Adaptation to Climate Change: How does Heterogeneity
in Adaptation Costs Affect Climate Coalitions?
Itziar Lazkano∗
Walid Marrouch†
Bruno Nkuiya‡
Preliminary and Incomplete
June 4, 2013
Abstract
Mitigation and adaptation to climate change are the two main options to tackle
climate change issues. International environmental agreements to reduce emissions,
however, ignore cross-country differences in adaptation costs. In this paper, we ask
what the implications are for international environmental agreements when countries
differ both in terms of current pollution levels and future adaptation costs. In particular,
we study how heterogeneity in adaptation costs affects the global level of pollution and
the stability of environmental agreements aimed at reducing global emissions. Our
results show how the stability of international agreements change when we account for
cross-country differences in adaptation costs.
Keywords: adaptation; mitigation; climate change; stability environmental agreements
JEL Classification Codes: Q50, Q54, Q58, Q59
∗
Department of Economics and SFS, University of Wisconsin-Milwaukee. P.O. Box 413, NWQ B, Room
4450 Milwaukee, WI 53201 E-mail:lazkano@uwm.edu.
†
CIRANO, Canada, and School of Business Lebanese American University, Lebanon.
E-mail:walid.marrouch@cirano.qc.ca.
‡
Department of Economics, University of Laval, Canada. E-mail:robeny-bruno.nkuiya-mbakop.1@ulaval.ca.
1
Introduction
The World Bank finds that the cost of adapting to an approximately 2C warmer world by
2050 is in the range of $70 billion to $100 billion a year between 2010 and 2050.1 This cost of
adaptation, however, differs widely across countries. While some heavily polluting nations
might expect high adaptation costs in the future, there is not necessarily a clear relationship
between one’s pollution today and adaptation costs in the future. In this paper, we ask
what the implications are for international environmental agreements when countries differ
both in terms of current pollution levels and future adaptation costs. In particular, we study
how heterogeneity in adaptation costs affects the global level of pollution and the stability
of environmental agreements aimed at reducing global emissions.
Mitigation and adaptation help us tackle the changing climate. While they are related to
one another, the inter-relationship between mitigation and adaptation is ambiguous. Some
consider them substitutes to deal with climate change while others claim that they are
complements. We study this inter-relationship between mitigation and adaptation since it is
essential to understand the strategic interactions within a country and with other countries.
More importantly, we analyze what this relationship implies for policies to facilitate climate
policy agreements between the North and South when they differ in adaptation costs.
We develop a model where the world consists of two regions, the North and the South,
with multiple countries in each region. Each country’s production activities generate a global
pollutant. Individual emissions establish each country’s benefits while the global pollutant
establishes the damages and the cost of adaptation to climate change. One new feature that
differentiates our model from others is that countries differ in the cost of adaptation. Another
new feature is that each country can choose their level of effective adaptation. Given these
1
The Economics of Adaptation to Climate Change (EACC) study by the World Bank. This is roughly
of the same order of magnitude as the current annual foreign aid from developed countries to developing
countries.
2
benefits, damages, and costs, each country chooses how much to emit and its adaptation
effort to maximize the country’s welfare given the emission and adaptation strategies of
other countries. Within this context, we study emission and adaptation strategies for each
country under non-cooperative and cooperative behavior. We also study the incentives to
join international environmental agreements and the stability of such coalitions.
In the first scenario, countries behave non-cooperatively. In this case, we find that rich
countries choose higher effective adaptation when the cost is lower than in the poor countries.
This finding is in line with stylized facts that show lower cost of adaptation and, therefore,
higher adaptation rates in richer countries. Second, we find that richer countries emit more
when the marginal damage of emissions is smaller. When global emissions cause lower
marginal damage in rich countries than in poor countries, richer countries emit more.
This is particularly interesting since stylized facts predict higher marginal damages in
poor countries. In fact, the World Bank predicts that developing countries will face the
highest adaptation costs. On a regional basis, adaptation costs are expected to be higher
in the East Asia and Pacific region, followed by Latin America and the Caribbean, and
Sub-Saharan Africa, while the Middle East and North Africa will face the lowest adaptation
costs. This is an important factor to consider in climate negotiations since it implies that
countries in the North impose an externality on the South. As a consequence, the North
will pollute more under non-cooperative behavior than full cooperation, since the countries
in the South will carry a relatively bigger share of the climate change burden. In the second
scenario, countries cooperatively choose emission and adaptation strategies to maximize
joint welfare. Our results are consistent with previous work on global public goods in that
global emissions and individual adaptation levels are lower when countries fully cooperate.
Furthermore, the South pollutes less than the North in equilibrium.
There is an extensive literature examining climate change negotiations.
Our paper
closely relates to two main strands of the literature: the literature examining international
3
environmental agreements with partial cooperation, and the literature looking at the inter-relationship
between mitigation and adaptation. We contribute to the literature by examining international
agreements when the cost of adaptation differs between richer and poorer nations.
There is a literature studying the relationship between mitigation and adaptation in
climate economics. A main goal of this literature is to explain whether mitigation and
adaptation are substitutes or complements. For example, Kane & Shogren (2000) examine
the optimal mix of the two measures in a one-country model with endogenous risk, where
mitigation reduces the risk of climate change while adaptation decreases the damage. They
show that the scale of adaptation depends on whether mitigation and adaptation are complements
or substitutes. Mendelsohn (2000) distinguishes private and public adaptation, and shows
that the level of private adaptation is efficient, while joint adaptation may be under-provided.
Onuma & Arino (2011) investigate how innovation of adaptation technology by a developed
country (the North) may affect a developing country (the South) as well as the North,
through changes in mitigation efforts by both countries. These studies focus on one-country
cases, while our paper looks at coalitions between countries in the North and the South.
Finally, there are a few papers that analyze the n-country case. For example, Buob &
Stephan (2011) and Buob & Stephan (2008) develop and use models with many regions, and
with mitigation and adaptation in a non-cooperative Nash game. Buob & Stephan (2011)
study the strategic interaction between mitigation and adaptation in a non-cooperative game
between different regions, assuming that mitigation and adaptation are perfect substitutes.
In Buob & Stephan (2008) they use a non-cooperative Nash game to analyze whether funding
adaptation is incentive compatible in the sense that it stimulates mitigation. Our paper
differs from these papers because we consider heterogeneity in adaptation costs as well as
mitigation and we treat effective adaptation as an endogenous decision.
In the next section we survey previous work. Section 3 presents a model with heterogeneous
adaptation costs and section 4 analyzes non-cooperative and cooperative behavior. In section
4
5, we study international climate coalitions. We consider several extensions in Section 6 and,
finally, Section 7 concludes.
2
Previous work
A branch of the literature focuses on studying how we face the challenge of adapting to
climate change. Most of this literature focuses on developing countries.
Barnett & Webber (2010) explains how climate change may increase future migration,
and which risks are associated with such migration. It also examines how some of this
migration may enhance the capacity of communities to adapt to climate change. Climate
change is likely to result in some increase above baseline rates of migration in the next 40
years. Most of this migration will occur within developing countries. Migration, a proven
development strategy, can increase the capacity of communities to adapt to climate change.
Blankespoor et al. (2010) address several questions that are relevant for the international
discussion: How will climate change alter the incidence of extreme weather events, and how
will their impact be distributed geographically? How will future socioeconomic development,
notably an increased focus on education and empowerment for women and girls, affect the
vulnerability of affected communities? And, of primary interest to negotiators and donors,
how much would it cost to neutralize the threat of additional losses in this context?
There are several case studies of the costs of adaptation to climate change by developing
countries (Adger et al. (2003), Hughes et al. (2010), Nelson (2009), Pandey (2010)).
Another branch of the literature on climate change focuses on the relationship between
adaptation and mitigation. Onuma & Arino (2011) investigate how innovation of adaptation
technology by a developed country (the North) may affect a developing country (the South)
as well as the North through changes of mitigation of both countries. This paper relates to
the literature on their joint study of mitigation and adaptation. Within this context, they
5
contribute to the literature by studying how the welfare and mitigation of each region change
if adaptation in a country or region becomes more effective due to innovation.
There are many studies looking at the linkages between mitigation and adaptation. The
following papers study one-country cases. The main objective of these papers is to study
whether mitigation and adaptation are substitutes or complements. For example, Kane &
Shogren (2000) examine the optimal mix of the two measures in a one-country model with
endogenous risk with the recognition that mitigation reduces the risk of climate change
while adaptation decreases the damage. They show that the scale of adaptation depends
on whether mitigation and adaptation are complements or substitutes. In addition, Lecocq
& Shalizi (2007) assume two types of adaptation — proactive and reactive — in a dynamic
model with different sectors and regions, and derive the optimal level of proactive and
reactive adaptation as well as mitigation. Mendelsohn (2000) distinguishes private and
public adaptation, and shows that private adaptation is efficient, while suggesting that joint
adaptation may be underprovided.
