1

A characterization of the environmental Kuznets curve:

The role of the elasticity of substitution

Eugenio Figueroa B.a, , Roberto Pasten C.b, ,

a Department of Economics, Universidad de Chile, Santiago, Chile; b Department of

Economics and Finance , Universidad de Talca, Talca, Chile.

Abstract: This paper analyzes social preferences consistent with an environmental Kuznets curve (EKC),

presenting a closed form of a social welfare function of market and non-market goods and services whose

maximization outcome is an optimal income-pollution path exhibiting the characteristic shape of an EKC.

The turning point predicted by the model depends on the elasticity of substitution between consumption

and environmental quality determined by preferences; the harmfulness of pollution; the degree of

substitution between capital and pollution in production; and the fact that preferences are properly and

adequately translated into explicit market prices and implicit shadow prices by the social decision-making

process. We show that this preference characterization of the EKC is a general case encompassing certain

special cases described in earlier characterizations of the EKC, and analyze how the elasticity of

substitution between consumption and environmental quality determined by preferences plays a key role

Keywords: Environmental Kuznets curve, aspiration consumption, income elasticity of substitution,

social welfare function

JEL Classification: C23, Q53, Q58

Corresponding author: Universidad de Talca, 2 Norte 685, Talca, Chile. Tel: 56 71 200308 Fax: 56 71 200457. E-mail: rpasten@utalca.cl.

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A characterization of the environmental Kuznets curve:

The role of the elasticity of substitution

Abstract: This paper analyzes social preferences consistent with an environmental Kuznets curve (EKC),

presenting a closed form of a social welfare function of market and non-market goods and services whose

maximization outcome is an optimal income-pollution path exhibiting the characteristic shape of an EKC.

The turning point predicted by the model depends on the elasticity of substitution between consumption

and environmental quality determined by preferences; the harmfulness of pollution; the degree of

substitution between capital and pollution in production; and the fact that preferences are properly and

adequately translated into explicit market prices and implicit shadow prices by the social decision-making

process. We show that this preference characterization of the EKC is a general case encompassing certain

special cases described in earlier characterizations of the EKC, and analyze how the elasticity of

substitution between consumption and environmental quality determined by preferences plays a key role

Keywords: Environmental Kuznets curve, aspiration consumption, income elasticity of substitution,

social welfare function

JEL Classification: C23, Q53, Q58

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1. Introduction

Since the early 1990s, the so-called environmental Kuznets curve (EKC), an empirical

inverted U curve which illustrates the relationship between pollution and income per

capita, has been studied in different contexts due to its potentially promising

implications for planning sustainable economic growth in the future. According to this

relationship, the emission levels of a given pollutant in the environment, or its

concentration levels in the environment, initially rise as the income per capita of a

country or city increases over time and then, after reaching a maximum (a ‘turning

point’), the emissions or concentration levels decline although income per capita

continues to grow (see Barbier, 1997; Dinda, 2004 and Yandle et al. 2004 for empirical

illustrations). Based on this, some authors expected economic growth to contain the

mechanisms for reversing the initial upward trend in pollution emissions or

concentrations observed in several countries and for several pollutants (Beckerman,

1992; Selden and Song, 1994; Grossman and Krueger, 1995). However, this initial

optimism about the implications of the EKC was soon challenged by other authors who

were skeptical of the existence of an automatism built into the EKC relationship

(Panayotou, 1997; Stern, 2004).

In more recent literature there have been several attempts to understand the underlying

behavioral mechanisms on the part of consumers and/or producers which could explain

the empirical occurrence of an EKC. Untangling these mechanisms, the thinking goes,

makes it possible to assess the extent to which an EKC is automatic and/or inducted by

policy. Also, doing so would reveal which regulatory or other public policy measures, if

any, can speed up development or bring down the costs of that development. The aim of

this paper is to contribute to these efforts, finding restrictions on people’s preferences

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which are consistent with the EKC hypothesis and can shed light on the conditions

under which its empirical occurrence can be expected in the real world.

We propose a theoretical model in which society, in the long run, can attain both high

consumption and high environmental quality but, starting from an initial very large

endowment of environmental quality, it is necessary first for this society to experience a

stage of decreasing environmental quality. In our model, rather than attempting to

maximize welfare through consumption alone as is the case in the typical one-good

model people have more balanced aspirations or objectives as early proposed by

theorists analyzing human economic behavior (Davis, 1945) and more recently by

researchers in behavioral and experimental economics (Kahneman et al 1999) . People

seek to increase their consumption but, at the same time, they want to enjoy other non-

market, valued goods such as a clean environment, a safe city, the ability to raise

healthy children, recognition from their peers, and so on. This desired "high

complementarity” between market and non-market valued goods can only be achieved

by wealthy individuals; low-income individuals with abundant clean environment and

levels of consumption which are close to subsistence can only regard both types of

goods environment and consumption, as perfect substitutes. If this is the case, then

the elasticity of substitution between consumption and environmental quality – a key

parameter neglected in the current literature- must be a decreasing function of income.

