On the Index of Environmental AwarenessTetsuo Ono
Yasuo Maeda
Discussion Paper 00-16

September 2000
この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。
Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, Japan

September 2000

On the Index of Environmental Awareness∗†
Tetsuo ONO
College of Economics, Osaka Prefecture University

Yasuo MAEDA
Faculty of Economics, Osaka University

Abstract
We develop a two-country model where each country contributes non-cooperatively to the global environment by improving its local environment. We introduce an index of environmental awareness,
which measures how much a country is aware of the global environment. Then, we show that the index
plays a key role in evaluating the eﬀects of income growth and international transfers on the global
environment.
Keywords: Environmental Awareness, Private Provision of Public Goods.
JEL Classiﬁcation: H00.

∗

Correspondence for: Tetsuo Ono, College of Economics, Osaka Prefecture University, 1-1, Gakuen-cho, Sakai,
Osaka 599-8531, Japan. Tel: 81-0722-54-9587; fax: 81-0722-54-9925;e-mail: tono@eco.osakafu-u.ac.jp†

Acknowledgment: This paper was presented at the Annual Meeting of the Japanese Economic Association
held at the University of Tokyo in Tokyo on October 16-17, 1999. We are grateful to Toshihiro Ihori for his
valuable comments and suggestions. Any remaining errors are our own responsibility.

1

Introduction

Disagreement over the control of the global environment was observed in the 1992 Rio de Janeiro
and 1997 Kyoto Congresses. This conﬂict seems to imply that developed and developing countries
diﬀer about preference for the environment. To capture such diﬀerence, we develop an index ofenvironmental awareness, which measures how much a country is aware of the global environment.
Then, we show that several comparative statics results depend crucially on the environmental
awareness of each country.
For the purpose of our analysis, we develop a two-country model with three features. First,
the global environment is an international public good shared by the two countries.1
model is an extension of models of private provision of public goods.2

Our

Second, each country

obtains utility from its local environment as well as the global environment which depends on
the quality of the local environment in each country. Third, each country’s consumption has
a negative eﬀect on the local environment but it is counterbalanced by the positive eﬀect ofmaintenance investment. These two eﬀects spread over the global environment.
In this framework, we introduce an index of environmental awareness. This index is anextended version of Andreoni (1989, 1990) that evaluates the degree of impure altruism. By
applying his analysis, we develop an index which measures how much a country is aware of the
global environment.
The index we develop in this paper plays a key role in the comparative statics analysis. First,
income growth of a country results in improvement in the global environment, and the eﬀect
becomes larger as the country is more aware of the global environment. Second, the eﬀects of
1

See, Buchholz and Konrad (1994), Niho (1996), Stranlund (1996), Murdoch and Sandler (1997), Ono (1998),
and Caplan et al. (1999).
2

See, for example, Warr (1983), Bergstrom et al. (1986), Buchholz and Konrad (1995), and Ihori (1996).

1

both conditional and unconditional aid programs on the global environment depend only on therelative degrees of environmental awareness between two countries. If the donor is more awareof the global environment than the recipient, then both types of aid programs result in thedeterioration of the global environment.
The organization of this paper is as follows. Section 2 develops the model and shows the existence and uniqueness of equilibrium. Section 3 introduces the index of environmental awarenessand shows its implication by considering the eﬀects of income growth on the global environment.
Section 4 evaluates the eﬀects of international transfers on the global environment by using theindex. Section 5 concludes.

2

The Model and Equilibrium

We consider a model with two countries, i = 1, 2. We assume that each country is represented
by a benevolent government acting on behalf of its citizens.
Country i is endowed with w i units of private goods. It divides income into consumption ci
and maintenance investment in the local environment, mi . The budget equation of country i is:
ci + mi = w i.

(1)

The local environment in country i, ei , is improved by country i’s maintenance investment
but is worsened by its consumption. We express this mechanism as the formula:ei = −β i ci + γ i mi ,(2)

where β i > 0 is a parameter which indicates the degree of consumption externality and γ i > 0
is a parameter which shows the eﬃciency of maintenance investment.3
3

Examples of maintenance investment are forestry programs, sewerage systems, development of electric cars,
and so on. Examples of environmentally harmful activities are deforestation, water pollution, emissions fromdiesel trucks, and so on.

2We assume that the quality of the global environment, E, is determined by:4
E=

2


ei .

