Effect of Feed-In Tariff with Deregulation on Directed Technical Change in the Energy Sector

Appendix A: Impacts on Biased Technical Change

Partially differentiate (17) with regards to η, and the impact of deregulation on the direction of technical change can be evaluated as follows:

Thus, we obtain the following inequalities:

where η ̄ = 1 − β 1 − β ( 1 − β ) . If we partially differentiate this partial derivative with regard to ν, we have the following relationship:

Appendix B: Impacts on the Clean Energy Ratio

We examine the impact of deregulation on the clean energy ratio. If (19) is partially differentiated with regard to η, we obtain the following partial derivative:

Then, we find the following inequalities:

If we partially differentiate this partial derivative with regard to ν, we obtain the following relationship:

Appendix C: Effects of FIT on Surcharge

Here, we evaluate the impacts of FIT scheme and deregulation on surcharge.

1. Consider first the effect of FIT on the surcharge-net tariff ratio γ. Assume that initially the degree of deregulation is constant. From the surcharge–tariff ratio (20), we have ξ = Γθ. Totally differentiate the equation and we obtain dξ = Γ dθ + θ dΓ. Because Γ = γ 1 + γ , we find d Γ d γ = Γ γ = 1 ( 1 + γ ) 2 . If the revenue-neutral constraint is totally differentiated, we have γ dθ + θ dγ = (1 + γ)dξ + ξ dγ or d ξ d θ = ξ 1 + ξ + θ − ξ 1 + γ d γ d θ . If the surcharge-net tariff ratio (23) is partially differentiated with regard to ξ and θ, we obtain γ ξ = − γ ϵ θ ( 1 + ξ ) ( 1 − θ + ξ ) and γ θ = γ ϵ 1 − θ + ξ . Then, totally differentiating γ while η is constant gives dγ = γ _ξ dξ + γ _θ dθ = γ _ξ (θ dΓ + Γ dθ) + γ _θ dθ or d γ d θ = γ ϵ d ξ d θ + γ θ . Substitute the above partial derivatives into this total differential, and we find that the impact of the tariff on the surcharge-net tariff ratio is positive:

   d γ d θ = γ ϵ ϵ ξ ( θ − ξ ) + ( 1 + ξ ) ( 1 − θ + ξ ) > 0 .

   Second, the effect of FIT on the surcharge–tariff ratio Γ is examined. The impact of tariff on the surcharge–tariff ratio can be evaluated as positive because of the following:

   d Γ d θ = d Γ d γ d γ d θ = 1 ( 1 + γ ) 2 γ ϵ ϵ ξ ( θ − ξ ) + ( 1 + ξ ) ( 1 − θ + ξ ) > 0 .

2. If the derivative d γ d θ is partially differentiated with regard to the substitution elasticity ϵ, we obtain the following partial derivative:

   ∂ d γ d θ ∂ ϵ = γ ϵ ln ϵ ϵ ξ ( θ − ξ ) + ( 1 + ξ ) ( 1 − θ + ξ ) > 0 .

   Therefore, the impact of the tariff on the surcharge-net tariff ratio is larger if the two types of energy are more substitutable.

3. Additionally, we check whether the deregulation reinforces the impact of FIT on the surcharge-net tariff ratio. If we partially differentiate d γ d θ with regard to η, we find that it depends on the elasticity of substitution between two types of energy as

   ∂ d γ d θ ∂ η = ( σ − 1 ) ϵ γ ϵ ξ ( θ − ξ ) + ( 1 + ξ ) ( 1 − θ + ξ ) η [ 1 − β ( 1 − β ) ] − ( 1 − β ) β η ( 1 − η ) [ 1 − β ( 1 − η ) ] .

   Provided that 0 ≤ τ = θ − ξ < 1, we find the followings.

1. In the case where the elasticity of substitution between two types of energy is more than unity σ > 1, we have

   ∂ d γ d θ ∂ η > 0   if η > η ̄   ≤ 0   if η ≤ η ̄   .

2. In the case where the elasticity of substitution between two types of energy is no more than unity σ ≤ 1, we have

   ∂ d γ d θ ∂ η < 0   if η > η ̄   ≥ 0   if η ≤ η ̄   .

Appendix D: Effects of FIT and Deregulation on Growth

First, the effect of FIT on growth is evaluated. From (24), the growth rate along the balanced growth path can be defined as g = g[θ, ξ(θ), η]. Assume that initially η is kept constant, that is, dη = 0. Partially differentiate (24) with respect to θ and ξ, and we obtain the following partial derivatives:

From Appendix C and ξ = Γθ, if the surcharge is totally differentiated with regard to tariff, we have d ξ d θ = d ξ d Γ d Γ d θ = ϵ ξ ( θ − ξ ) ϵ θ ξ ( θ − ξ ) + θ ( 1 + ξ ) ( 1 − θ + ξ ) > 0 since γ = ξ θ − ξ and ( 1 + γ ) 2 = θ θ − ξ 2 . Totally differentiating g with regard to ξ and θ generates the following derivative:

Consequently, we obtain the following inequalities:

where ν = 1 + ξ 1 − θ + ξ , and p = λ − β ( R r / R e ) − β Φ ( η ) β η .

Next, the effect of deregulation on growth is evaluated. Partially differentiating g with respect to η yields the following partial derivative:

As a result, we obtain the following inequalities: