Model

Dong-Woon Noh

84

-productivity growth in coal mining, and the decline in rail road transport rate due to deregulation in rail road industry.

with low-sulfur coal price or allowance price to achieve the given emission target, then the unit's owner will choose capital intensive strategy such as scrubber. When low-sulfur coal price is low, or is expected to be low as compared with capital price or allowance price, then the unit will switch its fuel from high-sulfur coal to low-sulfur coal. If owner expects the low allowance price, he will buy additional allowances. In addition to input prices, outputs and other variables will affect the choice of strategy.

Each unit will choose the compliance strategy whose cost is the lowest among available strategies in a competitive market. Moreover, units with lower MAC than allowance price will abate SO2 emissions down to the level where it's own MAC equals allowance price. These units will sell or bank the surplus allowance. Units with MAC higher than allowance price will buy allowances to meet the SO2 emission regulation.

In the long-run, MAC for all units and strategies will be the same and will converge at allowance price in allowance market since allowance price reflects supply and demand of SO2 emissions. This condition is necessary for electricity industry to achieve abatement at minimum cost(Bohi,1992 Pierce et al,1990).

3.2 Cost Minimization and Abatement Cost

Since each electric utility has to supply a sufficient amount of electricity to meet the electricity consumption in it's jurisdiction(Cronshaw et al,1996), electric unit may not choose electricity production level. In addition, since utilities are subject to electricity price regulation, electricity price is assumed to be given. Even though deregulation and restructuring are introduced in California(Tschirhart et al.1999), data set in this paper does not includes these units.⁸⁾ So utilities are not expected to change electricity output and price based on the profit maximization.

7) Owner of generating unit is assumed to have the right to decide the strategy choice even though the unit owner can not be separated from plant or utility owner.

8) Even though deregulation and restructuring are introduced in California(Tschirhart et al.1999), data set in this paper does not includes these units.

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-Each electric power plant unit will choose input quantity including net purchased allowances(a) to minimize the production cost(C) including emission reduction cost subject to output constraint(Q*) and environmental constraint(E). Output constraint is that each generating unit should supply sufficient electricity. Emission constraint is that the actual emission level(E) should be equal to the sum of allocated allowances(W) and net purchased allowance(a) and carried-over allowances from the previous period(S-1) minus banked allowances for the future uses(S)

M inC = k Pk+ l Pl+ fhs Pfh s+ fls Pfls+ a Pa

subject to

q (k,l,fhs,fls,a,E )≥Q ^*

E (k,l,fhs,fls,a) = W + a + S- 1 - S (1) where

C : total cost

k,l,fhs,fls,a:capital, labor, high- and low-sulfur coal and net purchased allowances P_k,P_l,P_{fh s},P_fls,P_a : prices of corresponding inputs

q,Q ^*: electricity production function and electricity output constraint

E,W ,S- 1,S : actual SO2 emissions, allocated, previous and banked allowances

In the optimization, each unit will choose inputs such that the marginal rate of technical substitution is equal to input price ratios. In this model, the unit is assumed to minimize the observed cost subject to constraints. However, the marginal rate of technical substitution is not equal to actual price ratios since there are several regulations on input factors and imperfect market structure of output(Kerkvliet,1991 Atkinson et al, 1989). To avoid the misspecification bias(Kerkvliet,1991), unit is assumed to minimize the behavioral cost subject to shadow input prices, output constraint and environmental constraint. Shadow input prices(

P

^{^}_i ^or iPi) are assumed to be different

from actual prices(Pi) and are function of regulatory variables such that:

P^ =i iPi where i= k, l, fhs, fls, a. (2)

i will measure the difference in the divergence between shadow input prices and actual input prices. If _i>1, then shadow price is greater than actual price, and the corresponding input will be underused inefficiently, and vice versa. Unobservable behavioral cost is a function of shadow input prices( _iP_i), output and emission level:

C^B( iPi,Q,E) = kPkXk^*+ lPlXl^* + fhsPfhsXfhs^* + flsPflsXfls^*+ aPaXa^* (3) where Xi*is a constrained cost minimizing input choice function.

3.3 Empirical Specification

Actual labor price is assumed to be equal to shadow labor price. Then behavioral input demand functions by Shephard Lemma are

Xi^* = 1

i

@ C^B

@ P_i ^where i= k,fhs,fls,as. (4)

The observable actual cost

C ^A(Pi,Q^*,,E^{* ) =}PkXk^*+ PlXl^* + Pfh sXfh s^* + PflsXfls^*+ PaXa^*. (5)

Solving behavioral cost function for X_i(3), and behavioral input demand function for X_i*(4), and substituting it into actual cost function, actual cost function(5) can be written in terms of shadow input prices:

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-C^A = C^B

l

+ @ C^B

@ P_k ^[Pk( 1

k

- 1

l

)] + @ C^B

@ P_fhs ^[Pfh s( 1

fhs

- 1

l

)]

+ @ C^B

@ P_fls ^[Pfls( 1

fls

- 1

l

)] + @ C^B

@ P_a ^[Pa( 1

a

- 1

l

)]

(6)

If translog behavioral cost function is assumed, then the behavioral cost is a function of shadow input prices, output, and emissions.

lnC ^B = 0 + q (lnQ ) + e(lnE) +

i i(ln iPi)

+ 1

2 °_{q q}(lnQ)² + 1

2 °_ee(lnE)² + °_{q e}(lnQ )(lnE) + 1

2 _{i j} °_ij(ln _iPi)(ln _jPj) +

i

°_iq(ln _iPi)(lnQ )

+

i

°_ie(ln _iP_i)(lnE)

(7)

where i,j= k, l, fhs, fls, a.

Differentiating the antilog of translog behavioral cost function(7) with respect to actual input prices,

@ C^B

@ P_i = C^B P_i [ i+

j

°ij(ln jP_j) + °iq(lnQ ) + °_ie(lnE )] = C^B

P_i [d_i] (8) where i= k, l, fhs, fls, a.

Substituting this equation(8) and antilog of translog behavioral cost function(7) into actual cost function(6), then actual cost function can be written in terms of shadow input prices:

C^A = C^B[ 1

l

+ [dk]( 1

k

- 1

l

) + [dfh s]( 1

fh s

- 1

l

)

+ [dfls]( 1

fls

- 1

l

) + [da]( 1

a

- 1

l

)]

(9)

The observable actual cost function taking a log of actual cost function(9) is :

lnC^A = lnC^B + ln [ 1

l

+ [dk]( 1

k

- 1

l

) + [dfh s]( 1

fh s

- 1

l

)

+ [dfls] ( 1

fls

- 1

l

) + [da]( 1

a

- 1

l

)]

(10)

Behavioral(S_i^B) and actual expenditure shares(

S

i^A) equations are

Si^B = ⁱPiXi^*

C^{B =}

iPi

C^{B (} 1

i

@ C^B

@ Pi

) = [di] (11)

Si^A= PiXi^*

C^{A =}

- 1i [di][ 1

l

+ [dk]( 1

k

- 1

l

) + [dfh s]( 1

fhs

- 1

l

)

+ [dfls]( 1

fls

- 1

l

) + [da]( 1

a

- 1

l

)]^{- 1}

(12)

where i= k, l, fhs, fls, a.

Linear homegeneity of input prices and symmetric restrictions are imposed on the equations

i

i= 1,

j ij=

j

jq =

j

je= 0 (13)

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-While some regulations will affect the total cost of compliance strategy through technical inefficiency, some regulations will affect the cost through the effect on the shadow input prices. The actual price of allowance is assumed to be different from shadow allowance price, while the actual prices of other inputs are assumed to be the same as the shadow prices.⁹⁾ The shadow price is assumed to take exponential functional form of actual price. The shadow allowance price is assumed to be a function of un-identified variable and allowance trade restriction(Dtr).