(3)

i=1

Country i obtains utility from consumption, the local environment, and the global environment. The utility of country i is ui(ci , ei , E) where ui : 3+ →  is continuous, increasing, strictly
quasi-concave, and twice continuously diﬀerentiable on 3++ with limx→0 uix = ∞ (x = ci , ei , orE) where uix means the partial derivative with respect to x.
We assume simultaneous and non-cooperative Nash behavior. Country i maximizes its utility
subject to (1), (2), and (3) given the local environment of the other country ej (j = i). By
substituting (1), (2), and (3) into the utility function, the maximization problem is equivalenttomax ui ({E}1
βi + γi(γ i w i + ej ) −1
βi + γi

E, E − ej , E),(4)where ej (j = i) is given.
Diﬀerentiating (4) with respect to E and setting it equal to zero, we can determine theoptimal level of E for country i : 5
E = f i(1βi + γi(γ i w i + ej ), ej )(5)where f i : 2+ → + is continuously diﬀerentiable on 2++ . This is country i’s demand function for
the global environment. The ﬁrst argument in f i comes from the global environment dimensionof the utility function, while the second argument comes from the local environment dimensionof the utility function.
4

We could consider that the quality of the global environment E is partially related to the local environment ofeach country in a complicated way. For example, traﬃc noise and water pollution only aﬀect the local environment.
On the other hand, air pollution can aﬀect the global environment; and the total stock of greenhouse gases in theatmosphere is actually composed of emissions of those gases by each country. To make the analysis tractable, we
express this complicated relationship between local and global environment in a simple manner expressed by (3).
5

We have mi > 0 from the boundary condition of the utility function.

3

By subtracting ej from both sides of (5), we obtain a demand function of country i for its
local environment:ei = f i (1(γ i w i + ej ), ej ) − ej .
i
i
β +γ

(6)

We can regard (6) as a Nash reaction function; country i chooses ei given the other country’s choice, ej (j = i). By using this reaction function, we show the existence of a unique noncooperative Nash equilibrium. A non-cooperative Nash equilibrium is an allocation {c1 , c2 , m1 , m2 , e1 , e2 , E}such that (a) e1 and e2 satisﬁes (6) for i, j = 1, 2; i = j; (b) E = e1 +e2 ; and (c) {ci , mi , ei } satisﬁes(1) and (2) for i = 1, 2. We obtain the following result:
Proposition 2.1: There exists a unique and interior non-cooperative Nash equilibrium.
Proof. See appendix.

3

The Index of Environmental Awareness: Deﬁnition and
Implication

3.1

Deﬁnition

In this subsection, we introduce the index of environmental awareness which measures how
much a country is aware of the global environment. To establish the index, we ﬁrst consider theproperties of the partial derivatives of f i , ∂f i /∂w i and ∂f i /∂ej which evaluate how changes inincome and other country’s choices regarding local environment aﬀect country i’s demand for
global environment, respectively. We then develop the index by using these derivatives.
Consider ﬁrst the income eﬀect: ∂f i /∂w i = γ i f1i /(β i + γ i ). If country i has no interest in
the global environment, it would spend any additional unit of endowment only on consumption:∂f i /∂w i = 0. On the other hand, if country i is only concerned about the global environment, it
would spend all additional endowment on environmental maintenance: ∂f i /∂w i = γ i . The valueof the derivative increases as country i becomes more aware of the global environment.
4

Consider next ∂f i /∂ej = f1i /(β i + γ i ) + f2i . Suppose that the global environment is improvedby one unit because of an increase in ej by one unit. Then country i (i = j) would respond by
decreasing its maintenance investment and increasing its consumption, thereby decreasing ei . In
other words, the global environmental quality may increase less than one unit: ∂f i /∂ej ∈ (0, 1).
To show the above result, we ﬁrst consider the case in which country i has no interest in the
global environment: ui = ui (ci , ei ). In this case, the problem of country i is to maximize ui (ci , ei )subject to ci + mi = w i and ei = −β i ci + γ i mi . Since ej does not aﬀect the choice of country i,
we have ∂f i /∂ej = 1. Thus, we have ∂f i /∂ej < 1 in the case of ui (ci , ei , E).
To show that 0 < ∂f i /∂ej , we rewrite the utility maximization problem as:
max ui (ci , ei , ei + ej ){ci ,ei }s.t. (1 +1
1βi i)c + i E = w i + i ej ≡ ŵ.
iγ
γγ