There are not many papers studying the effects between different countries. For example,
Buob & Stephan (2011) and Buob & Stephan (2008) study models with many regions
with mitigation and adaptation in a non-cooperative Nash game. Buob & Stephan (2011)
study the strategic interaction between mitigation and adaptation in a non-cooperative
game in which regions are players and mitigation and adaptation are perfect substitutes
in protecting against climate impacts. We allow for step by step decision making, with
mitigation chosen first and adaptation second, and where the benefits of mitigation accrue
only in the future. If marginal costs of adaptation decline with global mitigation, high income
regions simultaneously invest in mitigation and adaptation. Low income regions engage in
mitigation only. In Buob & Stephan (2008) they use a non-cooperative Nash game to analyze
whether funding adaptation is incentive compatible in the sense that it stipulates mitigation.
In particular it is the aim of this paper to discuss: (1) How does foreign funding of adaptation
6
affect mitigation and regional welfare? (2) Under which conditions is it economically rational
to fund adaptation in developing regions? We find that, if strict complementarity between
adaptation and mitigation exists, funding adaptation increases both global mitigation and
the donors’ welfare, but negatively affects the recipients’ welfare. The later only benefit,
if maladaptation or adaptation, which is neutral to mitigation, is funded, which, however,
makes the donors worse off.
3
The Model
We consider a world with n countries and two regions the North and the South. Let i denote
the country and j the region. For simplicity in notation, we refer to the North and the
South nations as Rich and Poor countries where R and P are the sets and nR and nP are
the cardinality of these sets, for rich and poor countries. The total number of countries is
n = nR + nP . All countries differ on their emissions and the cost of adapting to the effects
of a global pollutant. The level of effective adaptation chosen by country i in region j is aji .
In every country pollution is a by-product of the consumption and production activities.
Pn
We denote ei ≥ 0 the emission of a global pollutant in country i and E =
i=1 ei the
aggregate emissions of the global pollutant.
Emissions and effective adaptation affect countries in three ways. First, each countries’
own emissions yield benefits since emissions are a by-product of production. Let B (ei )
represents the benefit to country i from its own emissions.
B (ei ) = ei
ei α−β
2
(1)
with α > 0 and β > 0. We ensure the marginal benefit from pollution to be positive by
ensuring that e < αβ .
7
Second, we assume that the global pollutant damages rich and poor nations equally.2
While climate change affects all countries equally, the cost of effective adaptation varies
for every country. The damage function of a country depends on the effect of the global
pollutant and its own cost of adaptation. Let D(E, aji ) represent the damage to country i
and region j from emissions and adaptation.
D(E, aji ) ≡ ω − aji E
(2)
with ω > 0 is damage from global pollution and aji is effective adaptation. We ensure that
countries are not allowed to over adapt. This condition satisfies when a ≤ ω which states
how a country cannot adapt to climate change more than the impact of climate change on
the country. A key feature of our model is that effective adaptation is endogenous. We differ
from others in the literature because they consider that adaptation is endogenous while its
effectiveness is exogenous (i.e. Benchekroun et al. (2011)). From the damage function in (2),
let us note three characteristics. One, the marginal damage from emissions,
∂D(E,aji )
∂E
= ω−aji ,
is decreasing on effective adaptation aji . Two, a country’s pollution damage decreases in the
level of country i0 s adaptation,
∂ 2 D(E,aji )
∂E∂aji
=
∂ 2 D(E,aji )
∂aji ∂E
∂D(E,aji )
∂aji
= −E ≤ 0. Three, from (2) it also follows that
= −1 ≤ 0.
The third way in which emissions and adaptation affect the country is through the cost
of adaptation. Let C(aji ) represents the cost of adaptation of country i:
C(aji ) ≡
cj j 2
a
2 i
(3)
Note that the cost of adaptation is different for every country. This is a key feature that
2
Some might argue that poor nations are more affected by global pollutants. We abstract from this effect
since our interest is to highlight the importance of heterogeneity in adaptation costs. By assuming that
climate change affects all countries equally, we can isolate the importance of adaptation in the stability of
environmental agreements.