So, behavioral cost function is a function of shadow allowance price, actual input prices, actual output and actual SO2 emission level.

C ^B = C^B ( _iP_i,Q ,E ) (14)

9) More complicated form of shadow allowance price, shadow prices for capital and high-sulfur coal price, and direct regulatory variable are tried, but are rejected since convergent estimate was not possible. That is, The shadow allowance price is assumed to be a function of allowance trade restriction(Dtr), allowance sale restriction(Dse), allowance purchase restriction(Dbu). And shadow capital price is a function of high-sulfur coal usage encouragement(Dhs), the existence of cost recovery(Dco) for the capital expenditure on the abatement technology including scrubber. Shadow high-sulfur coal price is a function of encouragement of high-sulfur coal usage(Dhs). Direct regulatory effect(R) due to technical inefficiency is assumed to affect the cost through adopting of allowance strategy(Dal), ownership types(Dnp), existence of previous or local government's stringent emission regulations(Dpr), existence of substitution/compensation boilers(Dsu).

So, behavioral cost function is a function of shadow input prices, actual input prices, actual output, actual SO2emission level, and other direct regulatory variables.

C

^B

= C

^B

(

i

P

i

,Q,E,R )

Where

a

P

a

= exp (

0

+

tr

D

tr

+

se

D

se

+

bu

D bu )P

a

_k

P

k

= exp ( °

0

+ °

hs

D

hs

+ °

co

D

co

)P

k

_fhs

P

fhs

= exp (

0

+

hs

D

hs

)P

fhs

_fls

P

fls

= P

fls

_lPl= Pl

R =

0

+

al

D

al

+

np

D

np

+

pr

D

pr

+

su

D

su

Where

aPa = exp ( 0 + trDtr)Pa

k

P

_k

= P

_k

fh s

P

_{fh s}

= P

_{fh s}

fls

P

_fls

= P

_fls

l

P

_l

= P

_l

Observable cost function(10) and expenditure share equations(12) can be simplified as;

lnC

^A

= lnC

^B

+ ln [ 1

l

+ [d

a

]( 1

a

- 1

l

)] + E

c (15)

Si^A = PiXi^*

C^{A =}

- 1i [di][ 1

l

+ [da]( 1

a

- 1

l

)]^{- 1}Esi (16) where i= k, l, a.

Since most units used only one kind of coal between high-sulfur coal and low-sulfur coal, and thereby high-sulfur coal and low-sulfur coal shares have many missing observations, coal share equations are excluded from expenditure share equations(16) Since emission is an endogenous variable, emission is estimated as a function of input prices(Pi), output(Q*), sulfur removal efficiency of scrubber(REMEFF), sulfur content of coal(COSO2) and allowance variables(W,S-1,S) that are included in the environmental constraint function.

E = ₀ + _q (Q ^*) +

i

iPi+ _{rem eff}R EM EFF + coso2COS O₂ + W W + S_{- 1}S_{- 1} + SS + Ee

(17)

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-Non-linear observable actual cost function(15), non-linear actual expenditure shares equations(16) for labor, capital and allowance, and linear emission function(17) are estimated simultaneously using full information maximum likelihood technique. In addition, error terms are added to these equations.

Marginal abatement cost function(MAC) are derived from cost function(15) as

M AC = @ C ^A

@ E ⁼

@ lnC ^A

@ lnE

C ^A E

= C ^B

E ^{[ e + °e e(ln}E) + °q e(lnQ ) +

i

°ie(ln iP_i) + A D D ] (18)

where ADD is a non-linear additive effect of shadow allowance price, that is,

AD D = ln^







1

l

+ [d_a]( 1

a

- 1

l

) ^





(°q e- 1 ) 1  a

(19)

The mean MAC for four kinds of compliance strategies is calculated at each observation using the estimated coefficients from the cost function(15).

문서에서 대체에너지개발을 위한 보조금 및 조세정책의 경제적 파급효과* (페이지 89-97)