The social wealth ŵ increases as ej increases. Since consumption, local environment, and global
environment are normal goods with respect to social wealth, we have 0 < ∂f i /∂ej .
Suppose that country i is more aware of the global environment. Then, it reacts greatly tothe improvement of the global environment made by country j (j = i) so that it would respondby a larger decrease in its maintenance investment. On the other hand, if country i is less awareof the global environment, then it reacts little to the improvement. Therefore, ∂f i /∂ej becomes
smaller as country i is more aware of the global environment.
Since a larger ∂f i /∂w i and a smaller ∂f i /∂ej imply greater awareness of the global environment for country i, it is natural to construct an index of environmental awareness by having∂f i /∂w i in the numerator and ∂f i /∂ej in the denominator. Therefore, we deﬁne the index asfollows:

5

Deﬁnition 3.1: Country i’s environmental awareness, αi (i = 1, 2), is indexed byi

f1i β iγ+γ i∂f i /∂w i
= i 1
.
α ≡
∂f i /∂ej
f1 β i +γ i + f2ii(7)Country i is more aware of the global environment as αi becomes large.
The numerator of αi shows the increase in the demand for the global environment whencountry i is faced with income growth. The greater value of the numerator implies that country
i is more aware of the global environment. The denominator shows an increase in the demand
for the global environment when the other country increases the quality of its local environment.
A lower value of the denominator implies that country i is more aware of the global environment.
Thus, a larger αi means that country i is more aware of the global environment.

3.2

The Eﬀect of Income Growth on the Global Environment

In this subsection, we demonstrate how much environmental awareness is important in analyzing
the global environmental issues. In particular, we show that the eﬀect of income growth on the
global environment depends on the index of environmental awareness.
Diﬀerentiating the Nash reaction function of country i with respect to ei , ej , and w i (i = j),
we have:dei = (f1i

1
γi
i
j
i
+
f
−
1)de
+
f
dw i
2
1 i
βi + γiβ + γi(8)

Substituting dej = dE − dei and rearranging, we see that
i

de =

1
i
f1i β i +γ
i + f2 − 11i
f1i β i +γ
i + f2dE + αi dw i.

(9)Adding (9) for i = 1, j = 2 and (9) for i = 2, j = 1 and rearranging, we ﬁnd thatdE = c(α1 dw 1 + α2 dw 2),

6

(10)

wherec ≡ [1 +1i 1 − (f1i β i +γ
i + f2 )i=1,21i
f1i β i +γ
i + f2]−1 > 0.

We thus obtain the following result:

Proposition 3.1: Income growth of country i has a greater positive eﬀect on the global environment than that of country j (j = i) if and only if country i is more aware of the global
environment than country j.
The coeﬃcient c in (10) is the same regardless of which country is faced with income growth.
Hence, (10) shows that whether the eﬀect of country i’s income growth on the global environmentis greater than that of country j (j = i) depends on the relative degree of environmental awarenessbetween the two countries. As regard to the eﬀects of income growth on the local environment,
we obtain the following results; income growth of country i has a positive eﬀect on the local
environment of country i and a negative eﬀect on the local environment of country j (j = i).6
To understand this result, we ﬁrst consider a situation where country 1 experiences income
growth while country 2 does not. Country 1 can aﬀord to invest more in its local environment
because of the income eﬀect. This implies improvement in country 1’s local environment, andthereby improvement in the global environment.7 However, an improvement of country 1’s local
environment leads to strategic interaction with country 2: country 2 chooses to lower the qualityof its local environment thereby decreasing the quality of the global environment. In sum, the6

To show this result, we undertake comparative statics by using (8). Then, we obtain∂ei /∂wi=∂ej /∂wi=

γi/ |D| > 0,βi + γi
11
αi (f1i i+ f2i )(f1j j+ f2j − 1)/ |D| < 0,i
β +γ
β + γjαi f1ij1where |D| = 1 − Π2j=1 (f1j β j +γ
j + f2 − 1) > 0.
7

For example, if a country spends much resources to reduce domestic gas emissions, then the total amount ofemissions in the world would decrease.

7

eﬀect is evaluated by dE = cα1 dw 1 . On the other hand, if country 2 is faced with income growth,then it contributes to an improvement in the global environment while country 1 does not. The
total eﬀect is evaluated by dE = cα2 dw 2 . Which case of income growth has a greater eﬀect on
the global environment depends on the relative degrees of environmental awareness between two
countries.