8
differentiates our paper from others in the literature. Finally, we can define the social welfare
of every country with benefits, damages and costs. Social welfare of each country is then:
W E, aji ≡ B (ei ) − D(E, aji ) − C(aji )
(4)
where B (ei ) is equation (1), D(E, aji ) is equation (2) and C(aji ) is equation (3).
In the following we study how much each country pollutes and adapts to climate change
within this framework. We first analyze and compare the scenarios when countries behave
non-cooperatively and cooperatively. Once we analyze both extreme cases, we analyze the
partial equilibrium case when only some countries join a coalition to reduce climate change.
4
Non-cooperative and cooperative behavior
4.1
Non-cooperative outcome
We first analyze the scenario where countries behave non-cooperatively in their choice
of emissions and effective adaptation. The objective of each country’s government is to
simultaneously choose ei and aji so that they maximize their own welfare taking as given the
emissions and adaptation strategies of all the other countries.3 More formally,
maxj W E, aji
(5)
ei ,ai
where W E, aji is given in (4).
The the first order conditions for ei and aji are:
ejn =
1
α − ω + ajn ,
β
3
(6)
Note that since we consider linear functions, we are indifferent between choosing emissions and effective
adaptation simultaneously or not.
9
ajn =
En
.
cj
(7)
We combine (6) and (7) to get the optimality condition:
ejn
1
=
β
En
α−ω+ j
c
(8)
This optimality condition shows how heterogeneity in the cost of adaptation is important
in the choice of emissions. As the cost of adaptation is higher, firms have stronger incentives
to emit less. For now, let us consider that rich and poor nations differ in the cost of adaptation
to climate change. The optimality condition for rich and poor nations becomes:
eR
n
ePn
1
=
α−ω+
β
1
=
α−ω+
β
E
,
cR
E
.
cP
The combination of emissions from rich and poor nations yields global emissions:
P P
E n = nR e R
n + n en
(9)
where nR and nP are the number of rich and poor countries. We obtain the non cooperative
level of global emissions by replacing eR and eP in (9): En = nR β1 α − ω + EcRn +nP β1 α − ω +
P
n
nR
1
R
P
and En = β nα − ω(n + n ) + cP + cR En which lead to the total of global emissions
in the non-cooperative case:
En =
nα − ω(nR + nP )
.
nP
nR
β − cP + cR
(10)
Finally, replacing (10) in (7) we get the non cooperative effective adaptation for rich and
10
En
cP
poor countries.
En
,
cR
En
= P.
c
aR
n =
(11)
aPn
(12)
Non-cooperative behavior in the choice of emissions and adaptation lead to several results.
The first result relates to the relationship between effective adaptation and its costs.
Proposition 1. Rich countries choose to adapt to climate change more than poor countries
P
R
P
if and only if the cost of adaptation is lower for rich countries; aR
n ≷ an ⇔ c ≶ c .
From (11) and (12) we derive the negative relationship between adaptation and its costs.
As expected, the costlier to adapt to climate change, a country chooses to do less of it. The
World Bank, in the study the Economics of Adaptation to Climate Change (EACC), finds
that there are large cross country differences in the cost of adaptation to climate change.
Their study mainly focuses on developing nations where the cost of adaptation is high. In
reference to the stylized facts presented by the World Bank, our results suggest how poor
nations adapt less to climate change than rich nations because their cost of adaptation is
higher.
Let us next look at emissions. Using (10) we get emissions for rich and poor countries.
eR
n
ePn
1
=
α−ω+
β
1
=
α−ω+
β
En
,
cR
En
.
cP
(13)
(14)
We compare non-cooperative equilibrium emissions for rich and poor countries in proposition
(2).
Proposition 2. Rich countries pollute more if and only if their net of adaptation marginal
11
P
R
P
damage is smaller than in poor countries; eR
n ≷ en ⇔ ω − an ≶ ω − an .
Our proposition indicates how rich countries pollute more when the net impact of the
global pollutant is smaller than in poor nations. We refer to net impact of the global pollutant
as the difference between the exogenous impact from the global pollutant and each country’s
choice of effective adaptation. As expected, a country decides to pollute less when the net
impact of the global pollutant is high. It is interesting to look at this result as it will help
us explain in the next section the incentives of different countries to join climate coalitions.
4.2
Full cooperative outcome
Let us next look at how global emissions change when countries’ decide to fully cooperate on
emissions and effective adaptation. In this second scenario, countries simultaneously choose
emissions (ei ) and effective adaptation (aji ) to maximize joint welfare. As expected, every
country recognizes the impact of their emissions on the rest of the countries. Formally, the
problem is:
maxj
ei ,ai
Xn
i=1
W E, aji
(15)
where W E, aji is given in (4).