An elasticity of substitution that is a decreasing function of income is the main aspect

in our model. The shape of the income-pollution relationship curve – the EKC – is

determined in the model by the difference between the rate of growth of the marginal

benefits of pollution (the welfare provided by enjoying the marginal unit of income or

consumption) and the rate of growth of its opportunity cost (the welfare provided by

enjoying the marginal unit of environmental quality) as income increases. If the

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marginal benefits rises faster (slower) than the opportunity cost, pollution necessarily

increases (decreases) monotonically with income. If the marginal benefit rises at a

constant rate while the opportunity cost grows at a rate that is an increasing function of

income, pollution first rises and then decreases with income. A necessary and sufficient

condition for this to happen is a decreasing in income elasticity of substitution.

Certainly at early stages of development, low-income individuals are endowed with a

sufficiently large amount of clean environment relative to their “environmental

aspiration”, while at the same time they are likely to have level of consumption close to

subsistence in regard to several goods and services (i.e. their initial levels of

consumption are, with high probability, far below their “consumption aspirations”).

Therefore, in such circumstances, and if they have consumption aspirations beyond

simple subsistence, they would be willing to trade some environment in exchange for

consumption which enables them to attain greater consumption than the minimum

necessary for survival. In this context, pollution is viewed as the “good smell of

money”, as people in the city of Iquique, Chile, used to describe the unpleasant odor

from new fishmeal mills that pervaded the city in the early stages of the fish meal

industry’s growth in the 1960s. However, at more advanced stages of development, the

situation reverses: as people consume well above their minimum subsistence level and

move towards their aspiration level of consumption, the environmental quality which

has deteriorated as a result of the expansion of economic activity becomes scarce,

moving closer to the minimum acceptable level. At this point, people are willing to

sacrifice some consumption growth in exchange for higher levels of environmental

quality. This explains why in the 1980s, when the residents of Iquique enjoyed a much

higher level of income and lower environmental quality than they had in the 1960s, they

began to demand regulations to reduce the unpleasant effects of the fishmeal industry.

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Theoretical explanations for the EKC hypothesis have only recently been put forward.

Arrow et al (1995) pointed out that the pattern of environmental degradation is the

natural progression from a basic agrarian process with low environmental impact to

highly polluting industrial economies and then to “cleaner” services economies. The

explanation of Suri and Chapman (1998) is that advanced economies export intensive

pollution processes to less advanced economies. Jones and Manuelli (1995) argue that

externalities associated with intensive pollution processes can be better internalized by

advanced, collective decision-making institutional frameworks, which may only be

implemented in developed countries. John and Pechenino (1994) present an overlapping

generation model in which the environment degrades over time unless society invests in

it, which is only possible in advanced countries. Andreoni and Levinson (2001) propose

an explanation based on abatement technologies with increasing returns to scale, in

which high-income individuals demand more consumption and less pollution and as

pollution abatement becomes possible, these high-income individuals can more easily

achieve their demands. For Stokey (1998) an income threshold determines whether the

dirtiest or cleanest technology will be used.

The explanations proposed by Lopez (1994), Lieb (2002), McConnell (1997) and

Copeland and Taylor (2003) focus on preferences rather than technology. Lopez

presents a model of a small, open economy in which if preferences are homothetic,

pollution growths monotonically with income; however, if preferences are non-

homothetic, then a non-monotonic relationship between pollution and income (i.e., the

EKC) can be found, depending on the interaction between, on the one hand, the

elasticity of substitution between pollution and other conventional factors of production

and, on the other hand, the relative degree of curvature of utility in income. Copeland

and Taylor (2003) present a closed reduced form of the EKC, relying strongly on the

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assumption of an increasing elasticity of marginal damage. Since in their model

preferences are separable and the disutility of pollution is linear, their assumption of an

increasing elasticity of marginal damage is equivalent to Lopez´s assumption of an

increasing relative degree of curvature of the utility function.1 Lieb (2002) presents a

representative consumer model in which pollution is generated by consumption and is

abated as long as more resources are devoted to abatement. In his model, “an upper

bound in utility” is a necessary condition (along with some restrictions on the

technological side of the model) for an EKC to arise. In section 4 we will show that

Lieb’s satiation concept – implicit also in Lopez (2002) and other EKC models – is a

natural consequence of our more general model which requires an upper bound in

consumption as well as an upper bound in environmental quality to produce a

decreasing elasticity of substitution between consumption and environment quality.