4

International Transfers

In this section, we evaluate the eﬀects of international transfers, i.e., conditional and unconditional aid programs on the global environment by using the index of environmental awareness.

4.1

Unconditional Aid

In this subsection, we consider unconditional aid. Without loss of generality, we assume thatcountry 1 transfers a part of its income τl1 ∈ (0, w 1 ) to country 2 in a lump-sum fashion. Sincea marginal increase in lump-sum transfer implies dw 1 = −dτl1 and dw 2 = dτl1 in (10), we havedE = c(α2 − α1 )dτl1
wherec ≡ [1 +1i 1 − (f1i β i +γ
i + f2 )i=1,21i
f1i β i +γ
i + f2]−1 > 0.

We thus obtain the following result:

Proposition 4.1: Unconditional aid has a positive eﬀect on the global environment if and only
if the recipient is more aware of the global environment relative to the donor.

To interpret the results, suppose ﬁrst that neither country obtains utility from the local
environment. If country 1 implements a lump-sum transfer to country 2, then country 1 reduces
its maintenance investment by the same amount, while country 2 invests all the transfer in8its local environment. Thus, the global environment is unchanged as long as γ 1 = γ 2 (Warr(1983)).

Suppose next that both countries obtain utility from their local environment. Suchcountries prefer a higher quality of the local environment. Hence, country 1 is unwilling to reduce
its maintenance investment to oﬀset a reduction in income, and country 2 is also unwilling toincrease its maintenance investment following the increase in income. The relative degree towhich both countries are unwilling to make these substitutions is reﬂected in the diﬀerence
between the two indexes of environmental awareness, α2 − α1 .
Oﬃcial Development Assistance (ODA) to developing countries is often criticized in view ofenvironmental preservation. This is because developing countries tend to spend most transfers on
investment in infrastructure like buildings and dams, which are often harmful to the environment.
However, our result shows that unconditional aid is harmful to the global environment, notbecause recipient (developing) countries do not use transfers for environmental maintenance, but
because they are less aware of the global environment relative to donor countries. In order tomake unconditional aid beneﬁcial to the global environment, donor countries need to enlighten
people in developing countries as to how much the preservation of the global environment isimportant.

4.2

Conditional Aid

In this subsection, we consider conditional aid: a donor requires that a recipient spends thetransfer only on environmental maintenance. Without loss of generality, we assume that country
2
1 gives tied aid τm> 0 to country 2.
2and the local environment in country 1
The budget equation of country 1 is c1 +m1 = w 1 −τm2
2
is e1 = −β 1 c1 +γ 1 m1 . For country 2, the budget equation is c2 +(m2 +τm) = w 2 +τm
and the local
2
environment is e2 = −β 2 c2 + γ 2 (m2 + τm). Substituting these constraints into the corresponding

9

utility functions and solving the maximization problems, we can obtain Nash reaction functions
for countries 1 and 2. The allocation under conditional aid, {ê1 , ê2 }, is characterized by thefollowing Nash reaction functions:ê1 = f 1 (ê2 = f 2 (1
β1 + γ11
β2 + γ2

2(γ 1 (w 1 − τm
) + ê2 ), ê2 ) − ê2 ,(11)2(γ 2 (w 2 + τm
) + ê1 ), ê1 ) − ê1 .

(12)

2
and rearranging, we obtain:
By diﬀerentiating (11) - (12) with respect to ê1 , ê2 , τm2dÊ = ĉ(α2 − α1 )dτm

whereĉ ≡ [1 +1i 1 − (f1i β i +γ
i + f2 )i=1,21i
f1i β i +γ
i + f2]−1 > 0.

We obtain the following result:

Proposition 4.2: Conditional aid has a positive eﬀect on the global environment if and only
if the recipient is more aware of the global environment relative to the donor.

Many industrialized countries often implement conditional aid to developing countries. The
aim of conditional aid is to make developing countries invest in the environment. Our result,however, indicates that conditional aid has the same implication for the global environment as
unconditional aid. Whether conditional aid is beneﬁcial to the global environment depends on
the relative degrees of environmental awareness between the two countries.

