1 Is there an Environmental Kuznets Curve? • small open economy - fixed world price • normalize population so that N = 1. • growth treated as once-and-for-all changes in endowments or technology. Pollution Demand: τ D = G z ( p,K ,L ,z ) . Pollution supply: τ S = MD ( p, I β ( p ) , z) , Income: I = G( p,K ,L ,z ) . Three endogenous variables: τ, I, z.
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Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
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1
Is there an Environmental Kuznets Curve?
• small open economy - fixed world price
• normalize population so that N = 1.
• growth treated as once-and-for-all changes in
endowments or technology.
Pollution Demand:
�
τ D = Gz( p,K ,L ,z).
Pollution supply:
�
τ S = MD( p, Iβ (p)
,z),
Income:
�
I =G( p,K ,L ,z).
Three endogenous variables: τ, I, z.
2
3.3 Sources of Growth
Assume pollution tax fixed:
�
τ = τ .Implies emission intensity is fixed.
� �
z = e x(p,τ ,K,L)
�
I =G( p,K ,L ,z)
Consider growth via capital accumulation alone:
�
ˆ z = ε xKˆ K
�
ˆ I = srˆ K + sτ ˆ z .
sr > 0 and sτ > 0 shares of capital and emission charges in
national income,
�
ˆ z = dz / z, etc.,
εxK > 0 is the elasticity of X with respect to K
�
ˆ I = sr + sτε xK( ) ˆ K .
�
ˆ z =ε xK
sr + sτε xK
ˆ I
(+)
3
Alternatively, suppose growth occurs via accumulation of
human capital:
�
ˆ z = ε xLˆ L
�
ˆ I = swˆ L + sτ ˆ z = sw + sτε xL( ) ˆ L ,
where sw > 0 is the share of human capital in national
income.
�
ˆ z =ε xL
sw + sτε xL
ˆ I
(−)
If growth occurs via accumulation of the factor used
intensively in the clean industry, there is a negative
monotonic relation between pollution and income.
Similar result can be obtained even with an endogenous
policy response, provided that the income elasticity of
marginal damage is not too high.
4
3.4 Income Effects
Three assumptions:
• Neutral growth
• Firms at an interior solution for abatement purposes.
• Income elasticity of marginal damage rising in income
levels.
Neutral technical progress:
Given (K,L z,) feasible outputs of X and Y are both
shifted up by a factor λ
National income: λG(p,K,L,z)
For our more specific technology:
�
x = λ 1−θ( )F Kx ,Lx( )y = λH Ky ,Ly( )z = ϕ θ( )F Kx ,Lx( )
5
Equilibrium:
�
λGz (p,K,L,z) = MD( p,λG(p,K ,L,z)β(p)
,z)
�
dzdλ
=τ 1− ε
MD ,R( )Δ
,
where Δ > 0 and
�
εMD ,R is the elasticity of marginal damage
with respect to real income.
• Demand for pollution shifts out because the marginal
product of pollution rises.
• Supply shifts inward because real income has grown.
Result does not rely on the separability or Cobb-Douglas
assumptions of our more specific technology.
6
Neutral factor accumulation:
�
Gz( p,λK ,λL, z) = MD(p,G(p,λK ,λL,z)β(p)
,z)
�
dzdλ
=τ sr + sw( )
Δ˜ s r
σ ZK+
˜ s wσ ZL
− εMD ,R⎡ ⎣ ⎢
⎤ ⎦ ⎥
�
˜ s i ≡ si / (sr + sw ) is the share of factor i in income accruing
to primary factors (excluding emission payments)
�
σ ij ≡GiG j /GGij is the Hicks-Allen elasticity of
substitution between inputs i and j in generating aggregate
national income.
If it is easy to substitute either input for emissions then the
σij are large, and it is more likely for pollution to fall as the
supply of primary factors rises.
If it is difficult to substitute primary factors for emissions,
then the σij are small, and pollution is more likely to rise
with factor accumulation.
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Lopez (1994) considers the special case where
�
σ ZK = σ ZL ≡ σ .
�
dzdλ
=τ sr + sw( )
Δ1σ−εMD,R
⎡ ⎣ ⎢
⎤ ⎦ ⎥ (0.1)
Example. Suppose only one good X with specific
technology above:
�
G(p,K,L,z) = pzαF(K,L)1−α ,
Then
�
σ ZK = σ ZL =1. Factor accumulation will raise emissions if the income
elasticity of marginal damage is less than 1, and lower