McConnell (1997) focuses on the role of the income elasticity of demand for

environmental quality in a model where pollution is generated by consumption and is

reduced by abatement. He finds no special role for income elasticity equal to or greater

than one. Contrary to McConnell’s results, we show that if it is possible to disentangle

the income elasticity of demand for environmental quality between a structural elasticity

and an equilibrium elasticity, there is a role for an elasticity equal to or greater than one.

Comprehensive reviews of analytical models can be found in Andreoni and Levinson

(2001) and particularly in the third chapter of Copeland and Taylor (2003).

This paper is organized as follows: in Section 2 we set up the model. In Section 3 we

derive a closed form for the environmental Kuznets curve and in Section 4 we compare

the model to other relevant ones and we discuss in further detail the intuition upon

1 However, neither Lopez (1994) nor Copeland and Taylor (2003) provide any behavioral content or explanation for the increasing curvature of preferences as we do here.

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which the model is based and this paper’s contribution to the existing literature. Finally,

in Section 5 we present our conclusions.

2. Set-up of the model

We develop a static general equilibrium model in which a social planner maximizes a

social welfare function which is increasing in consumption (c ) and decreasing in

pollution (e ) . For simplicity, intra- and inter-generational aspects are not addressed

here. Technological progress is assumed to be exogenous, as in Lopez (1994) and

Stokey (1998). Social preferences are given by the following welfare function:

W =W (c , e) (1)

W ( ∙ ) is increasing in c and strictly decreasing in e. W (∙) is assumed to be strictly

concave and separable in c and e. Let r=d−e, where d is the best environmental

quality attainable and r is environmental quality.

The production function f ( ∙ ) is kept deliberately simple in order to isolate preferences

from technology; we only impose constant returns to scale in production factors.

Production function is given by:

c=f =f (k , e) (2)

where aggregate consumption (c ) is identical to aggregate income f , k is a broad

definition of capital that includes both physical and human capital and grows over time

(neutral growth); and e is the flow of pollution generated and used in the productive

process. The production function is based on all the usual assumptions (increasing and

concave in factors, Inada conditions, etc). In this model, following Tahvonen and

Kuuluvainen (1993) and Lopez (1994), pollution plays a role as a factor of production.

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Maximizing social welfare subject to the production possibilities of the economy

implies maximization of (1) subject to (2) and results in the following first-order

condition (subscripts denote differentiation);

−W e=W c f e (3)

The right-hand side of this expression is the value of the marginal product of pollution

(valued at the marginal utility of consumption), and the left-hand side is the marginal

cost of pollution, given by the reduction in welfare due to a marginal increase in

pollution. At the optimizing margin both effects cancel each other out.

The maximization condition in equation (3) is illustrated in Figure 1 by the point of

tangency of functions W i and f i when their slopes are equal to the slope of the

corresponding Pi line.2 The expansion path (segmented curve TT') depicts the EKC

behavioral pattern followed by society when maximizing welfare.

To explain and characterize the empirical occurrence of the EKC the literature has

focused, as would seem necessary from Figure 1, on describing the conditions under

which the segmented expansion path TT’ is a consequence of economic growth (i.e., as

income – and therefore consumption – increases). So far, all explanations have relied on

combinations of assumptions regarding preferences and production technology which

are usually not only arbitrary but also quite artificial in the sense that these assumptions

need to be imposed at some stage of economic development and in an ad hoc fashion in

order to produce (generate) the desired EKC pattern.3 We take a different approach,

searching for basic assumptions regarding peoples preferences which on the one hand

are theoretically reasonable and on the other hand are compatible with a maximizing

2 Note that these slopes also correspond to the relative price between clean environment and the consumption good under full internalization of the externality. Figure 1 shows that if an EKC exists this price increases with consumption (and income). As is well known, it is possible to generate such prices as separate hyperplanes. 3 For example, in a recent paper Brock and Taylor (2010) obtain an EKC with a model in which the growth rate of pollution abatement spending exceeds the rate of growth of the economy. Therefore, they do not discuss or explore the behavioral causes explaining why people and the society in general decide to invest in abatement at a growing pace.

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behavior by economic agents that naturally leads to the segmented curve TT’ depicting

the EKC pattern in Figure 1 when the economy is growing. As a result, we find a closed

form of preferences with the necessary properties which does not need the imposing of

additional ad hoc restrictions on the usual maximizing behavior of economic agents

(consumers and/or producers) to generate the EKC pattern when economic growth

occurs.

FIGURE 1

For a constant level of social welfare W , the slopes of the indifference curves W i in

Figure 1 are given by the (negative) marginal rate of substitution (MRS) between

consumption and pollution making possible to write:

dcde W =W

=−W e

W c=h(c , e) (4)

If h(∙) is positive and differentiable and preferences exhibit a diminishing marginal rate

of substitution between consumption and pollution reduction, the following expression

holds:

d2cd e2

W=W

=h (c , e ) hc ( c , e )+he (c , e )>0 (5)

in (5) hc and he are the partial derivatives of h with respect to c and e respectively.

Condition (4) allows us to express the first-order condition in (3) in terms of the

equality of the marginal rate of substitution between consumption and pollution h(c , e)

and the marginal rate of transformation between income (consumption) and pollution

f e(k , e), such that:

h (c , e )=f e(k ,e ) (6)

The slope for the consumption path and for the pollution path can be found by

differentiating (2) and (6) with respect to k ,

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dcdk

=f ek f e+ f k (he−f ee)

f e hc+he−f ee(7)

The expression above is positive as long as f ek>0 (i.e., if pollution(e ) and the

conventional factor of production(k ) are complements). Similarly,

dedk

=f ek−f k hc

f e hc+he− f ee⋛0 (8)

In equation (8) the sign of the derivative is ambiguous and depends on the interplay

between income and substitution effects. Rearranging terms and dividing (8) by (7), it is

possible to show that the slope of the pollution-income relationship describing the TT’

path in Figure 1 is given by:

dedc

=1h

f ek hc

( f ek f e+ f k (he−f ee)) [ hhc

−f k f e

f ek fc ]⋛0 (9)

To obtain equation (9), equations (8) and (7) were used with the conditions c=f

(equation 2) and h=f e(equation 6). As will be shown in the following sections, the

expression inside the square brackets on the right-hand side of (9) has a well-defined

form and is a function of two key parameters: the elasticity of substitution between

consumption and environmental quality in preferences and the elasticity of substitution

between pollution and the conventional factor of production in the production function.

However, from (9), at this point it is evident that without more structure on preferences

or technology it is impossible to say something about the shape of the income-pollution

relationship. And although it is possible to impose some restriction on technology –

particularly on the elasticity of substitution between pollution and conventional factors

– and still obtain an inverted U relationship, the mechanism is likely to be weak (Lopez

and Mitra, 2000). Consequently, we must model preferences as the main force driving

the EKC. In order to do this, in the following section we study which restrictions have

to be imposed on preferences. We use a social preference utility function that is general

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and flexible enough to encompass most of the functional forms which are already

known.

3. Deriving the environmental Kuznets curve

To gain more insights from equation (9), we use the explicit form of the implicit welfare

function in (1) in the following fashion:

W (c , e )= −μ1+μ (m− c

μ )1+μ

− e1+μ

1+μ m ≥0 (10)

Note that no restrictions are imposed on the signs of the parameters in (10) other than

m being non-negative. The first term on the right-hand side of (10) is social utility in

income, with a form similar to an hyperbolic absolute risk aversion (HARA) class of

preferences broadly used in the economics of risk and uncertainty (see, for example,

Eeckhoudt, Gollier and Schlesinger, 2005). The HARA system of preferences

encompasses the most commonly used forms of utility functions depending on the

values assigned to the underlying parameters μ and m (see Feigenbaulm 2003 for a

comprehensive description of this class of utility functions). To have a well-behaved

utility function, if μ ≥ 0 (10) is defined for c ≤ μm such that μm is an upper bound on

consumption that can be interpreted as an aspiration level of consumption. On the

contrary, if μ ≤ 0 the welfare function is defined in the domain c ≥−μm, such that −μm

is a lower bound in consumption that can be interpreted as a subsistence level of

consumption.4 If m=0 and μ<0, (10) collapses to the constant elasticity of substitution

(CES) utility function with elasticity of substitution −1/ μ. Furthermore, the parameter

μ reflects the weight given to pollution in the welfare function, and thus it is possible to

associate the parameter μ with the level of perceived harmfulness of the contaminant,

with a higher value of μ implying a less harmful pollutant.

4 Technically when μ=0, consumption is unbounded.

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According to (10) the marginal rate of substitution between consumption and

pollution is given by:

h (c , e )=( μeμm−c )

μ

(11)

Equation (11) allows for expressing the first term inside the square brackets on the

right-hand side of equation (9) as:

hhc

=μm−cμ (12)

In addition, following Lopez (1994), the second term in brackets on the right- hand side

of (9) can be expressed as:

f k f e

f ek f= ρ (13)

where ρis the elasticity of substitution between pollution and conventional factors of

production in the production function.

Using expression (9) and rearranging the terms, the slope of the income-pollution

relationship can be expressed as:

dedc

= ch

f ek hc

( f ek f e+ f k (he−f ee)) [ μm−cμc

−ρ] (14)

Thus, the slope of the income-pollution path (IPP) will depend on the sign of the

last expression inside the squares brackets, which in turns depends on the level of

consumption (c ) and a mix of the different parameters in the model. Particularly, if ρ>0,

which is plausible, a sufficient condition for an EKC to arise is μ>0; and therefore, a

sufficient condition is to have a type of social preferences with an upper bound of

consumption. It is important to point out, however, that in our model an EKC arises

even if this upper bound tends to infinite (i.e., as long as μ → ∞).

The expression in (14) can also be expressed as a function of the elasticity of

substitution between consumption and environmental quality ϵ= (h/ x )∂ x /∂ h, where

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x=c /r corresponds to the ratio of consumption to environmental quality and h is the

marginal rate of substitution (MRS) between consumption and environmental quality as

given by (11). Using (11) this elasticity can be expressed as:

ε (c)=μm−cμc (15)

Note that in the particular case of m=0, this elasticity becomes ε=−1/ μ, which

corresponds to the standard case of a constant elasticity of substitution. Otherwise, if

m>0, the elasticity of substitution is a decreasing function of income:

∂ ϵ∂ c

=−μ2 m(μc)2 <0 (16)

Using (15) it is possible to rewrite equation (14) as:

dedc

= ch

f ek hc

( f ek f e+ f k (he−f ee))[ε (c )−ρ ] (17)

Equation (17) allows for the analysis of the underlying factors which explain the

presence of an EKC. It states that the shape of the income-pollution relationship

depends on the sign of the expression in brackets on the right-hand side, i.e., it depends

on the difference between the preference elasticity of substitution between consumption

and environment quality, ε (c ) and the production elasticity of substitution between

polluting and non-polluting factors, ρ. The preference elasticity of substitution

decreases with income while the production elasticity of substitution is constant.

Therefore, at low levels of income (i.e., at early stages of development) the slope of the

income-pollution relationship is positive; it decreases toward zero as income increases,

is zero when income has grown sufficiently for ε to equal ρ; and it is negative thereafter

(i.e., when income increases beyond the point at which ε=ρ).

The reason for a decreasing in income elasticity of substitution (the key element

explaining the presence of an EKC) has been put forward elsewhere in this paper. A

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growth path that balances consumption and environment is preferred by high-income

people; however, when people are poor, with a large amount of clean environment

available and a level of consumption well below their aspiration, they have no other

option but to regard both goods as substitutes and consequently, the elasticity of

substitution between both goods will be a decreasing function of income. Therefore, a

decreasing elasticity of substitution between consumption and environmental quality is

a consequence of people having positive consumption aspirations along with an initial

positive endowment of environmental quality.

Preferences change as the distance between current consumption and aspiration

consumption changes. Thus, as income increases, these changing preferences cause a

decline in people’s willingness to sacrifice environmental quality for higher levels of

consumption.

From (14) it is possible to derive the corresponding turning point cT as given by:

cT ( μ ,m, ρ )= μm1+μρ

≥ 0. (18)

Differentiating (18), we have

c μT ( μ ,m, ρ )= m

(1+μρ )2≥ 0

cmT ( μ , m, ρ )= 1

1+μρ≥ 0

c ρT ( μ ,m, ρ )= μ2m

1+μρ≤ 0 (19)

An increase in either μ or m or a decrease in ρ would increase the income level at

which the turning point cT occurs. An increase in μ – associated with a less harmful

pollutant – increases the preference elasticity of substitution ε for each level of income,

allowing a preference for higher levels of consumption for each unit of pollution and,

consequently, a higher turning point. An increase in m increases the aspiration

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consumption μm for a given level of harmfulness of the pollutant μ, leading to a higher

turning point and therefore implying that societies become “greener” at higher levels of

income in comparison to societies with lower values of m. This is consistent with recent

empirical studies showing different turning points for different countries (Koop and

Tole, 1999; List and Gallet, 1999; Markandya et al, 2006) and particularly with

Figueroa and Pasten (2009) which found that for a given pollutant, Canada and the

United States have higher turning points than European countries (also see note 8).

Finally, a decrease in ρ implies that for firms it is more difficult to substitute polluting

factors with non-polluting factors and therefore a turning point would be reached at

higher levels of income (i.e., ε will equal ρ at a higher level of income).

The consumption-environment (income-pollution) relationship derived from (14) is

represented by the segmented curve in Figure 2

FIGURE 2

To shed more light on the behavior of the underlying parameters of the environmental

Kuznets curve, and since our focus here is on preferences rather than technology; we

will assume a simple Cobb-Douglas production function of the following form:

c=f =A kα e1−α (20)

Maximizing (10) subject to (20) yields the following first-order condition:

( μeμm−c )

μ

=P=(1−α ) ce

(21)

where P corresponds to the equilibrium relative price of pollution in terms of

consumption. The left-hand side of (21) is the marginal damage caused by pollution

while the right-hand side is its marginal benefit. If the marginal damage is fully

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internalized by society, the EKC income-pollution relationship can be derived in a

straightforward fashion from (21):

e=(1−α )1

1+μ c1

1+μ ( μm−cμ )

μ1+μ (22)

Taking logs in (19), totally differentiating and making use of e=d−r it is possible to

find the equilibrium income elasticity for environmental quality, i.e., the income

elasticity when all prices adjust to their equilibrium values.5

η= 11+μ ( μc

μm−c−1)( d−r

r ) (23)

where η represents the equilibrium income elasticity of environmental quality and the

first term inside the first brackets represents the structural income elasticity. Note that

while the equilibrium elasticity is negative below the turning point and positive above

it, the structural elasticity is less than one below the turning point and greater than one

above it. Expression (23) clarifies the debate in the EKC literature about whether there

is a particular role for an income elasticity which is equal to or greater than one (see

McConnell 1997 and Lieb 2002). According to (23) income elasticity does not play

such a key role if the reference is the equilibrium income elasticity; however, there is a

relevant role in the case of structural income elasticity. In fact, having a structural

income elasticity greater than one is the necessary condition for the downward-sloping

portion of the EKC. 6

4. Two relevant issues related to the literature

4.1. On technical issues of the EKC characterization

5 There is a difference between the “structural income elasticity of pollution” μc / (μm−c ) and the “equilibrium elasticity of pollution” η. The former corresponds to the income elasticity of the pollution supply (and therefore when prices are fixed) while the latter corresponds to an elasticity in the aggregate income-pollution relationship, and therefore when all prices adjust to equilibrium prices.6 An important caveat, however, is that we are assuming a Cobb-Douglas production function and hence ρ=1

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For a clearer understanding of the contribution of the model developed here to

determining behavioral mechanisms which explain the occurrence of the EKC, it is

worth analyzing the connections of the model with four important previous works on

the topic: Lopez (1994), Lieb (2002), Stokey (1998) and Copeland and Taylor (2003) .

In the first of these papers (Lopez, 1994), the existence of an EKC arises when the

following condition holds:

dedf⋛0 if and only if

1ρ⋛a (f ) (24)

Where a ( f )=−f W ff /W f is the degree of curvature of the utility function in income

when separability in preferences holds. Lopez simply assumes that a (f ) is an

increasing function of income (i.e., da /df >0, see equation (13) on his page 171), He

makes this assumption because is a “plausible” condition necessary for his results.

Contrarily to Lopez, we derive da /df >0 as a consequence of our more general model

with an upper bound in material consumption. In fact, in our model, a ( f )=1/ ε and

dε /dc<0 as long as m>0 (see equation 16). Therefore, as long as there is a positive

endowment of environment (freely provided by nature) and people have positive

consumption aspirations, they are willing to substitute environmental quality for

consumption. As consumption increases toward aspirations, the elasticity of substitution

between consumption and environmental quality decreases toward zero and,

consequently, its inverse (the degree of curvature of preferences in income) increases

toward infinite as in Lopez. As a result, the first contribution of this paper to Lopez’s

work is that, rather than simply assuming it, we derive a theoretically sound decreasing

elasticity of substitution in preferences with a reasonable and a possibly “realistic”

behavioral content. A second contribution of this paper to Lopez’s work and current

EKC literature overall is that we have found a closed form for the EKC (in equation 17),

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which makes the EKC empirically testable as a behavioral hypothesis with well-defined

theoretical and empirical interpretations.