The first order conditions for emissions and effective and effective adaptation are:
1
α + ajc − ω ,
β
Ec
= j.
c
ejc =
(16)
ajc
(17)
We combine equations (16) and (17) to obtain the global pollutant.
Ec =
n(α − nω)
P
R
β − n ncP + ncR
12
(18)
As before, we look at the situation in which the cost of adaptation differs for rich and
poor countries. This differentiates adaptation strategies for rich and poor countries:
Ec
,
cR
Ec
= P.
c
aR
=
c
(19)
aPc
(20)
Rich and poor nations have different adaptation strategies, however, their emission strategies
are identical in the cooperative case.
eR
c
=
ePc
1
=
β
α − nω +
nP
nR
+
cP
cR
Ec .
(21)
This is a surprising result. We find how rich and poor nations emit the same amount
of pollution even though the effect of pollution differs. The intuition behind this result is
better understood when we compare adaptation from rich and poor countries. Note than
in a model without adaptation, rich and poor countries would emit different amounts of
pollutant. However, when we allow countries to choose the level of their adaptation, emissions
are identical for rich and poor countries. Since rich and poor nations differ on the impacts
from pollution, they choose a different level of adaptation to climate change. However, their
emissions are identical. Therefore, adaptation strategies capture all heterogeneity among
countries. This result has several implications for current climate change policy debates.
We compare the two polar cases, non-cooperation and full cooperation, to better understand
total emissions before moving on to coalition formation in the next section. We analyze
what are the conditions under which global emissions are higher under non-cooperation
than cooperation, En > Ec . We expect total emissions to be higher when countries do not
internalize the effect of their actions on others.
13
Using (10) and (18), we derive
P
R
βω − α ncP + ncR
En − Ec = n (n − 1) P
R
P
β − ncP + ncR
β − n ncP +
nR
cR
.
This calculation allows us to derrive the result.
Proposition 3. The cooperative setting leads to total emissions greater as compared to the
α nP
nR
non-cooperative equilibrium when ω > β cP + cR .
In pollution control problems, when countries are identical, it is well known that total
emissions of countries acting non-cooperatively is always greater than that of the cooperative
case (see, for instance, Barrett, 1994, Nkuiya, 2011). This is the case because each country
private marginal cost of polluting is lower than the social marginal cost of polluting. Proposition
3 suggests that when countries have different adaptation costs, this intuitive result may not
hold.
5
Climate change coalitions
In this section we study the incentives to join a global coalition to deal with climate change
and the stability of such agreements. Our work differs from previous work in that we study
how heterogeneity in adaptation costs affects environmental agreements and their stability.
Consider the scenario where some countries in the rich group (north) and the poor group
(south) decide to join an international environmental agreement. We denote the number
of those countries as kR and kP , for the north and south respectively. Therefore, kR + kP
countries join the coalition while n − kR − kP do not join. The total emissions generated
by the coalition is given by Es = (kR + kP ) es , where es is the emission of a representative
signatory country. Similarly, Ens = (n − kR − kP )ens is the total emissions generated by
the complement of the coalition with ens being the emissions generated by a representative
14
non-signatory. Global emissions are then given by E = Es + Ens . We denote S and N \S as
the set of signatories and non-signatories countries.
Non-signatory and signatory countries simultaneously choose their emission strategies
and effective adaptation levels. Let us start by looking at non-signatory countries.
5.1
Non-signatory countries
The maximization problem of a non-signatory country is:
maxj W E, aji
(22)
ei ,ai
where i refers to whether countries join the coalition and j refers to rich or poor countries.
The best response functions are:
ei =
aji =
ei +
1
α − ω + aji ,
β
Pn−s−1
l6=i
el +
Ps
k ek
cj
i ∈ N \S and j = R, P
(23)
,
i ∈ N \S, k ∈ S and j = R, P
(24)
Combining (24) and (23) we obtain the condition for equilibrium level of pollution:
ejns
1
=
β
E
α−ω+ j
c
(25)
There are rich and poor countries that decide not to join the coalition. While their
incentives to emit are the same, the cost of adaptation differs among rich and poor countries.
15
Their emission levels therefore differ:
1
=
α−ω+
β
1
α−ω+
=
β
eR
ns
ePns
5.2
E
cR
E
cP
(26)
(27)
Signatory countries
Let us now analyze the emission and adaptation strategies of the countries that join a
coalition to reduce global emissions. The maximization problem of a signatory country is:
maxj
X
i∈S
ei ,ai
W E, aji
(28)
where i refers to whether countries join the coalition and j refers to rich or poor countries.
The best response functions of emissions and adaptation are:
ei =
aji
=
1
P P
α − kω + k R aR
i + k ai ,
β
ei +
Pn−s
l
el +
cj
Ps−1
k
ek
i ∈ S and j = R, P
(29)
i ∈ S and k ∈ S and j = R, P
,
(30)
We combine (29) and (30), which yields the emission level that signatory countries satisfy
in equilibrium:
ejs
1
=
β
R
k
kP
+ P E
α − kω +
cR
c
(31)
Comparing equations (26), (27) and (31), we find how there are incentives for rich
countries to free ride on poor countries within a coalition. Let us first look at non-signatory
countries. In equations (26), (27) we find that rich and poor countries differ in their emission
levels when they do not belong to a coalition. Instead, when we look at countries within a
16
coalition, we note how both rich and poor countries emit the same amount ( eq. (31). Note,
however, how they adaptation costs are different and therefore, we see how rich countries,
with low adaptation costs, free ride on poor countries, with high adaptation costs. This
result is interesting as it highlights another reason why it is hard for countries to join in a
coalition with a global goal.
We know that global emissions are the sum of emissions of signatory and non-signatory
P P
R
R R
P
P P
countries: E = k R eR
s + k es + (n − k )ens + (n − k )ens . Also, from equation (31) we
know that all signatory countries emit the same amount independently of whether they are
rich or poor. Therefore,
P
P P
E = kes + (nR − k R )eR
ns + (n − k )ens
(32)
P
where es , eR
ns , and ens are given by (31), (26), and (26). From this relationship, we can solve
for the global pollutant E, and the emissions and adaptation strategies of signatory and
R R
P
P
non-signatory countries, = α(n) − ω(n + k 2 − k) + E n +kcR(k−1) + n +kcP(k−1) .
When only some countries form a coalition, total emissions are:
E=
5.3
nα − ω(n + k 2 − k)
β−
nR +kR (k−1)
cR
−
nP +kP (k−1)
cP
(33)
Stability conditions
In this section we study the incentives of each country to deviate from decision to join or
not an agreements and the stability of the coalitions. Following the stability concept first
introduced by ??. We first analyze the incentives to stay in the coalition, i.e. the internal
stability conditions. To do so, we compare how a country’s welfare changes if they leave the
17
coalition. Let us differentiate between rich and poor countries.
WsR k R , k P
R
k R − 1, k P
≥ Wns
(34)
WsP k R , k P
P
≥ Wns
kR , kP − 1
(35)
where R and P stand for rich and poor nations and W stands for welfare. For countries
outside of the coalitions, we study their incentives to join the coalition. These external
stability conditions for rich and poor countries are:
R
Wns
kR , kP
≥ WsR k R + 1, k P
P
Wns
kR , kP
≥ WsP k R , k P + 1
(36)
(37)
Let us next look at the stability functions. The stability functions help us find which countries
join the coalition in equilibrium. We know a coalition is stable when both the internal and
external conditions in equations (34) - 37) are stable. Following Hoel & Schneider (1997),
the stability conditions for rich and poor countries are:
φR k R , k P
R
= WsR (k R , k P ) − Wns
(k R − 1, k P )
(38)
φP k R , k P
P
= WsP (k R , k P ) − Wns
(k R , k P − 1)
(39)
Proposition 1. In the case countries are identical, the grand coalition can arise as stable
coalition when β1s ≤ β ≤ β2s , where β1s , and β2s are defined in the appendix.
Proposition 1 has interesting ramifications within the IEAs literature. It is well known
that under linear or quadratic damages and quadratic benefits the size stable coalitions
consist of no more than 3 countries, when adaptation is not possible (see, Finus, 2003). Our
result also shed more light on the IEAs literature dealing with adaptation. Using quadratic
18
damages and benefits within the Cournot approach, the literature suggests that the puzzle of
small coalition cannot be solved (see, Benchekroun et al., 2011). Our result suggests that this
puzzle may not hold in the presence of adaptation. We will next examine the implications
of asymmetry.