5

Conclusion

In this paper, we introduce an index of environmental awareness, which measures how much a
country is aware of the global environment relative to its local environment. Then, we show

10

that environmental awareness plays a key role in evaluating the eﬀects of income growth andinternational transfers on the global environment.
There have been many studies which analyze the eﬀects of income growth and internationaltransfers on the global environment in two- or many-country non-cooperative Nash equilibrium
models. However, they have ignored the role of environmental awareness in evaluating theeﬀects. Contrary to previous studies, we show that the eﬀects of income growth and internationaltransfers on the global environment depend critically on environmental awareness.

11Appendix
We ﬁrst show the existence of a Nash equilibrium.

From (1) and (2), we have mi =1
(β i w i + ei ). By substituting (6) into the above equation and eliminating ei , we obtainβ i +γ imi =1βi + γi{β iw i − ej + f i}.

(13)

Let W = {m in 2 : 0 ≤ mi ≤ w i for i = 1, 2}. This is a compact and convex set. The
function (13) is a continuous function from the set W to itself. Hence, by Brouwer’s Fixed Point
Theorem, there exists a ﬁxed point, which is a Nash equilibrium vector m.
We next show the uniqueness of a Nash equilibrium. Suppose that E ∗ and E ∗∗ are two
diﬀerent equilibria of global environmental quality. We assume, without loss of generality, E ∗ >E ∗∗ . Since E = e1 + e2 and ei = −β i ci + γ i mi , i = 1, 2, in equilibrium at E ∗ , at least for one
country i, ei∗ > ei∗∗ holds. This implies that country i invests more in the environment thanin the equilibrium at E ∗∗ , i.e., mi∗ > mi∗∗ . Hence, from the budget constraint ci + mi = w i ,ci∗ < ci∗∗ holds. However, from the normality assumption, the ﬁrst-order condition of utility
maximization problem uici = (β i + γ i )(uiei + uiE ) is rewritten as ci = φi (ei , E) where ∂φi /∂ei > 0
and ∂φi /∂E > 0. Then, ci∗ < ci∗∗ and ei∗ > ei∗∗ implies E ∗ < E ∗∗ which is a contradiction.
Therefore, the equilibrium of the global environmental quality is unique.
By combining (1) and (2), the reduced form of constraints in equilibrium is
ci +

1
γ iwi
i
e
=
.
βi + γiβi + γi(14)

Substituting ci = φi (ei , E) into the above, we haveφi (ei , E) +

1
γ iwi
i
e
=
.
βi + γiβi + γi(15)

Given E, the left-hand side of (15) is strictly increasing in ei so that (15) uniquely determines ei ,and also (14) uniquely determines ci . Finally, mi is uniquely determined by the budget constraint.
The solution is interior (mi > 0) from the boundary condition of the utility function.
12

References
Andreoni, J., 1989, Giving with Impure Altruism: Applications to Charity and Ricardian
Equivalence, Journal of Political Economy 97, 1447-1458.
Andreoni, J., 1990, Impure Altruism and Donations to Public Goods: A Theory of WarmGlow Giving, Economic Journal 100, 464-477.
Bergstrom, T., Blume, L., and Varian, H., 1986, On the Private Provision of Public Goods,
Journal of Public Economics 29, 25-49.
Buchholz, W., and Konrad, K., 1994, Global Environmental Problems and the Strategic
Choice of Technology, Journal of Economics 60, 299-321.
Buchholz, W., and Konrad, K., 1995, Strategic Transfers and Private Provision of Public
Goods, Journal of Public Economics 57, 489-505.
Caplan, A., Ellis, C., and Silva, E., 1999, Winners and Losers in a World with Global
Warming: Noncooperation, Altruism, and Social Welfare, Journal of Environmental Economics and Management 37, 256-271.
Ihori, T., 1996, International Public Goods and Contribution Productivity Diﬀerentials,
Journal of Public Economics 61, 139-154.
Murdoch, J., and Sandler, T., 1997, The Voluntary Provision of a Pure Public Good: The
Case of Reduced CFC Emissions and the Montreal Protocol, Journal of Public Economics
63, 331-349.
Niho, Y., 1996, Eﬀects of an International Income Transfer on the Global Environmental
Quality, Japan and the World Economy 8, 401-10.
Ono, T., 1998, Consumption Externalities and the Eﬀects of International Income Transferson the Global Environment, Journal of Economics 68, 255-69.
Stranlund, J., 1996, On the Strategic Potential of Technological Aid in International Environmental Relations, Journal of Economics 64, 1-22.
Warr, P., 1983, The Private Provision of a Public Good is Independent of the Distributionof Income, Economics Letters 13, 207-211.

13