On the other hand, Lieb (2002) uses graphic explanations to show that an EKC arises

when there is an upper bound in the utility function. However, in our model utility is

bounded because consumption is bounded as long as μ>0, with an explicit aspiration

level of consumption equal to c A=μm which could possibly be infinite.

Regarding the model proposed by Stokey (1998), it is worth noting here that in

equation (15) if m=0 and μ<0, then 1/σ corresponds to the constant elasticity of

substitution between consumption and environment where σ=−μ. Moreover, from

equation (17) in this particular case it is possible to express the income elasticity of

environment as:

η= 11+μ

(σ−1 )( d−rr ) (25)

and environmental quality increases monotonically with income if σ>1, decreases

with income if σ<1 and is constant when σ=1. These are the same conditions

highlighted by Stokey (1998) in analyzing the shape of the EKC. However, the constant

elasticity of substitution, as seen in equation (25), does not yield an inverted U curve;

rather, it simply explains monotonic relationships. In thresholds models like Stokey´s,

an additional mechanism must be imposed to describe an EKC. This ad-hoc mechanism

implicitly assumes that the elasticity of substitution below the income threshold is

infinite (σ=0and therefore pollution is driven by production regardless of social

preferences) and it is lower than one (σ>1¿ beyond that threshold therefore describing

an inverted V-shaped relationship. However, we believe that the EKC is better

explained by the changing and smooth adaptive character of preferences as described

here rather than by thresholds mechanisms.

20

Finally, Copeland and Taylor (2003, page 84) present a closed structural form for the

EKC based on constant absolute risk aversion (CARA) preferences in the consumption

component of utility (the first term on the right-hand side of equation (10)). As

explained above, the HARA class of preferences includes all of the best-known types.

In particular, expression (10) collapses to Copeland and Taylor’s CARA preferences as

long as μ → ∞. Therefore, Copeland and Taylor is a quite specific and restricted case of

our more general closed form of an EKC. Moreover, it is possible to show that the

elasticity of marginal damage derived from the left-hand side in equation (21) is given

by:

ϵ MD,C= μcμm−c (26)

and becomes the particular form on page 85 of Copeland and Taylor (2003) when

μ→ ∞.

ϵ MD,C= cm (27)

Therefore, Copeland and Taylor’s model is embedded within our more general model.

4.2. On the paradigm(s) of (balanced) aspiration consumption and environment

levels

In our model, individuals have “balanced aspiration” levels of

market (consumption) and non-market (environment) goods.

However, at low levels of income, individuals are endowed by nature

with a positive amount of clean environment, while in terms of

consumption they exhibit minimum (survival or just above it) levels

which are well below their aspiration consumption. This initial

imbalance determines an initial high income elasticity of substitution

between consumption and environmental quality while they are poor,

21

and therefore it is rational that at the initial low levels of income they

trade some relatively abundant environment in exchange for

additional amounts of relatively scarce consumption that would push

them far above and away their survival level of consumption and

move toward their aspiration consumption level.

This decreasing in income preference-elasticity of substitution

interplays with the production-elasticity of substitution between

polluting and non-polluting factors, which for simplicity is assumed

constant, and they jointly reflect into the price system the changes in

the relative income-environmental quality scarcity and the level of

income at which –in equilibrium- it becomes socially optimal to

demand more rather than less environment. What is crucial in our

model for this win-win result is the ability of the social planner to

adjust the relative price of consumption/pollution to reflect the

increasing willingness to pay for better environmental quality.7

In our model, as long as material consumption tends to an aspiration level, welfare –

ceteris paribus- tends to an upper bound. This idea is embodied also in Easterlin (2001),

who states that at any given point in time, happiness (an indicator of individual well-

being) is positively associated with income but tends to be stationary during the

lifecycle of an individual; and in Frank (1997), who provides empirical evidence

suggesting that beyond a certain consumption level consuming more goods does not

make people happier.. For more empirical evidence on the topic see Ahuvia (2008).

Stutzer (2004) tests the effect of income aspiration in people´s utility function finding

evidence that income aspiration –ceteris paribus- reduces satisfaction with life. Equation 7 In the real world, this implies that there are enough adequately sufficient market and regulatory mechanisms which translate social preferences, appropriately and adequately, into the relevant explicit and shadow prices.