Given the ambiguity of the impact of adaptation on the stability of environmental
coalitions, we use numerical simulations to illustrate our results. We consider parameter
values nr = 15; np = 25; cr = 0.85; cp = 1.15; w = 0.01; α = 1; β = 1602.1 ∈ [β1s , β2s ]. Our
analysis suggests that stable coalition size cannot be greater than 2. This result appears to
be robust under various parameter specifications.
6
Conclusions
TBW
19
Appendix
A
Details for the symmetric case
When all the countries are identical, the stability function is
φ (k) = Ws (k) − Wns (k − 1)
φ (k, n, α, β, ω, c) =
(k−1)(nα−cβω)2
1
Ω(k, n),
2β (c2 β 2 −2ck2 β+4ckβ−2cnβ−2cβ+k4 −4k3 +2k2 n+5k2 −4kn−2k+n2 +2n)2
where,
Ω(k, n) = (3 − k) c2 β 2 + 2 (k 3 − 4k 2 + (n + 3) k − (n + 2)) cβ + 5k 4 − k 5 − (2n + 7) k 3 +
(4n + 3) k 2 + (2n − n2 ) k − n2 .
The grand coalition is stable if and only if Ω(n, n) =
(3 − n) (βc)2 + (2n3 − 6n2 + 4n − 4) βc + (3n4 − n5 − 4n3 + 4n2 ) ≥ 0.
This inequality works if and only if β ∈ [β1s , β2s ]
√ 1
3
2
β1s = − 2(3−n)c (2n − 6n + 4n − 4) − ∆ ,
√ 1
3
2
β2s = − 2(3−n)c (2n − 6n + 4n − 4) + ∆ ,
2
where ∆ = 4 (3 − n) (3n4 − n5 − 4n3 + 4n2 ) + (2n3 − 6n2 + 4n − 4) .
Notice that cβis , i = 1, 2 are the two roots of Ω(n, n), which is considered as a polynomial
in βc.
References
Adger, W., Huq, S., Brown, K., Conway, D., & Hulme, M. (2003). Adaptation to climate
change in the developing world. Progress in development studies, 3(3), 179–195.
Barnett, J. & Webber, M. (2010). Accommodating migration to promote adaptation to
climate change. World Bank Policy Research Working Paper Series, Vol.
Benchekroun, H., Marrouch, W., & Chaudhuri, A. (2011). Adaptation Effectiveness and
20
Free-Riding Incentives in International Environmental Agreements.
Discussion Paper
2011-120, Tilburg University, Center for Economic Research.
Blankespoor, B., Dasgupta, S., Laplante, B., & Wheeler, D. (2010).
of adaptation to extreme weather events in developing countries.
The economics
Center for Global
Development Working Paper, (199).
Buob, S. & Stephan, G. (2008). Global climate change and the funding of adaptation.
Discussion Papers, Universität Bern, Switzerland.
Buob, S. & Stephan, G. (2011). To mitigate or to adapt: how to confront global climate
change. European Journal of Political Economy, 27(1), 1–16.
Hoel, M. & Schneider, K. (1997). Incentives to participate in an international environmental
agreement. Environmental and Resource economics, 9(2), 153–170.
Hughes, G., Chinowsky, P., & Strzepek, K. (2010). The costs of adaptation to climate change
for water infrastructure in oecd countries. Utilities Policy, 18(3), 142–153.
Kane, S. & Shogren, J. (2000). Linking adaptation and mitigation in climate change policy.
Climatic Change, 45(1), 75–102.
Lecocq, F. & Shalizi, Z. (2007). Balancing expenditures on mitigation of and adaptation
to climate change: an exploration of issues relevant to developing countries. World Bank
Policy Research Working Paper, (4299).
Marrouch, W. & Chaudhuri, A. (2011). International Environmental Agreements in the
Presence of Adaptation. Discussion Paper 2011.35, Fondazione Eni Enrico Mattei.
Mendelsohn, R. (2000). Efficient adaptation to climate change. Climatic Change, 45(3),
583–600.
21
Nelson, G. (2009).
Climate change: Impact on agriculture and costs of adaptation.
International Food Policy Research Inst.
Onuma, A. & Arino, Y. (2011).
Greenhouse gas emission, mitigation and innovation
of adaptation technology in a north-south economy.
Environment and Development
Economics, 16(6), 639–656.
Pandey, K. (2010). Cost of adapting to climate change for human health in developing
countries. Development and Climate Change Discussion Papers, 11.
22