energy as factor inputs in the second level of the traditional two-input CES production function.
In the G-CEEP model, energy consumption is further divided into that for
electricity (EN) and non-electricity (NN). Thus, there are four inputs: capital stock
(KN), labor (LN), electricity, and non-electricity. The two-level CES production
function can be written as:
YN ¼ γ δ δ 1 KN
Àρ 1 þ 1 À δ 1
ð
ÞLN
Àρ 1
ð
Þ
ρ
ρ 1 þ 1 À δ
ð
Þ δ 2 EN
Àρ 2 þ 1 À δ 2
ð
ÞNN
Àρ 2
ð
Þ
ρ
ρ 2
h
i À
1
ρ
ð4:1Þ
where YN is the output; 0 < δ, δ 1 , δ 2 < 1 are distribution parameters; and ρ (ρ 1 ,
ρ 2 ) ! À1 are substitution parameters. The elasticity of substitution is specified as:
σ ¼
1
1 þ ρ
ð4:2Þ
where σ is a constant dependent on the substitution parameter, ρ (ρ 1 , ρ 2 ). When
estimated ρ (ρ 1 , ρ 2 ) is less than À1, the elasticity of substitution σ is negative, which
is a theoretical impossibility (Prywes 1986). If substitution elasticity σ < 1, the two
related input factors can be interpreted as complements. When σ > 1 the two related
input factors are substitutes.
The G-CEEP model describes the relationship between capital stock, labor, and
energy with a two-level CES production function. This introduces nonlinearity to the
large-scale optimization model, which increases computational complexity but
renders the model more integrated and economically meaningful. In addition to
the two-level CES production function, another nonlinearity, technological learning,
is introduced.
4.1.2.2 Technological Learning
Technological learning is widely used as a key factor to analyze the decreasing cost
of novel technologies. Although the introduction of endogenous technological
change will inevitably increase computational complexity due to nonlinearity associated with the learning curve, we have tried to incorporate the technological
learning method in order to analyze the prospects of specific technological options
and the related potential cost decreases.
The single factor learning curve is expressed as the following (Kahouli-Brahmi
2008):
C t Q t
ð Þ ¼ a t Q t
Àα
ð4:3Þ
4 Modeling the East Asian Low-Carbon Community
85
In the G-CEEP model, energy consumption is further divided into that for
electricity (EN) and non-electricity (NN). Thus, there are four inputs: capital stock
(KN), labor (LN), electricity, and non-electricity. The two-level CES production
function can be written as:
YN ¼ γ δ δ 1 KN
Àρ 1 þ 1 À δ 1
ð
ÞLN
Àρ 1
ð
Þ
ρ
ρ 1 þ 1 À δ
ð
Þ δ 2 EN
Àρ 2 þ 1 À δ 2
ð
ÞNN
Àρ 2
ð
Þ
ρ
ρ 2
h
i À
1
ρ
ð4:1Þ
where YN is the output; 0 < δ, δ 1 , δ 2 < 1 are distribution parameters; and ρ (ρ 1 ,
ρ 2 ) ! À1 are substitution parameters. The elasticity of substitution is specified as:
σ ¼
1
1 þ ρ
ð4:2Þ
where σ is a constant dependent on the substitution parameter, ρ (ρ 1 , ρ 2 ). When
estimated ρ (ρ 1 , ρ 2 ) is less than À1, the elasticity of substitution σ is negative, which
is a theoretical impossibility (Prywes 1986). If substitution elasticity σ < 1, the two
related input factors can be interpreted as complements. When σ > 1 the two related
input factors are substitutes.
The G-CEEP model describes the relationship between capital stock, labor, and
energy with a two-level CES production function. This introduces nonlinearity to the
large-scale optimization model, which increases computational complexity but
renders the model more integrated and economically meaningful. In addition to
the two-level CES production function, another nonlinearity, technological learning,
is introduced.
4.1.2.2 Technological Learning
Technological learning is widely used as a key factor to analyze the decreasing cost
of novel technologies. Although the introduction of endogenous technological
change will inevitably increase computational complexity due to nonlinearity associated with the learning curve, we have tried to incorporate the technological
learning method in order to analyze the prospects of specific technological options
and the related potential cost decreases.
The single factor learning curve is expressed as the following (Kahouli-Brahmi
2008):
C t Q t
ð Þ ¼ a t Q t
Àα
ð4:3Þ
4 Modeling the East Asian Low-Carbon Community
85