induce full participation of an IEA.
Other linkage(s), e.g. R&D spillover or other types of sanctions, must also be included
in the IEA to give importing or self-sufficient countries incentives to sign the IEA.
6
Shortcomings and future research
I focus on a partial equilibrium model, in which there is only one tradable good. Effects
in other markets are ignored. In the real world, there are many tradable goods. Countries
can be exporters of a good but importers of other goods at the same time. More insights
could be gained with a paper extending this analysis to a general equilibrium model,
in which there is more than one tradable good, and the effects of more than one good
markets are examined. Also, change in CS is considered as a welfare measure in this
analysis. This is only accurate in partial equilibrium model with a specific set up such
that there is no income effect and thus the Marshallian demand is the same as the Hicksian
demand. CV/EV should be used in a general equilibrium analysis, however, there are
also restrictions that have to be placed on the model to use these concepts appropriately.
In this paper only consumption externalities are considered, and is assumed to be
linearly dependent on emissions. Production externalities, which vary country by country
per unit of good produced due to different technologies, are not incorporated in the model.
A model that includes both externalities would be more realistic.
As there are welfare differences for an individual country on whether a production
tax or a consumption tax is levied, the effects of levying different types of tax can be
further analyzed. The social welfare effects of each type of country could be examined
with an IEA that requires the imposition of a consumption tax, or a combination of
a production tax and a consumption tax. Since exporting countries attain more T R
41
with a production tax, they prefer production tax over consumption tax. For importing
countries, the opposite is true. An analysis of which types of tax to impose may therefore
shed light on how a balanced playing field for all countries could be created.
42
A
Production Externalities
When production externalities are considered, countries’ emissions also depend on how
clean their facilities that are used to produce good x are. Assume that emissions are
linearly related to this parameter:
ei = η i x i
(1)
ei is the amount of emission in Country i. ηi is the parameter describing how clean
the technology for production of good x in Country i is. The cleaner the technology, the
lower η is. xi is the amount of good x produced in Country i.
An optimal unit tax, t∗ , is levied on each unit of emission instead of each unit of good.
Therefore, firms’ objectives are now
M axxi P xi − C(xi ) − t∗ ei
(2)
In which C(xi ) is the cost function as defined in the main text and ei = ηi xi .
Firms now supply according to the following supply schedule:
S : P = α i x i + t∗ η i
(3)
∗
The supply schedules of the firms shift up by t ηi , comparing to the case of no tax
imposed. It is dependent on the parameter ηi . This is reasonable as what we care about
is emission, not how much of the good is consumed.
To determine the optimal tax rate, t∗ , one can compare MEC with net marginal benefit
(NMB) of emissions, given by the sum of world marginal consumer surplus (MCS) and
marginal producer surplus (MPS) at any given level of emissions.
The sum of MCS and MPS at any given quantity of good x consumed,X, is the
difference between private marginal benefit (PMB) and private marginal cost (PMC) at
X.
The PMB is the inverse world demand function. Let P M B = d − bX. The PMC is
the inverse world supply function. P M C = PNX 1 .
N M B = P M B − P M C = d − (b − PN1
i=1 αi
1
i=1 αi
)X
This shows the NMB from consuming X quantity of good. This quantity of good is
also associated with an amount of emission. The amount of emission associated with this
and ei = ηi xi .
quantity can be found by the PMC. Since P M C(X) = αi xi , xi = P MαC(X)
i
e
=
=
=
=
=
PN
ei
Pi=1
N
P M C(X)
η
i=1 i
αi
P
N
P M C(X) i=1 αηii
PN η i
X
PN 1
i=1 αi
αi
Pi=1
N
ηi
αi
Pi=1
X
N
1
i=1 αi
From this we can express NMB in terms of e.
43
(4)
NMB
=
=
d − (b − PN1
1
i=1 αi
d − (b − PN1
1
i=1 αi
PN
Since from equation (4), X = Pi=1
N
1
αi
ηi
i=1 αi
e.
)X
PN
i=1
) PN
1
αi
ηi
i=1 αi
(5)
e
The optimal tax is the price in which the e of NMB(e) = MEC(e).
B
Welfare of Country 2 and Country 3 when a prohibitive tariff is imposed on Country 1
Figure 1: Welfare Of Country 2 And Country 3 With Prohibitive Tariff
Country 2
Sa2
Country 3
Sa3
S2
P1n
P1n
S3
Price
Pu∗
Price
Pu∗
D2
D3
u 1nc uc
x1n
2 x2 x2 x2
Quantity in country 2
uc 1nc u
x1n
3 x3 x3 x3
Quantity in country 3
In the case of Country 3, when imposing the tariff, all of the CS loss is recaptured by
the increase in T R. And there is extra gain in T R as indicated by the bold area. The
triangle indicates the gain in P S from imposing the tariff. Country 3 is strictly better off
by imposing the tariff.
In the case of Country 2, only part of the CS loss is recaptured, and the net CS loss
from imposing the tariff is indicated by the trapezium. There is gain in T R indicated by
the rectangle from imposing the prohibitive tariff. There is also gain in P S from imposing
44
the tariff as indicated by the triangle. It is ambiguous whether Country 2 will be better
off. For the tariff to be credible, Country 3 may have to compensate Country 2 so that
Country 2 is not worse off imposing the tariff.
C
Condition for the prohibitive tariff to be a credible
threat
Figure 17 shows the welfare of the union when it imposes the prohibitive tariff and when it
∗
1nc
does not. As explained in the main text, the threat is credible if (x∗u −x1n
u )−(xu −xu ) >
0.
By substituting Pu∗ and P 1n into the union’s supply and demand curves, we get the
following:
au − b∗t
)
bu + α u
(6)
a w − bw t ∗ − α 1 t ∗
)
bw + α w
(7)
x∗u = αu (
x1n
u = αu (
x1nc
= a u − bu (
u
a w + α w t∗ − α 1 t∗
)
bw + α w
(8)
From these we get the condition for the threat to be credible:
2αu (
D
a u − bu t ∗
a u − bu t ∗ − α 1 t ∗
bu a w + b u α w t ∗ − bu α 1 t ∗
) − αu (
) − au + (
)>0
bu + α u
bw + α w
bw + α w
(9)
Mathematical appendix for the analysis of the incentives for Country 2 to deviate with a trade embargo
When a trade embargo is imposed on Country 2 when it deviates, Country 2 incurs a
CS loss and a P S gain when deviates. The loss in CS is the area of the top triangle as
shown in figure 18:
∗
a∗
(xa∗c
− xa∗s
2
2 )(P2 − P )
2
The increase in P S from deviating is the area of the other triangle:
∆CS =
∗
(xa∗s
− xa∗
2
2 )t
2
into S2 and S2a , we get the following:
∆P S =
By substituting P a∗
xa∗s
= α2 (
2
a w + α w t∗
)
bw + α w
45
(10)
(11)
(12)
xa∗c
= a 2 − b2 (
2
a w + α w t∗
)
bw + α w
(13)
From these, we can express ∆CS and ∆P Sin terms of the parameters of the supply
and demand curves.
∗
∆CS =
a2
wt
[a2 − ( abww+α
+αw )(b2 + α2 )][ α2 +b2 −
2
aw +αw t∗
bw +αw ]
(14)
α2 t∗2
(15)
2
Partial differentiating ∆CS with respect to b2 and α2 respectively give ambiguous
results. Partial differentiating ∆P S with respect to b2 is zero, i.e. it does not change as
b2 changes, while partial differentiating with respect to α2 is positive, i.e. as b2 increases,
increase in P S from deviating increases.
∆P S =
46
References
[1] S. Barrett. International environmental agreements as games. Conflicts and cooperation in managing environmental resources, pages 18–33, 1992.
[2] S. Barrett. Self-enforcing international environmental agreements. Oxford Economic
Papers, 46:878–894, 1994.
[3] S. Barrett. The strategy of trade sanctions in international environmental agreements. Resource and Energy Economics, 19(4):345–361, 1997.
[4] S. Barrett. The credibility of trade sanctions in international environmental agreements. Trade, global policy, and the environment, page 161, 1999.
[5] S. Barrett. Environment and statecraft: the strategy of environmental treaty-making.
Oxford University Press, USA, 2005.
[6] F. Biermann and R. Brohm. Implementing the Kyoto Protocol without the USA: the
strategic role of energy tax adjustments at the border. Climate Policy, 4(3):289–302,
2005.
[7] D. Brack. International trade and the Montreal Protocol. Earthscan, 1996.
[8] J. Brander and B. Spencer. Tariff protection and imperfect competition. Imperfect
competition and international trade, pages 107–139, 1984.
[9] B. Buchner, C. Carraro, I. Cersosimo, and C. Marchiori. Back to Kyoto? US participation and the linkage between R&D and climate cooperation. The Coupling of
Climate and Economic Dynamics, pages 173–204, 2005.
[10] C. Carraro. The structure of international environmental agreements. International
Environmental Agreements on Climate Change, pages 9–25, 1999.
[11] C. Carraro and D. Siniscalco. R&D cooperation and the stability of international
environmental agreements. CEPR Discussion Papers, 1995.
[12] C. Carraro and D. Siniscalco. International environmental agreements: Incentives
and political economy. European Economic Review, 42(3):561–572, 1998.
[13] C. Domenico et al. Strategies for the international protection of the environment.
Journal of Public Economics, 52(3):309–328, 1993.
[14] Martin Feldstein. Will cap-and-trade incite protectionism? Project Syndicate, 2009.
[15] R. Ismer and K. Neuhoff. Border tax adjustment: a feasible way to support stringent
emission trading. European Journal of Law and Economics, 24(2):137–164, 2007.
[16] C. Kemfert. Climate coalitions and international trade: assessment of cooperation
incentives by issue linkage. Energy Policy, 32(4):455–465, 2004.
[17] P.R. Krugman and M. Obstfeld.
Addison-Wesley, 2008.
International economics: theory and policy.
47
[18] K. Lessmann, R. Marschinski, and O. Edenhofer. The effects of tariffs on coalition
formation in a dynamic global warming game. Economic Modelling, 26(3):641–649,
2009.
[19] A. Mas-Colell, M.D. Whinston, and J.R. Green. Microeconomic theory. Oxford
university press New York, 1995.
[20] J. Stiglitz. A new agenda for global warming. The Economists’ Voice, 3(7):3, 2006.
[21] J.E. Stiglitz. Making globalisation work. Esri, 2006.
[22] S.E. Stoft and G.E.P. Center. Game Theory for Global Climate Policy.
[23] R.W. Tresch. Public finance: A normative theory. Academic Pr, 2002.
[24] R. Van Slooten. The case of the Montreal Protocol. Trade and environment: Processes and production methods, pages 87–91, 1994.
48