22

(10) in our paper is just a formalization of Stutzer´s idea since

. Furthermore, the idea of an aspiration level of

consumption is not a novel idea. For example, it is implicit in the “consumption

standard” concept put forward by Davis (1945), who states that “The consumption

standard of an individual or group is the consumption level that is earnestly desired and

eagerly striven for, in respect of quantities, qualities and proportions of the various

goods consumed or wanted for consumption. In the Western World, the consumption

standard is typically above the consumption level proper; but it is not an ideal or mere

dream.”8

The concept of aspirations which balance material and non-material goods is also

implicit in Davis (1945) when he writes, “The plane or content of life is a reality

experienced by an individual or group. It is made up of a complex combination of

consumption, working conditions, possessions, freedoms and “atmosphere’ and the

balance or harmony among them, in relation to needs and felt wants.”9

Davis also provides some clues about differences in aspiration consumption among

countries which can explain the observed differences in their concern for environmental

conservation. In fact, he says, “People differ greatly, of course, in their preferred pattern

of living. The French are noted for their consumption efficiency; on smaller volumes of

consumption, they can live better than many other peoples can. By contrast, Americans

are notoriously wasteful in their consumption habits, and therefore require a far larger

volume of consumption to yield the same result in terms of living. Some individuals,

groups, and peoples set great store by security and leisure, while others prefer to work

harder and accept ups and downs if they can enjoy convenience, variety, and a sense of

opulence. Freedoms of various kinds are much dearer to some groups than to others.

8 Davis (1945), page 6.9 Davis (1945), page 7.

23

Certain characteristics of the standard of living of a people or group get crystallized into

the structure of their planes of living”.10

Finally, this tendency to reach an upper bound in utility as income approaches

aspiration has also been recognized empirically (Kahneman et al. 2006) as well as

implicitly self-reported by certain wealthy individuals11

5. Conclusions

The objective of this paper is to determine what kind of social preferences can explain

that a society attempting to maximize its welfare and behaving according to the usual

assumptions of economic theory will exhibit a development path with the shape of an

environmental Kuznets curve (EKC). Its principal result is a closed form of social

welfare function with no ad hoc behavioral restrictions. With this social welfare

function, a welfare-maximizing society shows an EKC if its individuals have balanced

consumption and environment aspirations, there is some degree of substitution between

capital and pollution in the production function and social decision-making mechanisms

properly reflect in market and shadow prices the way in which social preferences

evolves with changes in the distance between current and aspiration consumption as the

economy grows.

At early stages of development, individuals are well endowed with environment but

fall short of their consumption aspirations. If they have “balanced aspirations” of market

(consumption) and non-market (environmental) goods, it makes sense for them to trade

some environment in exchange for additional consumption that will put them on a track

toward their aspiration levels of consumption. On the contrary, at medium income

levels, consumption rapidly approaches peoples’ income aspiration level, but the

10 Davis (1945), page 1111 . For example, Arnold Schwarzenegger, the current governor of California, has been quoted saying that “Money does not make you happy. I now have $50 million, but I was just as happy when I had $ 48 million” (cited by Konow and Earley (2007), page 5).

24

environment reaches a level of degradation that makes it optimal to demand more

environment through a reduction in consumption growth (although not a reduction in

the level) that will allow people, in the long run, to reach both their aspiration levels of

consumption and environmental quality.

Necessary and sufficient conditions for the occurrence of the virtuous path described

above are a positive degree of substitution between capital and pollution in production

and a social decision-making processes that accurately reflect changes in preferences

driven by a change in the distance between current and aspiration consumption as

income increases.

The closed form of social welfare function we present is similar in structure to the

well-known hyperbolic absolute risk aversion (HARA) preferences. It requires no ad

hoc, additional restrictions on the demand or supply side of individuals’ behavior for

society to follow a development path which exhibits the shape of the environmental

Kuznets curve as income increases. Some additional restrictions, for example, on the

degree of the curvature of preferences or the point in time at which pollution abatement

technologies are incorporated, proposed in previous literature to generate the EKC, can

be treated as special cases of the social preference-driven model presented here.

Moreover, the social preference-driven explanation of the EKC we propose is aligned

not only with basic intuition and broadly accepted ideas in the literature, but also with

economic theory and recent experimental evidence from behavioral sciences. Thus, it

opens new and interesting areas for study, employing more dynamic analytical

frameworks than the static one used here. For example, on the supply side, the induced

technical change hypothesis would make the occurrence of the EKC both more

plausible and rapid.

25

Finally, regarding the debate about the eventual “automatism” of the EKC, it is worth

reiterating that in our model the social development path will have an EKC shape only

if market and implicit prices adequately reflect changes in preferences provoked by

economic growth. This implies that, in the real world, the occurrence of the EKC it is

very much conditioned not only by the efficient operation of markets, but also by the

adequate design and implementation of environmental regulations.

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FIGURE 1: The environmental Kuznets curve

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FIGURE 2: Social preferences and the EKC